B.M. Misra & Sarat Dhal*
According to the finance literature, risks associated with various financial instruments and their corresponding market segments could be stochastic and evolve continuously over time, reflecting the developments in the macroeconomy and the financial system. This study undertakes an empirical analysis of risk pricing for India's financial markets using Generalised Autoregressive Conditional Heteroskedasticity (GARCH) model. Empirical results provide various insights about the nature of risk pricing underlying money, credit, bonds, equity and foreign exchange market segments. Broadly, all market segments, excepting the corporate bond market, showed the ability to price risks over the sample period. International integration was found to accentuate risk pricing in the domestic stock market. From policy perspective, these findings may contribute to financial stability analysis and serve useful for monitoring financial markets and devising strategies for their further developments in the Indian context.
1. INTRODUCTION
Economists have learned lessons from various crises across the emerging market economies, which occurred during the late 1990s and the early part of the current decade, and the global crisis originating from an advanced economy such as the US in the more recent period. First, sustained economic progress cannot be achieved without efficient and stable financial systems. Second, a stable financial system is reflected in the ability of constituent financial market segments to price risks associated with various financial instruments (Mohan, 2007^{1} , Trichet, 2009). Third, the crisis to a financial system could occur through various risks pertaining to liquidity, credit, interest rate, exchange rate and asset prices, apart from macroeconomic risks. Fourth, it is useful to have continuous assessment and monitoring of the riskpricing mechanism underlying the financial markets for policy purposes.
In the Indian context, a key objective of financial sector reform beginning from the early 1990s has been to promote price discovery process in financial markets and thereby, improve allocation and operating efficiencies of intermediaries and market participants. The reform process has completed two decades. It is now generally agreed that Indian financial markets have shown considerable maturity in terms of price discovery process. There is evidence of integration among various market segments, reflecting on the operating efficiency of financial markets (Bhoi and Dhal, 1999, RCF 200506). However, there is dearth of empirical analysis on risk pricing in Indian financial markets. From the latter perspective, several pertinent questions arise in the Indian context. Whether the various financial market segments are capable of pricing risks dynamically? Whether various financial market segments behave differently in this regard? Which risks are important for the Indian financial system? These questions motivate the authors for undertaking the present study. Taking leads from the finance literature, the study engages in analysis of riskpricing as reflected in the movement of various interest rates, exchange rate and equity prices using the generalised autoregressive conditional heteroskedasticity (GARCH) model. The idea here is that each financial variable represents a market segment identified with its underlying risk characteristics. Illustratively, the interbank call money segment reflects on liquidity effect. Commercial paper and corporate bond yields could reflect on credit market and the associated risks. Yields on treasury instruments could reflect on interest rate risk or the market risk. The stock market could be attributable to asset price risks while the spot and forward exchange rates could be related to risks associated with the external sector in terms of exchange rate and capital flows. Rest of the paper is structured into four sections. Pertaining to review of literature, methodology and data used in the study, empirical findings and conclusion in order.
2. THE REVIEW OF LITERATURE
According to the theoretical finance literature, the concept of risk pricing owes to the modern portfolio theory (MPT) or popularly, the meanvariance optimization theorem (MVT) of Markowitz (1952), and subsequently, the capital asset pricing model (Treynor, 1962, Sharpe,1964, Lintner,1965 and Mossin,1966), the arbitrage pricing theory (Ross, 1976), several interest rate models (Vasicek, 1977, Brennan and Schwartz, 1980 and Cox, Ingersoll and Ross,1985, and Chan et.al. (1992) and derivatives pricing models (Black and Scholes, 1973, Merton, 1973). According to the MVT, investors are rational and averse to risks. Given two assets that offer the same expected return, investors will prefer the less risky one. A rational investor will not invest in a portfolio if a second portfolio exists with a more favorable riskreturn profile. Thus, an investor wanting higher returns must accept more risk, and the exact tradeoff will depend upon individual risk aversion characteristics. Inspired by Markowitz’s seminal contribution, the capital asset pricing model (CAPM) postulated a theoretically appropriate required rate of return of an asset, if that asset is to be added to an already welldiversified portfolio, given that asset’s nondiversifiable risk. The CAPM took into account the asset’s sensitivity to nondiversifiable risk (also known as systemic risk or market risk), often represented by the quantity beta (β) in the financial industry, as well as the expected return of the market and the expected return of a riskfree asset. The arbitrage pricing theory (APT) holds that the expected return of a financial asset can be modeled as a linear function of various macroeconomic factors or theoretical market indices, where sensitivity to changes in each factor is represented by a factorspecific beta coefficient. The modelderived rate of return will then be used to price the asset correctly  the asset price should equal the expected end of period price discounted at the rate implied by model. If the price diverges, arbitrage should bring it back into equilibrium.
Theoretical models of asset prices were based on certain key assumptions. First, in the CAPM model, the risk free interest rate was assumed to follow a deterministic process with a linear drift and Gaussian white noise process. Also, deviations from the security market line (SML) were assumed to be normally distributed with zero drift and a constant variance to ensure the absence of abnormal returns under efficient market conditions. As opposed to the deterministic risk free interest rate, Vasicek (1977), Brennan and Schwartz (1980) and Cox, Ingersoll and Ross (1985) suggested affine class term structure of interest rates such that the latter could be characterised as stochastic process with a jump diffusion process. Chan et.al.,(1992) suggested a generalised diffusion model^{2} , popularly known as CKLS model. Das (2002), Johannes (2004), and Piazzesi (2005) also identified a jump component in the interestrate movement. The jump component generates interestrate innovations that are not normally distributed. Despite this improvement, popular models of the short rate produced untenable results when fitted to the data (Gray, 1996, Ball and Torous, 1999, Duffee, 1993, Duan and Jacobs, 2001). Second, it was assumed that an asset’s risk is time invariant and it could be characterised as a constant unconditional measure such as sample standard deviation or variance. Several studies found that this assumption was always violated in the real world. Mandelbrot (1963) and Fama (1965) recognised volatility clustering, i.e., large changes in the price of an asset are often followed by other large changes and small changes are often followed by small changes. A formal model was developed by Engle (1982). He postulated the concept of conditional volatility, since risks to economic and financial variables could follow a dynamic stochastic process and evolve with time. Thus, he developed the autoregressive conditional heteroskedasticity (ARCH) model for measuring stochastic volatility. Subsequently, the model was extended to the generalized ARCH (GARCH) by Bollerslev (1986). Furthermore, Engle, Lilien, and Robins (1987) suggested the ARCHinMean (ARCHM) model, which allows the mean of a sequence to depend on its own conditional variance on the basis of the ARCH framework. Nelson (1991) developed the exponential GARCH (EGARCH) model, based on the conditional variance defined over logarithm scale. Glosten, Jagannathan, and Runkle (1993), and Zakoian (1994) introduced the threshold ARCH (TARCH) model to account for the leverage effect on the ARCH models, thus, allowing for asymmetric or differential impact of positive and negative shocks on volatility. Hamilton and Susmel (1994) developed regime switching ARCH (SWARCH) model. Baillie, Bollerslev and Mikkelsen (1996) developed fractionally integrated GARCH, i.e., FIGARCH(p; d; q) model of conditional volatility to analyse longmemory in financial variables.
The works of Engle (1982), Bollerslev (1986), Engle, Lilien, and Robins (1987), Nelson (1991) and Glosten, Jagannathan, and Runkle (1993) have inspired a large empirical literature focused on measuring riskpricing in financial markets. Initially, the ARCH model was used for measuring the inflation risk, recognising that the uncertainty of inflation tends to change over time (Engle, 1982, and Engle and Kraft, 1983). Following their work, several authors including Longstaf and Schwartz (1992), Brenner et. al. (1996), Koedijk et.al., (1997), Andersen and Lund (1997), Ball and Torous (1999), Bali (2000), Christiansen (2005), and Honget et.al., (2004) exploited the GARCH model in order to improve upon the short rate models and found that an additional stochastic volatility factor or a GARCHtype process is useful to accommodate the strong conditional heteroskedasticity in shortterm interest rates. Deriving from these studies, GARCH models have witnessed applications to the entire spectrum of financial markets including money, credit, bond, common stocks and foreign exchange markets across several countries. Providing a review of the bourgeoning literature is beyond the scope of this paper. For illustrative purpose, a list of studies using GARCH models is shown in Box 1.
2.2 Key Aspects of Risk Pricing
What is striking about the numerous studies using GARCH analysis of financial markets is that they provide a generalised perspectives on risk pricing and bring to the fore various crucial features of modern financial markets, as succinctly demonstrated by Engle and Patton (2001). These aspects of risk pricing are discussed below.
First, volatility clustering and persistence are key features of financial markets. In other words, past volatility explains current volatility. Financial markets are characterised with time varying conditional mean and variance of return on various instruments.
Second, due to risk aversion and dynamic portfolio adjustment, which is made possible by the advanced technology infrastructure, investors are able to quickly process information. This implies that investors’ expected return also depends upon the conditional variance of the financial instruments consistent with continuous time meanvariance optimization or riskreturn tradeoff hypothesis.
Third, financial markets exhibit asymmetric response to good and bad news, implying differential impact of positive and negative innovations or shocks on volatility and the expected rerun of an asset.
Box 1: Studies on GARCH Models applied to Financial Markets 
Studies 
Details 
1. Interest Rates 

Bali and Wu (2005) 
Used three interest rates: fed funds rate, 7day euro dollar rate, 3m Tbill rate, GARCH, Nonstandard distribution – Generalised Error Distribution (GED) 
Brailsford and Maheswaran (1998) 
Shortterm interest rate in Australia, 30day BAB rate preferred to 90 and 180 day. TGARCH analysis 
Christiansen (2008) 
Regime switching level Univariate and Bivariate GARCH short rates; US (1m euro dollar rate), UK (1m LIBOR) and Germany (1m euromark) 
Duan and Jacobs (2001, 2007) 
FIGARCH for short term interest rates (1week euro dollar rate, daily and weekly data), test of longmemory 
Edwards, S (1998) 
30day deposit rates in Argentina, Chile, and Mexico, GARCH analysis 
Edwards and Susmel (2003) 
Univariate and multivariate SWARCH model, interest rates in EMES, i.e., Argentina, Brazil, Chile, Hong Kong and Mexico; 30day deposit and interbank rates 
Galac, et.al. (2007) 
Croatia money markey (overnight, 91day,180day and 364day treausry bills), explanatory variables (repo, liquidity, etc), ARIMAGARCH analysis 
Gray (1996) 
GARCH with regime switch, Weekly data 1m US Tbill rate 
Kleibergen (1993) 
Bayesian approach to GARCH, US treasury bill rate, addressed the nonstationary problem 
Koedijk, et.al. (1997) 
GARCH and CKLS models for onemonth US treasury bill rate, used weekly and monthly data. 
Murta (2007) 
Portuguese money market (overnight interest rate) intraday data, GARCH analysis 
Nowman and yahia (2008) 
LevelGARCH for EURIBOR (1m & 6m maturities) and FIBOR (1m) interest rates 
Raunig and Scharten (2006) 
GARCH, linkage between money market uncertainty and retail interest rates (deposit and lending rates), 10 OECD countries compared. 
Rosenblum and Strongin (1983) 
Federal funds rate, commercial paper, not GARCH model, moving standard deviation. 
Shahiduzzaman and Naser (2007) 
GARCH model for the Overnight call money rate in Bangladesh 
Smith (2002) 
CKLS and GARCH model for US 30day Tbill rate, used monthly data 
Suardi 2008 
CKLS, GARCH(1,1) for US 3m treasury bill, Australia 90day bank bills rate 
Box 1: Studies on GARCH Models applied to Financial Markets 
Studies 
Details 
Syklos and Skoczylas (2002) 
ARIMAGARCHinMean for Real interest rates, interest rates are borrowing and lending rates, studied 10 industrialised countries 
2. Equity Market 
Durand and Scott (2003) 
Ishares Australia, EGARCHm, found negative impact of risk on return 
French et.al. (1985) 
Expected market risk premium (Stock return less Treasury bill rate); GarchinMean model; positive relationship between risk and return 
Kiani (2006) 
Excess stock return in Pakistan (stock return over Treasury bill rate) GARCH with state space representation 
Kim and Sheen (1998) 
Bivariate GARCH, International linkage of interest rate volatilityAustralia and the US (3month treasury bill rate and 10year government bond yield) 
Lamoureux (1990) 
GARCH Daily stock returns in the US 
Nam et.al. (2002) 
Asymmetric nonlinear smooth transition GARCH, the US excess stock return; month equity return for three stock exchanges NYSE, AMEX and NASDAQ (stock return over 1month treasury bill rate) 
Ozun (2007) 
GARCH for 14 stock markets (emerging and developed) return and US 10yr treasury rate explanatory variable 
3. Exchange rate/Forward Premium 
Bidarkota (2004) 
Forward premium (us dollar/pound) 
Corte, et.al. (2007) 

Bhar, et.al. (2007) 
Currency forward premium 1m, 2m, and 3m maturities, daily data Franc/US dollar and Yen/Dollar, interest rate spread, data 3m treasury bill rate (France, Japan, and the US) 
McCurdy and Morgan (1991) 
BVGARCH model Uncovered interest rate parity, US interest rate and Euro currency US dollar exchange rate US 
4. Multivariate GARCH 
Bauwens et.al. (1997) 
Cointegrated VARGARCH model for short and long rates, for five developed countries (US, UK, France, Germany and Belgium) 
Berument (1999) 
Interest rate with expected inflation, GARCH, test of fisher hypothesis 
Ferreira and Lopez (2004) 
MVGARCH model Interest rate (3m libor rate for dollar, deutch mark, and yen) and exchange rate, used for analysing Value at Risk, 
Hansen and Lunde (2001) 
Exchange rate and stock prices, intraday data, GARCH 
LI and Zou (2007) 
MVGARCH(DCC) for China Treasury bond and stock market 
Yang et.al. (2009) 
MVGARCH (monthly stock and bond yield data) US and UK, 150 years (18552001) 
Fourth, the price discovery process in efficient markets is characterised with interlinkage among various market segments and their comovement led by a common benchmark risk free instrument.
Fifth, exogenous variables relating to macroeconomic developments could also play an important role in influencing the conditional return and variance of financial markets.
Sixth, financial markets, generally, follow nonstandard statistical distribution function, implying that investors can exploit arbitrage opportunities in the short run.
Seventh, volatility characteristics of financial markets could be distinguished across the frequencies such as daily, weekly, monthly and quarterly dimensions, reflecting upon synchronous or nonsynchronous nature of trading and information efficiency of markets.
3. METHODOLOGY AND DATA
As discussed in the earlier section, various aspects of risk pricing in financial markets could be analysed through the thresholdGARCHinmean model (TGARCHM) of Engle, Lilien and Robins (1987) and the exponential GARCHinMean (EGARCHM) model of Nelson (1988), consistent with the standard riskreturn tradeoff hypothesis and the asymmetric news and leverage effects. Basically, a GARCH model for a financial asset variable comprises two equations; one for the mean (or expected return) and the other for variance of a financial time series variable. It could be formulated in terms of a univariate model or multivariate model with or without explanatory variables in the mean and variance equations. In our case, we adopt the univariate TGARCHM or EGARCHM model suitable to specific market segment. The TGARCHM specified in terms of mean and the conditional variance of a stationary financial variable (y) is as follows:
A GARCH model provides a generalized perspective on risk pricing mechanism and can be applied to various interest rates and asset return variables. For a meaningful analysis of whether riskpricing in financial markets is efficient, the GARCH model could be enriched with various key theoretical and applied finance perspectives.
First, the standard benchmark principle used by various studies and official agencies may be considered. Illustratively, the Congressional Budget Office in the US analyses risks associated with various financial markets in terms of spread variables, defined as the spread of interest rates on market instruments over the risk free rate such as the 3month Treasury bill rate. The underlying principle here is that the return on a market instrument (R_{j}) should equal the sum of return on à riskfree instrument, typically, the Treasury bill rate (R_{g}) and the risk premium (ρ). The risk premium could again be broken into some deterministic identifiable component driven by the X variables (including a drift or intercept term) and the idiosyncratic component or innovation (ε). Therefore, we define the spread variable as
S_{j},_{t} = (R_{j},_{t} – R_{g},_{t}) (8)
which could follow a GARCH model with appropriate mean and variance equations from equation (1) through equation (6). In our case, such specification could be adopted for interest rates pertaining to certificates of deposits, commercial papers, and the longterm bond yield.
Second, the finance literature also suggests some market specific principles. For the interbank borrowing and lending segment, the benchmark interest rate could be the policy shortterm interest rate such as the repo rate in the Indian context, since the latter provides a corridor to the former (Singh and
3.2 Data
In this study, we use monthly data on interest rates, exchange rate and stock prices culled out from the official source such as the RBI (Handbook of Statistics on the Indian Economy and Monthly Bulletin and Thomson’s Datastream). The sample period is April 1993 to March 2009. The variables used in the study are weighted average call money rate (call), commercial paper rate(CPS), certificates of deposit rate (CDS), 91day treasury bills rate (G91), 10year Government of India bond yield (G10) and RupeeUS dollar forward exchange rate premium for maturities of 1month (FR1) and 3month (FR3). The stock return (BSER) is derived from the BSE sensitive index.
4. EMPIRICAL ANALYSIS
Table 1 provides summary statistics for various interest rate spread variables based on monthly data over the sample period March 1993 to March 2009. All spread variables, had significant nonzero mean. The spread variables also had significant positive skewness and kurtosis statistic. The JarqueBera (JB) statistic, defined in terms of skewness and kurtosis measures, is significantly large, suggesting that the financial variables cannot be normally distributed. Interest rate spreads relating to commercial paper, certificates of deposits and longterm government bond yield had more or less similar sample standard deviation. The forward exchange rate premium variables had sample standard deviation twice larger than the same for commercial paper, certificates of deposits and longterm bond yield. The equity return^{4} spread has largest mean and standard deviation but low skewness and kurtosis. Nevertheless, the JB statistic showed that the equity return departed from the normal distribution like all other financial variables.
Table 1: Summary Statistics of Financial Market Variables 
Financial Variables 
Statistics 
Call 
CDS 
CPS 
FR1 
FR3 
G91 
G10 
BSER 
1 
2 
3 
4 
5 
6 
7 
8 
9 
Mean 
1.67 
1.20 
2.43 
0.77 
0.51 
1.65 
2.00 
1.17 
Median 
0.64 
1.10 
2.11 
0.05 
0.06 
1.28 
1.55 
0.23 
Maximum 
28.08 
5.89 
7.73 
27.00 
19.05 
6.22 
6.46 
60.49 
Minimum 
5.27 
0.98 
0.21 
6.61 
6.34 
1.67 
0.65 
78.92 
Std. Dev. 
3.71 
1.29 
1.51 
3.98 
3.42 
1.73 
1.57 
31.08 
Skewness 
3.98 
0.79 
1.08 
2.98 
1.78 
1.00 
1.10 
0.25 
Kurtosis 
24.02 
3.77 
3.97 
17.33 
9.03 
3.62 
3.46 
2.44 
JarqueBera (JB) 
4040.55 
24.49 
44.75 
1665.15 
392.23 
35.09 
32.48 
4.47 
Probability (JB) 
0.00 
0.00 
0.00 
0.00 
0.00 
0.00 
0.00 
0.11 
Note : All variables are defined in terms of spread over their respective benchmark variables as defined below: Call: call money rate minus Repo rate. CDS: Certificates of Deposit rate minus 91day Treasury Bill rate. CPS: Commercial Paper rate minus 91day Treasury Bill rate. G91: 91day Treasury bill rate minus Repo rate. G10: 10year Government bond yield minus 91day Treasury Bill rate. FR1: 1month forward exchange premium minus the interest rate differential between 91day Treasury bill rate. FR3: 3month forward exchange premium minus the interest rate differential between 91day Treasury bill rate and the US 3month Treasury bill rate. BSER: BSE Sensex equity return minus the 91day Treasury Bill rate. 
Table 2 presents the results of unit root test based on the Augmented DickeyFuller (ADF) and PhilipsPerron methodologies. In terms of PhilipsPerron test, the computed test statistic in absolute terms was greater than the 5 per cent critical value, implying that the spread variables were stationary in nature. For the ADF test, all variables excepting the equity return turned out to be stationary at 5 per cent level of significance. The equity return could be stationery at 10 percent level of significance.
For identifying the suitable ARMA model for the mean of the interest rate spread variables, it is necessary to examine the autocorrelation (ACF) and partial autocorrelation functions (PACF) of the spread variables (Table 3). There are certain common features. First, for all spread variables, the PACF declined sharply after the first lag. On the other hand, the ACF decayed slowly for CDS, CPS, FR3, G10 and BSER and rapidly for the call money rate. Such ACF and PACF imply that the conditional mean of the spread variables could be characterized with first order autoregressive AR(1) model.
Table 2: Unit Root Test 
Interest Rate Spreads 
PhilipsPerron Test 
ADF Test 
1 
2 
3 
Call 
8.38 
3.38 
CDS 
3.79 
3.96 
CPS 
3.94 
4.00 
FR1 
5.12 
5.12 
FR3 
7.44 
4.33 
G10 
2.75 
2.89 
BSER 
2.78 
2.77 
5% critical value is 2.88 
The ACF and PACF for the square of spread variables after being adjusted to their sample mean could be used to examine whether their variance could be characterized with ARCH/GARCH models (Table 4). It was evident that the ACF and PACF for most variables declined rapidly after the first lag, implying that the first order GARCH(1,1) model could be appropriate for the conditional variance of the spread variables. For a more formal test, we estimated two types of mean model for each variable, AR(1) and ARMA(1,1) and then the ARCH effect was tested using LM test as shown in Table 5. For most of the spread variables, the coefficient of MA(1) term was not statistically significant at 5 per cent level of significance. Thus, the AR(1) model was found as the appropriate mean model for the spread variables. For this model, the ARCH effect could not be rejected for all spread variables excepting the 10year yield spread.
With the above statistical results, we now turn to the GARCH analysis for each market segment. The empirical analysis for each financial variable was carried out in a structured manner. First, the standard mean equation using ARMA(1,0) or the AR(1) model was estimated. Subsequently, we extended the AR(1) model to GARCH variance equation, under alternative specifications with distributional assumption changing from normal to generalised distribution, GARCHinmean effect and the threshold/asymmetric effects. For choosing a final model, we looked at the loglikely hood function and various information criteria. The results of our empirical exercises in respect of various market segments are as follows.
Table 3: Autocorrelation Structure of Financial Variables 
Lags 
ACF Call 
PACF 
Qstatistics 
ACF CDS 
PACF 
Qstatistics 
1 
2 
3 
4 
5 
6 
7 
1 
0.53 
0.53 
54.77 
0.85 
0.85 
140.65 
2 
0.38 
0.13 
82.54 
0.73 
0.03 
244.71 
3 
0.36 
0.16 
107.58 
0.62 
0.02 
320.02 
4 
0.42 
0.22 
141.92 
0.55 
0.09 
379.85 
5 
0.31 
0.03 
160.79 
0.49 
0.03 
428.45 
6 
0.21 
0.05 
169.47 
0.45 
0.03 
469.18 
Lags 
CPS 


FR1 


1 
0.82 
0.82 
131.36 
0.73 
0.73 
90.55 
2 
0.70 
0.09 
228.10 
0.49 
0.10 
131.33 
3 
0.57 
0.09 
292.29 
0.41 
0.19 
159.56 
4 
0.45 
0.04 
333.21 
0.39 
0.09 
185.58 
5 
0.39 
0.11 
364.13 
0.28 
0.15 
198.85 
6 
0.34 
0.03 
387.71 
0.18 
0.01 
204.23 
Lags 
FR3 


G91 


1 
0.86 
0.86 
144.06 
0.92 
0.92 
164.53 
2 
0.70 
0.16 
239.26 
0.84 
0.02 
302.91 
3 
0.63 
0.27 
316.46 
0.78 
0.04 
421.26 
4 
0.58 
0.03 
382.18 
0.74 
0.14 
528.70 
5 
0.50 
0.04 
432.01 
0.71 
0.05 
628.26 
6 
0.43 
0.03 
469.37 
0.69 
0.07 
722.70 
Lags 
G10 


BSER 


1 
0.95 
0.95 
141.05 
0.93 
0.93 
169.68 
2 
0.90 
0.06 
270.34 
0.85 
0.18 
310.28 
3 
0.86 
0.00 
388.67 
0.75 
0.14 
420.34 
4 
0.83 
0.09 
499.38 
0.64 
0.12 
500.93 
5 
0.79 
0.08 
600.58 
0.52 
0.10 
555.25 
6 
0.75 
0.05 
692.18 
0.40 
0.09 
587.76 
Note: ACF and PACF are autocorrelation and partial autocorrelation of financial spread variables. 
4.1 Call Money Rate
The call money rate spread over the repo rate could be characterised through an AR(1)TGARCHM(LV) model with log variance in the mean equation (Table 6). The GARCH model suggests that the mean spread of the call money rate over the repo rate as reflected in intercept term in the mean equation could be 28 basis points, which is significantly lower than the estimate (164 basis points) in the ARMA(1,0) model without GARCH effect. The threshold term had negative impact on variance, implying for the favourable impact of good news in terms of moderating risk in this market segment. However, the variance of call money spread over the repo rate showed high (low) persistence with bad (good) news affect the market, as reflected in the sum of ARCH and GARCH coefficients higher than unity under bad news but lower than unity (including the threshold coefficient) under good news. The ARCHM term implying for the volatility in the call money market had statistically significant positive impact on the call money rate, thus, reflecting on the pricing of liquidity risk. However, its size was low, implying that as large as 25 per cent volatility could be associated with a percentage point increase in call rate’s spread over the repo rate. Moreover, the market was found to be characterised with nonstandard distribution, reflecting the impact of extreme movement in this market.
Table 4: Test of ARCH Effect 
Lags 
ACF Call 
PACF 
Qstatistics 
ACF CDS 
PACF 
Qstatistics 
1 
2 
3 
4 
5 
6 
7 
1 
0.53 
0.53 
54.77 
0.87 
0.87 
149.47 
2 
0.38 
0.13 
82.54 
0.76 
0.01 
263.66 
3 
0.36 
0.16 
107.58 
0.65 
0.05 
347.58 
4 
0.42 
0.22 
141.92 
0.56 
0.04 
411.33 
5 
0.31 
0.03 
160.79 
0.50 
0.06 
462.52 
6 
0.21 
0.05 
169.47 
0.46 
0.05 
505.89 

CPS 


FR1 


1 
0.83 
0.83 
134.30 
0.73 
0.73 
90.55 
2 
0.71 
0.08 
234.05 
0.49 
0.10 
131.33 
3 
0.57 
0.11 
299.29 
0.41 
0.19 
159.56 
4 
0.45 
0.06 
339.63 
0.39 
0.09 
185.58 
5 
0.39 
0.12 
369.54 
0.28 
0.15 
198.85 
6 
0.33 
0.03 
391.74 
0.18 
0.01 
204.23 

FR3 


G91 


1 
0.86 
0.86 
144.06 
0.92 
0.92 
164.53 
2 
0.70 
0.16 
239.26 
0.84 
0.02 
302.91 
3 
0.63 
0.27 
316.46 
0.78 
0.04 
421.26 
4 
0.58 
0.03 
382.18 
0.74 
0.14 
528.70 
5 
0.50 
0.04 
432.01 
0.71 
0.05 
628.26 
6 
0.43 
0.03 
469.37 
0.69 
0.07 
722.70 

G10 


BSER 


1 
0.95 
0.95 
141.05 
0.94 
0.94 
192.04 
2 
0.90 
0.06 
270.34 
0.84 
0.30 
347.09 
3 
0.86 
0.00 
388.67 
0.73 
0.12 
463.97 
4 
0.83 
0.09 
499.38 
0.61 
0.11 
545.28 
5 
0.79 
0.08 
600.58 
0.49 
0.04 
599.35 
6 
0.75 
0.05 
692.18 
0.39 
0.03 
633.25 
Note : ACF and PACF are autocorrelation and partial autocorrelation of the square of financial spread variables adjusted to their sample mean. ‘Q’ statistic reported in the table are significant at 5 per cent level of significance. 
Table 5: Test of First order ARCH(1) Effect in Interest Rate Spreads 

AR(1) Coefficient 
t stat 
ARMA(1,1) Coefficient 
t stat 
AR(1) Coefficient 
t stat 
ARMA(1,1) Coefficient 
t stat 
1 
2 
3 
4 
5 
6 
7 
8 
9 
Regressors 
CDs 



CPS 



Intercept 
1.1208 
3.32 
1.1172 
3.26 
2.4357 
6.49 
2.4274 
5.89 
AR (1) 
0.8682 
26.10 
0.8715 
23.56 
0.8426 
21.42 
0.8721 
20.78 
MA (1) 


0.0162 
0.20 


0.1064 
1.25 
R^{–z} 
0.78 

0.78 

0.71 

0.71 

LL 
179.42 

179.41 

232.92 

232.00 

DW 
2.02 

1.99 

2.15 

1.99 

AIC 
1.880 

1.890 

2.447 

2.448 

BIC 
1.914 

1.941 

2.481 

2.499 

ARCH (1) 
26.51 

26.97 

4.89 

3.48 


FR1 



FR3 



Intercept 
0.8139 
1.164 
0.8039 
1.15 
0.4187 
0.46 
0.4631 
0.621 
AR (1) 
0.7320 
13.360 
0.6376 
7.85 
0.8599 
23.19 
0.7712 
21.097 
MA (1) 


0.2033 
1.97 


0.3417 
2.874 
R^{–2} 
0.53 

0.54 

0.74 

0.75 

LL 
398.22 

396.92 

377.14 

371.85 

DW 
1.86 

2.02 

1.72 

2.08 

AIC 
4.851 

4.847 

3.970 

3.925 

BIC 
4.889 

4.904 

4.004 

3.976 

ARCH (1) 
60.07 

63.29 

65.66 

54.72 


G10 



BSER 



Intercept 
0.1023 
1.56 
0.0813 
4.191 
0.2544 
0.34 
0.2508 
0.27 
AR (1) 
0.9490 
36.97 
0.9589 
26.183 
0.9519 
38.76 
0.9242 
29.78 
MA (1) 


0.0979 
0.801 


0.2498 
3.39 
R^{–2} 
0.90 

0.90 

0.89 

0.89 

LL 
109.47 

108.86 

726.77 

721.14 

DW 
2.10 

1.94 

1.45 

1.92 

AIC 
1.457 

1.462 

7.552 

7.504 

BIC 
1.497 

1.522 

7.586 

7.555 

ARCH(1) 
2.15 

1.56 

16.06 

4.70 


Call 



G91 



Intercept 
1.6423 
3.34 
1.6095 
2.08 
0.1338 
1.78 
0.0721 
1.21 
AR (1) 
0.5296 
8.55 
0.8561 
14.05 
0.9152 
31.04 
0.9515 
38.50 
MA (1) 


0.5056 
4.99 


0.2331 
3.03 
R^{–2} 
0.28 

0.31 

0.84 

0.84 

LL 
485.63 

485.36 

226.61 

223.40 

DW 
2.14 

1.89 

2.26 

1.91 

AIC 
5.160 

5.114 

2.394 

2.371 

BIC 
5.194 

5.165 

2.428 

2.422 

ARCH(1) 
16.25 

6.54 

21.23 

13.84 

Notes: LL: Log Likelihood. DW: DurbinWatson Statistics
AIC and BIC are Araike and SchwartzBayes information Criterion, respectively, and t stat is ‘t’ statistics.
The ARCH(1) statistic refers to ‘F’ statistic. The 5 per cent critical value of F(1,191) is about 3.8. The large sample
critical values of ‘t’ stat and ‘z’ stat at 5 per cent level of significance are +/ 1.95 and +/ 1.65, respectively. 
Table 6 : Call Money Rate 

AR(1) 
AR(1) GARCH 
AR(1) GARCH 
AR(1) GARCHM (*) 
AR(1) GARCHM ($) 

Coefficient 
tstat 
Coefficient 
zstat 
Coefficient 
zstat 
Coefficient 
zstat 
Coefficient 
zstat 
1 
2 
3 
4 
5 
6 
7 
8 
9 
10 
11 
Mean Equation 
Intercept (α_{1} ) 
1.6423 
3.34 
1.4506 
1.3 
0.0115 
0.51 
1.4977 
7.32 
0.2833 
4.03 
AR(1): (β_{1}) 
0.5296 
8.55 
0.7155 
5.95 
0.7605 
83.85 
0.4327 
72.94 
0.5651 
36.38 
ARCHM (β_{1}) 






0.9254 
9.9 
0.0464 
3.12 
Veriance Equation 
Intercept (α_{2} ) 


3.0537 
6.91 
0.022 
1.12 
0.7928 
14.79 
0.0431 
2.11 
ARCH (1) (β_{2}) 


0.3603 
3.36 
1.0233 
2.1 
0.1973 
10.56 
0.9475 
2.49 
GARCH (1) (β_{3}) 


0.3481 
3.93 
0.6301 
8.18 
0.8588 
85.65 
0.6407 
9.54 
Threshold (β_{4}) 






0.4775 
9.72 
0.8951 
2.19 
Distribution (β_{5}) 




0.5023 
10.72 
0.3737 
13.35 
0.5616 
13.57 
R^{–2} 
0.28 

0.25 

0.22 

0.24 

0.26 

LL 
485.63 

447.81 

298.86 

308.67 

295.14 

DW 
2.14 

2.48 

2.51 

2.33 

2.16 

AIC 
5.1601 

4.8774 

3.7366 

3.3509 

3.2079 

SIC 
5.1944 

4.973 

3.329 

3.4882 

3.3451 

Notes: * and $ refer to ARCHM term in the form of GARCH standard deviation and GARCH variance in logarithm form, respectively, This applies to all other tables in the paper. 
4.2 Commercial Paper
For the commercial paper, the threshold ARMA(1,0)GARCHinmean model (with standard deviation in the mean equation) turned out to be the appropriate model as compared with the ARMA(1,0) model (Table 7). In this model, the intercept coefficient estimated at 2.56 in the mean equation was statistically significant, which implied the extent to which the commercial paper rate could deviate from the 91day Treasury bill rate on average in the medium term. The coefficient of the ARCHM term was positive and statistically significant, suggesting that the market segment was capable of pricing risks on a continuous basis. In terms of the coefficient size of ARCHM term, an increase in standard deviation by 3 percentage points could lead to one percentage point increase in the commercial paper rate over the 91day Treasury bill rate. The threshold term was negative and statistically significant, implying that good (bad) news led to lower (higher) volatility in this market segment. However, the market segment exhibited volatility persistence under bad news since the sum of ARCH and GARCH effects exceeded unity. The market was associated with nonstandard distribution.
Table 7: Commercial Paper Rate 
Variables 
AR(1) 
AR(1)GARCH 
AR(1)GARCH 
AR(1)GARCH* 
AR(1)GARCH* 
Coefficient 
t stat 
Coefficient 
Z stat 
Coefficient 
Z stat 
Coefficient 
Z stat 
Coefficient 
Z stat 
1 
2 
3 
4 
5 
6 
7 
8 
9 
10 
11 
Mean Equation 
Intercept 
2.4357 
6.49 
1.6797 
5.38 
1.6434 
5.21 
2.5298 
7.55 
2.5584 
8.03 
AR (1) 
0.8426 
21.42 
0.8664 
23.31 
0.8819 
26.57 
0.8113 
18.44 
0.7993 
14.06 
ARCHM 






0.3485 
2.64 
0.3246 
1.98 
Variance Equation 
Intercept 


0.0155 
1.76* 
0.0235 
1.31** 
0.0161 
1.39* 
0.0233 
2.34 
ARCH (1) 


0.1857 
3.44 
0.22280 
2.27 
0.1755 
2.27 
0.3441 
2.34 
GARCH (1) 


0.8141 
20.06 
0.7652 
10.42 
0.8220 
13.78 
0.7945 
13.97 
Threshold 








0.3264 
1.99 
Distribution (GD) 




1.1899 
6.50 
1.1433 
6.74 
1.1636 
7.07 
R^{–2} 
0.71 

0.69 

0.69 

0.70 

0.70 

LL 
232.92 

210.02 

202.3975 

199.08 

197.17 

DW 
2.15 

2.17 

2.1708 

2.18 

2.22 

AIC 
2.4471 

2.2398 

2.2726 

2.1467 

2.1372 

SIC 
2.4810 

2.3246 

2.2108 

2.2654 

2.2729 

4.3 Certificates of Deposits
For the certificates of deposits (CDS), the ARMA(1,0)GARCHinmean without threshold effect was found to be the appropriate model (Table 8). The statistically significant intercept term in the mean equation showed that on average, the CDS rate could be higher than the Treasury bill rate by 1.5 percentage points, somewhat higher than the AR(1) model. The CD spread also exhibited volatility persistence. The threshold term had significant impact on the variance of CDS spread attributable to good and bad news. The coefficient of the ARCHM term was significant, implying for the risk pricing in the market segment.
Table 8 : Certificates of Deposit Rate 
Variables 
AR(1) 
AR(1)GARCH 
AR(1)GARCH 
AR(1)GARCH* 
AR(1)GARCH* 
Coefficient 
t stat 
Coefficient 
Z stat 
Coefficient 
Z stat 
Coefficient 
Z stat 
Coefficient 
Z stat 
1 
2 
3 
4 
5 
6 
7 
8 
9 
10 
11 
Mean Equation 
Intercept 
1.1208 
3.32 
0.2339 
0.93** 
0.1562 
0.50** 
1.4699 
3.37 
1.5255 
3.15 
AR(1) 
0.8682 
26.10 
0.9237 
44.57 
0.9324 
44.16 
0.8795 
26.14 
0.862 
23.80 
ARCHM 






0.2136 
2.35 
0.2110 
2.10 
Variance Equation 
Intercept 


0.0044 
1.45** 
0.0040 
1.15** 
0.0027 
1.06** 
0.0040 
1.55** 
ARCH(1) 


0.3658 
4.68 
0.3448 
2.95 
0.2657 
2.85 
0.3386 
2.52 
GARCH(1) 


0.6898 
12.62 
0.7111 
8.91 
0.7778 
11.59 
0.7695 
10.81 
Threshold 








0.1939 
1.05** 
Distribution 




1.2411 
6.20 
1.1296 
6.89 
1.1603 
6.90 
R^{–2} 
0.78 

0.77 

0.77 

0.78 

0.78 

LL 
179.42 

124.15 

119.97 

117.12 

116.76 

DW 
2.02 

2.08 

2.08 

2.12 

2.14 

AIC 
1.8801 

1.33383 

1.3054 

1.2862 

1.2928 

SIC 
1.9139 

1.4229 

1.4068 

1.4046 

1.4281 

4.4 Government Bond Yield
For the yield spread, i.e., the spread of 10year government bond over the 91day treasury bill rate, the ARMA(1,0)TGARCH model was found appropriate for the analysis (Table 9a). In this model, the intercept term was significant and the size of coefficient suggested that the long rate could be higher than the short rate by 144 basis points. The coefficient of ARCH effect in the mean equation, which is indicative of risk pricing, was also found statistically significant. For every percentage point increase in the standard deviation, the mean spread could be higher by 0.65 percentage points. The threshold term was positive and significant, but its size was quite low. In the variance equation, the persistence was more or less due to the GARCH effect. The statistically significant coefficient for the generalised distribution was indicative of the nonstandard distribution of the yield spread.
Table 9a: Government (10Year) Bond Yield 
Variables 
AR(1) 
AR(1)GARCH 
AR(1)GARCH* 
AR(1)GARCH* 
Coefficient 
t stat 
Coefficient 
Z stat 
Coefficient 
Z stat 
Coefficient 
Z stat 
1 
2 
3 
4 
5 
6 
7 
8 
9 
Mean Equation 
Intercept 
0.1023 
1.56 
0.1173 
1.71 
0.0363 
0.90 
1.4426 
5.28 
AR(1) 
0.9490 
36.97 
0.9223 
25.36 
0.9453 
48.74 
0.8105 
26.64 
ARCHM 






0.6584 
5.90 
Variance Equation 
Intercept 


0.0112 
4.03 
0.0108 
1.77 
0.0061 
4.07 
ARCH(1) 


0.0179 
1.62 
0.0090 
0.47 
0.0078 
3.01 
GARCH(1) 


0.9153 
48.97 
0.9209 
23.62 
0.9480 
127.25 
Threshold 






0.0475 
2.39 
Distribution 




0.9814 
8.03 
0.8560 
8.28 
R^{–2} 
0.90 

0.90 

0.89 

0.91 

LL 
109.47 

98.37 

81.60 

68.97 

DW 
2.10 

2.03 

2.06 

2.12 

AIC 
1.4571 

1.3513 

1.1451 

1.0061 

SIC 
1.4967 

1.4503 

1.2639 

1.1646 

For the shortend of the Government securities market, the spread of 91day Treasury bill rate over the repo rate^{5} was consistent with AR(1)GARCH with logarithm of conditional variance in the mean equation (Table 9b). The intercept term in the mean equation was statistically significant and positive but small at 22 basis points. Thus, the 91day Treasury bill could exceed repo rate on average by a quarter percentage point. The conditional variance had positive effect, reflecting on the risk to the market segment had a positive effect on the 91day Treasury bill spread as the coefficient of conditional variance term was found statistically significant in the mean equation. The conditional variance associated with the market segment was found to be persistent, as the sum of ARCH and GARCH terms were closer to unity. However, the market segment was not affected by news as the threshold term was statistically insignificant.
Table 9b: Government 91day Treasury Bill 
Variables 
ARMA 
ARMA GARCH* 
Coefficient 
t stat 
Coefficient 
Z stat 
1 
2 
3 
4 
5 
Mean Equation 
Intercept 
0.1338 
1.78 
0.2272 
3.35 
AR(1) 
0.9152 
31.04 
0.9599 
90.89 
ARCHM 


0.1198 
2.74 
Variance Equation 
Intercept 


0.1012 
2.65 
ARCH(1) 


0.6149 
1.81 
GARCH(1) 


0.3451 
2.83 
Threshold 


0.0720 
0.20 
Distribution 


0.7784 
7.77 
R^{–2} 
0.84 

0.83 

LL 
226.61 

151.88 

DW 
2.26 

2.34 

AIC 
2.394 

1.674 

SIC 
2.428 

1.810 

4.5 Forward and Spot Exchange Rates
For the 1month forward exchange rate premium, the intercept coefficient in the mean equation for the spread of the 1month forward exchange rate premium over the interest rate differential turned out negative in the GARCH model, whereas it was 81 basis points in the simple AR(1) model (Table 10). The coefficient of the GARCH volatility was significant but negative. Interestingly, when the model was allowed to have a threshold term to capture the news impact, the latter did not turn out to be significant. Unlike the GARCH model, the EGARCH model could show a positive impact of GARCH variance in the mean equation, and a significant impact of news effect on the market volatility. An interesting finding was that the drift parameter in the mean equation was negative but not significant. This could imply two features of the market: a stronger rupee and the absence of arbitrage opportunity in the exchange market. Another interesting aspect of the EGARCH model was that the sum of ARCH and GARCH coefficients were negative and less than unity, implying that volatility could not be persistent in foreign exchange market. This result was not surprising, when one takes into account the stable exchange market objective and intervention strategy of the authorities. These findings were also evident for the threemonth forward exchange rate premium (Table 11).
Table 10: Onemonth Forward Exchange Rate Premium 
Variables 
AR(1) 
AR(1)GARCH 
AR(1)GARCH 
AR(1)GARCH* 
AR(1)GARCH* 
AR(1)EGARCH$ 
Coef
ficient 
t stat 
Coef
ficient 
Z stat 
Coef
ficient 
Z stat 
Coef
ficient 
Z stat 
Coef
ficient 
Z stat 
Coef
ficient 
Z stat 
1 
2 
3 
4 
5 
6 
7 
8 
9 
10 
11 
12 
13 
Mean Equation 
Intercept 
0.8139 
1.03 
0.2159 
0.59 
0.4918 
2.23 
1.2104 
1.608 
1.4075 
2.07 
0.9055 
1.31 
AR(1) 
0.7320 
13.74 
0.6956 
14.31 
0.7386 
19.82 
0.7254 
17.98 
0.7530 
19.17 
0.6016 
46.75 
ARCHM 






0.1889 
1.96 
0.1730 
1.72 
1.3786 
6.82 
Variance Equation 
Intercept 


0.4248 
4.52 
0.3494 
1.99 
0.4370 
2.12 
0.44 
2.25 
2.27534 
6.78 
ARCH(1) 


0.6956 
5.14 
0.5389 
2.23 
0.5875 
2.12 
0.6677 
2.01 
0.1334 
3.26 
Threshold 








0.1905 
0.39 
0.0847 
5.496 
GARCH(1) 


0.3852 
5.86 
0.4751 
3.33 
0.4263 
3.00 
0.4230 
2.98 
0.6231 
11.13 
Distribution 




0.8954 
7.64 
0.8370 
7.24 
0.8395 
7.35 
0.5611 
8.71 
R^{–2} 
0.53 

0.52 

0.51 

0.50 

0.50 

0.47 

LL 
398.22 

315.98 

296.52 

295.35 

295.19 

321.77 

DW 
1.86 

1.77 

1.84 

1.68 

1.73 

1.50 

AIC 
4.8512 

3.8906 

3.618 

3.6649 

3.6750 

3.9973 

SIC 
4.8889 

3.9847 

3.735 

3.7967 

3.8256 

4.1479 

For the spot exchange rate of Indian Rupee per US dollar, the spread of annual depreciation over the interest rate differential (call money rate less 3month LIBOR rate) was found to be consistent with AR(1)GARCH model with logarithm of variance in the mean (Table 12). In this model, the intercept term in the mean equation was positive but statistically insignificant, suggesting that the spot exchange rate did not show a tendency to be away from uncovered interest parity in the longrun. Similarly, in the variance equation, the threshold term was not statistically significant, implying that the market did not respond asymmetrically to good or bad news. However, the conditional variance term had positive and significant effect in the mean equation, implying that risk to the market had a passthrough effect on expected variation in the spot exchange rate. The most notable aspect of spot exchange rate was the volatility persistence, which was evident from the ARCH and GARCH coefficients in the conditional variance equation. The sum of these two coefficients was significantly higher than unity. Also, the generalised error distribution term was statistically significant, as conditional volatility in the market was affected by skewness and kurtosis attributable to the episodes of some sharp variations in the exchange rate.
Table 11: Threemonth Forward Exchange Rate Premium 
Variables 
AR (1) 
AR (1)GARCH 
AR (1)GARCH 
AR (1)GARCH* 
AREGARCH* 
AREGARCH$ 
Coef
ficient 
t stat 
Coef
ficient 
Z stat 
Coef
ficient 
Z stat 
Coef
ficient 
Z stat 
Coef
ficient 
Z stat 
Coef
ficient 
Z stat 
1 
2 
3 
4 
5 
6 
7 
8 
9 
10 
11 
12 
13 
Mean Equation 
Intercept 
0.4187 
0.46 
0.2943 
0.53 
0.6096 
1.23 
1.6422 
0.63 
0.3511 
0.59 
0.1740 
0.16 
AR(1) 
0.8599 
23.19 
0.9008 
31.01 
0.8993 
30.49 
0.9066 
30.28 
0.6963 
41.25 
0.7248 
35.15 
ARCHM 






0.0544 
0.44 
0.8630 
7.81 
1.4635 
8.12 
Variance Equation 
Intercept 


0.0549 
2.38 
0.0816 
1.62 
0.0821 
1.60 
1.9032 
4.91 
2.0788 
6.95 
ARCH(1) 


0.5180 
5.34 
0.6018 
2.94 
0.5949 
2.98 
0.3493 
3.60 
0.6386 
4.89 
Threshold 








0.4810 
6.50 
0.3737 
5.34 
GARCH(1) 


0.5904 
13.02 
0.5162 
4.92 
0.5193 
4.92 
0.4353 
3.52 
0.3031 
6.71 
Distribution 




1.1857 
7.79 
1.1847 
7.80 
0.5944 
8.07 
0.5736 
9.31 
R^{–2} 
0.74 

0.73 

0.73 

0.73 

0.67 



LL 
377.14 

290.89 

282.22 

282.19 

331.41 



DW 
1.72 

1.78 

1.77 

1.77 

1.27 



AIC 
3.9700 

3.0983 

3.018 

3.0281 

3.5540 



SIC 
4.0041 

3.1835 

3.1202 

3.1473 

3.6902 



Table 12 : Spot Exchange Rate 
Variables 
AR(1) 
AR(1)GARCH 
AR(1)GARCH 
AR(1)GARCH (*) 
AR(1)GARCH ($) 
Coefficient 
t stat 
Coefficient 
Z stat 
Coefficient 
Z stat 
Coefficient 
Z stat 
Coefficient 
Z stat 
1 
2 
3 
4 
5 
6 
7 
8 
9 
10 
11 
Mean Equation 
Intercept 
0.4502 
0.26 
9.5766 
2.65 
10.77 
2.14 
2.3631 
1.20 
1.7099 
1.04 
AR(1) 
0.8321 
19.32 
0.9271 
32.51 
0.9739 
67.48 
0.9191 
41.48 
0.8938 
38.06 
ARCHM 






0.0931 
2.22 
0.4334 
3.55 
Variance Equation 
Intercept 


1.2583 
4.16 
1.2348 
2.05 
0.9456 
1.82 
0.5876 
2.14 
ARCH(1) 


0.8238 
6.43 
0.8745 
2.90 
1.1269 
2.36 
1.0701 
2.68 
GARCH(1) 


0.3755 
6.64 
0.3645 
3.17 
0.4060 
3.42 
0.4904 
6.08 
Threshold 






0.4739 
0.79 
0.5375 
1.14 
Distribution 




0.8824 
8.66 
0.9157 
7.94 
0.8493 
8.37 
R^{–2} 
0.66 

0.64 

0.63 

0.65 

0.66 

LL 
537.00 

483.56 

461.96 

460.72 

456.33 

DW 
2.21 

2.30 

2.39 

2.38 

2.38 

AIC 
5.64 

5.11 

4.90 

4.91 

4.86 

SIC 
5.68 

5.20 

5.00 

5.04 

4.99 

4.6 Equity Market Return
For the equity market, the ARMA(1,0)TGARCHM model was suitable for modeling the spread of domestic equity return over the 91day Treasury bill rate (Table 13). Here, we estimated four GARCH models. Two models were estimated with the mean equation having riskreturn tradeoff alternatively in terms of conditional standard deviation and variance. Further, for analysing the impact of international integration, two other GARCH models were estimated by incorporating the equity return spread for a global market, i.e., the US market as an explanatory variable in the mean equation. The estimated GARCH models provide some crucial insights about the risk pricing in the Indian context as compared with other market segments. First, the mean of equity return spread, as reflected in the intercept term in the mean equation in the ARMAGARCH model was significantly higher than the simple ARMA(1,0) model. Second, the coefficient of ARCHM, reflecting on riskreturn tradeoff was found statistically significant. A notable point here is that the coefficient of ARCHM in the mean equation, which measures the riskreturn tradeoff, was negative, unlike the positive impact estimated for interest rates and the associated financial market segments discussed earlier. The asymmetry effect was positive, unlike the other market segments. These finding are in line with the theoretical and empirical literature. Black (1972) suggested this phenomenon as the leverage effect as volatilities and asset returns are negatively correlated. Because, declining stock prices imply an increased leverage on firms, worsening the debt/equity ratio. Thus, agents presume investing in the firm to be riskier, resulting in volatility. Rising volatility, on the other hand, also makes investments riskier, and prices should fall in order to reflect this. Third, when global market was introduced in the GARCH model, the mean return increased by two fold and also, the ARCHM coefficient rose significantly, thereby, suggesting that international integration accentuate risk pricing in the domestic market. Fourth, the intercept term in the variance equation was significantly moderated in the GARCH model in the presence of global market, thus, reflective on the benefit of international integration in terms of risk pricing over longer horizon.
Table 13: BSE SENSEX Equity Return 

AR(1) 
Without the impact Global Market 
With the impact of Global market 
AR(1)GARCH(*) 
AR(1)GARCH($) 
AR(1)GARCH* 
AR(1)GARCH$ 
Variables 
Coef
ficient 
t stat 
Coef
ficient 
Zstat 
Coef
ficient 
Zstat 
Coef
ficient 
Zstat 
Coef
ficient 
Zstat 
1 
2 
3 
4 
5 
6 
7 
8 
9 
10 
11 
Mean Equation 
Intercept 
0.2544 
0.34 
27.9347 
4.98 
95.5609 
3.15 
50.6805 
13.26 
160.6576 
9.06 
AR(1) 
0.9519 
38.76 
0.8935 
15.97 
0.9090 
20.10 
0.6084 
8.14 
0.5639 
9.22 
ARCHM 


2.8402 
4.98 
21.1323 
3.21 
5.7171 
24.71 
37.3597 
9.98 
Global stock 






0.6860 
8.14 
0.7736 
8.99 
Variance Equation 
Intercept 


17.4071 
2.08 
36.5300 
2.46 
4.8029 
2.13 
4.7917 
2.09 
ARCH(1) 


0.1461 
3.45 
0.0844 
2.58 
0.1209 
5.02 
0.1052 
5.23 
GARCH(1) 


0.8522 
9.19 
0.6079 
3.79 
0.9373 
26.47 
0.9453 
27.39 
Threshold 


0.1743 
3.40 
0.1205 
2.66 
0.2208 
5.97 
0.1623 
6.11 
Distribution 


1.3263 
7.26 
1.4205 
7.28 
1.6933 
4.99 
1.9053 
5.22 
R^{–2} 
0.89 

0.89 

0.90 

0.89 

0.89 

LL 
726.77 

704.17 

705.46 

690.90 

690.16 

DW 
1.45 

1.84 

1.96 

1.77 

1.57 

AIC 
7.5520 

7.3800 

7.3933 

7.2528 

7.2452 

SIC 
7.5858 

7.5152 

7.5286 

7.4049 

7.3974 

4.7 Corporate Bond Yield
For the corporate bond yield, we examined the behavior of the spread of AAA rated 10year corporate bond yield over the risk free rate alternatively with respect to 91day Treasury bill, 364day Treasury bill and 10year Government bond yield based on data available for the sample period April 2000 to March 2009. Initially, we estimated the ARMA(1,0) model and then tested whether the residuals arising from the model could be subject to first order ARCH effect through LM test, so that the GARCH modeling could be taken up for the market segment. Results from the AR(1) model showed that on average, corporate bond yield could be higher than the 91day Treasury bill, 364day treasury bill and the 10year Government bond yield by 244, 234 and 134 basis points, respectively (Table 14). However, none of the three alternative corporate bond yield spread variables could pass through residual ARCH test and therefore, the GARCH exercise could not be taken up. This result suggests that risk pricing could be lacking for this market segment. It may be noted that the finding is line with the literature in the Indian context (RCF, 200506). The Committee on corporate debt market (Chairman: R. H. Patil) pointed out various problems including the risk pricing affecting this market segment and made various recommendations for developing the market segment in India.
Table 14: Corporate Bond Yield Spread 
Variables 
Spread over 91day Treasury bill ARMA(1,0) 
Spread over 364day Treasury bill ARMA(1,0) 
Spread over 10year
Government bond yield
ARMA(1,0) 
Coefficient 
T stat 
Coefficient 
T stat 
Coefficient 
T stat 
1 
2 
3 
4 
5 
6 
7 
Intercept 
2.44 
8.33 
2.34 
4.56 
1.34 
2.88 
AR(1) 
0.86 
14.63 
0.93 
17.59 

25.49 
R^{–2} 
0.67 

0.74 


0.86 
LL 
57.2 

35.26 


5.42 
DW 
1.96 

2.03 


1.99 
AIC 
1.10 

0.69 


0.14 
SIC 
1.15 

0.74 


0.19 
First Order ARCH LM test : 






Fstat (probability) 
2.48 (0.12) 

0.01(0.99) 


0.56(.45) 
4.8 Risk Pricing during Global Crisis
In the earlier section, our empirical analysis was based on the full sample period, i.e., April 1993 to March 2009, which included the period since January 2008 associated with the global crisis. A critical issue arises here. Did the risk pricing mechanism underlying the Indian financial markets change since January 2008? Thus, the sample period was restricted to December 2007 for the chosen GARCH models (Table 15). A comparision between models under the restricted sample and full sample provided some interesting insights into the risk pricing mechanism. First, for the call money market, there was a significant increase in the ARCH and GARCH coefficients in the variance equation. The coefficient of threshold variable almost doubled in the environment of global crisis, implying for the sensitivity to bad (good) news about liquidity risk. However, on a positive note, the ARCHM coefficient declined rapidly in the mean equation in the more recent period than the earlier period. Second, for the commercial paper, its long run mean spread over the 91day Treasury bill, i.e. (intercept term in the mean equation) declined, attributable to the monetary easing pursued in the more recent period. There was no significant change in the volatility persistence as reflected in the coefficients of ARCH and GARCH terms. The threshold terms in the variance equation, however, increased to reflect greater sensitivity to good/bad news.
Table 15 :Risk Pricing and Global Crisis 
Variables 
Full Sample (19932009) 
Restricted (19932007) 
Full Sample (19932009) 
Restricted (19932007) 
Coefficient 
Z stat 
Coefficient 
Z stat 
Coefficient 
Z stat 
Coefficient 
Z stat 
1 
2 
3 
4 
5 
6 
7 
8 
9 

Call 



CPS 






Mean Equation 




Intercept 
0.2833 
4.03 
6.83 
17.29 
2.5584 
8.03 
3.17 
5.23 
AR(1) 
0.5651 
36.38 
0.32 
23.54 
0.7993 
14.06 
0.9 
45.5 
ARCHM 
0.0464 
3.12 
3.24 
20.3 
0.3246 
1.98 
0.22 
3.4 



Variance Equation 




Intercept 
0.0431 
2.11 
2.5 
10.16 
0.0233 
2.34 
0.007 
2.7 
ARCH(1) 
0.9475 
2.49 
0.22 
24.06 
0.3441 
2.34 
0.08 
20.2 
GARCH(1) 
0.6407 
9.54 
0.73 
36.22 
0.7945 
13.97 
1.02 
60.9 
Threshold 
0.8951 
2.19 
0.47 
34.76 
0.3264 
1.99 
0.27 
6.06 
Distribution 
0.5616 
13.57 
0.35 
12.7 
1.1636 
7.07 
1.37 
7.58 
Rsq 
0.26 

0.22 

0.7 

0.72 

LL 
295.14 

299.99 

197.17 

157.8 

DW 
2.16 

2.2 

2.22 

2.2 


CDS 



G10 






Mean Equation 




Intercept 
1.5255 
3.15 
1.48 
3 
1.4426 
5.28 
0.25 
0.6 
AR(1) 
0.862 
23.8 
0.89 
27.2 
0.8105 
26.64 
0.97 
55 
ARCHM 
0.211 
2.1 
0.21 
2.25 
0.6584 
5.9 
0.16 
0.6 



Variance Equation 




Intercept 
0.004 
1.55** 
0.004 
1.32 
0.0061 
4.07 
0.25 
2.6 
ARCH(1) 
0.3386 
2.52 
0.3 
2.3 
0.0078 
3.01 
0.01 
0.39 
GARCH(1) 
0.7695 
10.81 
0.76 
10.1 
0.948 
127.25 
0.25 
0.8 
Threshold 
0.1939 
1.05** 
0.08 
0.42 
0.0475 
2.39 
0.14 
0.74 
Distribution 
1.1603 
6.9 
1.1 
6.8 
0.856 
8.28 
1 
7.4 
Rsq 
0.78 

0.8 

0.91 

0.89 

LL 
116.76 

96.2 

68.97 

76 

DW 
2.14 

2.2 

2.12 

2.2 


FR1 



FR3 






Mean Equation 




Intercept 
1.21 
1.96 
0.95 
1.44 
2.47 
3.57 
2.53 
4.3 
AR(1) 
0.76 
19.7 
0.77 
19.63 
0.78 
20.47 
0.72 
16.94 
ARCHM 
0.36 
2.6 
0.3 
2.03 
0.51 
3.83 
0.71 
4.9 



Variance Equation 




Intercept 
0.39 
3.4 
0.5 
3.09 
0.41 
3.34 
0.37 
4.35 
ARCH(1) 
0.73 
3.98 
0.88 
3.51 
0.83 
4.4 
0.72 
6.2 
GARCH(1) 
0.89 
18.2 
0.84 
12.8 
0.85 
16.2 
0.88 
23.4 
Threshold 
0.23 
1.8 
0.25 
1.54 
0.06 
0.52 
0.08 
0.93 
Distribution 
0.91 
6.1 
1 
5.6 
0.9 
10.1 
0.87 
10.1 
Rsq 
0.56 

0.57 

0.44 

0.42 

LL 
291.1 

257.5 

353.3 

322.2 

DW 
2.36 

2.44 

2.7 

2.7 


BSER (without global) 


BSER (with global) 





Mean Equation 




Intercept 
27.9347 
4.98 
26.69 
4.9 
50.6805 
13.26 
27.1 
6.5 
AR(1) 
0.8935 
15.97 
0.9 
16.7 
0.6084 
8.14 
0.82 
17.1 
ARCHM 
2.8402 
4.98 
2.77 
4.64 
5.7171 
24.71 
3.2 
6.7 
Global 




0.686 
8.14 
0.43 
4.28 
Intercept 
17.4071 
2.08 
19.67 
2.19 
4.8029 
2.13 
7.35 
2.5 



Variance Equation 




ARCH(1) 
0.1461 
3.45 
0.14 
3.02 
0.1209 
5.02 
0.14 
4 
GARCH(1) 
0.8522 
9.19 
0.81 
7.19 
0.9373 
26.47 
0.93 
20.7 
Threshold 
0.1743 
3.4 
0.17 
2.8 
0.2208 
5.97 
0.2 
3.8 
Distribution 
1.3263 
7.26 
1.6 

1.6933 
4.99 
1.75 
4.93 
Rsq 
0.89 

0.89 

0.89 

0.89 

LL 
704.17 

644 

690.9 

635 

DW 
1.84 

1.94 

1.77 

1.82 

The ARCH effect in the mean equation also increased, implying greater riskreturn tradeoff in this market. A similar finding also held for the certificates of deposits. Third, the 10year government bond yield showed a significant increase in its average spread over the shortrate as implied by the intercept term in the mean equation. It also witnessed a significant accentuation of riskreturn trade–off in the more recent period. Fourth, as regards the forward exchange premium, the mean spread increased for the 1month maturity but remained more or less stable for the 3month maturity. A similar pattern held for the ARCHM term or the riskreturn trade–off parameter. The market showed more or less stability in the threshold term relating to the news impact. Fifth, for the equity market, the expected return (the intercept term) showed stability in the absence of global market variable. In the presence of the latter, however, there was a sharp increase in the expected return. A similar pattern of results also held for the riskreturn tradeoff parameter. A notable point was that the underlying persistence characteristic of the market did not show any significant change. Moreover, the market’s response to good (bad) news was not much affected. Finally, the spot exchange rate showed two interesting aspect of change in terms of underlying risk pricing for the alternative sample period (Table 16). On the one hand, the GARCH model without the threshold effect showed a shift from a statistically significant to insignificant intercept term in the mean equation for the spread of annual variation in exchange rate over the interest rate differential. On the other hand, the coefficient size of conditional variance term in the mean equation declined when the sample included the recent crisis period. This result could be attributable to the effectiveness of exchange rate management in the more recent period.
Table 16: Risk Pricing in Spot Exchange Rate and Global Crisis 
Variables

Full Sample (19932009) 
Restricted (19932007) 
Coefficient 
Z stat 
Coefficient 
Z stat 
1 
2 
3 
4 
5 

Mean Equation 
Intercept 
1.5578 
0.73 
4.5587 
1.94 
AR(1) 
0.9212 
50.37 
0.9100 
51.18 
ARCHM 
0.3698 
3.59 
0.5780 
4.40 

Variance Equation 
Intercept 
0.7480 
2.03 
0.6764 
2.40 
ARCH(1) 
0.8333 
3.02 
0.6592 
3.10 
GARCH(1) 
0.4548 
4.63 
0.5111 
6.16 
Distribution 
0.8370 
8.68 
0.8432 
8.90 
R^{–2} 
0.66 

0.59 

LL 
456.99 

416.66 

DW 
2.39 

2.51 

5. CONCLUSION
In this study, we used the univariate GARCH model to evaluate the ability of various financial market segments to price risks in the Indian context. Empirical analyses brought to the fore several insights in this regard. First, the various segments of financial markets, excepting the corporate bond yield, exhibited their ability to price risks. A crucial finding here was that the underlying risk pricing mechanism for various interest rates was different from that of the equity returns. In particular, the conditional measure of risk arising from the GARCH model had positive impact on the conditional mean of various interest rate spreads, reflecting the tradeoff between risk and return in the associated markets. On the other hand, the conditional risk showed inverse relationship with equity return, attributable to the leverage effect as postulated in the finance literature. Second, different market segments pertaining to liquidity, interest rate, credit, exchange rate and asset prices exhibited different volatility persistence. Third, money market interest rates, forward exchange rate premium and equity prices showed significant asymmetric response to good (bad) news. Fourth, the spot exchange rate did not show a tendency to depart from the interest rate parity over longer horizon, despite showing volatility persistence. Fourth, all financial variables were found to be consistent with nonstandard generalised error distribution. This implied that markets also took into account skewness and kurtosis measures influenced by the extreme movements as part of pricing risks. Fifth, international integration accentuated risk pricing in the domestic stock market in terms of higher mean and riskreturn trade off.
From policy perspective, an understanding of the risk pricing mechanism assumes importance in many ways. The ability of markets to price various risks could reflect on the risk management by financial intermediaries and participants to hedge against risks, devise optimal hedging strategies, establish trading strategies and make portfolio allocation decisions. Also, risk pricing could imply for operating efficiency on the part of financial intermediaries and other market participants. Such efficiency in turn contribute to efficiency in allocation of resources to productive sectors, thereby, leading to a more matured and developed financial system. In terms of our empirical analysis, two key findings need to be mentioned here. First, financial markets at shortend showed their ability to price risks. Second, at the long end of the market, the sensitiveness of the equity market to international integration and the absence of risk pricing in the longterm corporate bond market segment require some thoughts on developing these market segments further.
Going beyond the study, the risk pricing analysis could be extended in three ways for further research. First, a multivariate GARCH analysis involving interest rates, exchange rate and equity prices could serve useful in terms of identifying how different risks percolate across market segments. Second, the GARCH analysis could be carried out using macroeconomic factors so as to identify whether the various types of risks connect with fundamentals such as inflation, growth, liquidity and turnover. Third, the evidence from the risk pricing analysis arising from monthly data could be compared with daily and weekly data in order to derive insights on the risk pricing due to the speed of markets in processing information. Taken together, these aspects of risk pricing could enrich financial stability analysis in the Indian context.
References
Antoniou, A. A. Bernales S. and D. W. Beuermann (2005), ‘The Dynamics of the ShortTerm Interest Rate in the UK’.
Andersen, T.G., and Bollerslev, Tim, (1998a), ‘Deutsche MarkDollar Volatility: Intraday Activity Patterns, Macroeconomic Announcements, and Longer Run Dependencies’, Journal of Finance, Vol. 53, No.1.
Andersen, T.G., and Bollerslev Tim, (1998b), ‘Answering the Skeptics: Yes, Standard Volatility Models Do Provide Accurate Forecasts’, International Economic Review, 39.
Andersen, Torben G., Bollerslev, Tim, Diebold, Francis X. And Labys, Paul, (1999), ‘The Distribution of Exchange Rate Volatility’, Wharton Financial Institutions Center Working Paper 9908 and NBER Working Paper 6961.
Baillie, Richard T., Bollerslev, Tim and Mikkelsen, Hans Ole (1996), ‘Fractionally Integrated Generalized Autoregressive Conditional Heteroskedasticity’, Journal of Econometrics, 74(1), 330.
Bali, T., (2000). ‘Testing the Empirical Performance Of Stochastic Volatility Models of The Short Term Interest Rates’. Journal Of Financial And Quantitative Analysis 35 (2), 191–215.
Bali, T.G. and L. Wu (2005), ‘A Comprehensive Analysis of the ShortTerm InterestRate Dynamics’, Journal of Banking and Finance, Xxx–Xxx
Ball, C. and Torous, W. N. (1995), ‘The Stochastic Volatility of Shortterm Interest Rates : Some International Evidence,’ Joural of Finance, Vol. 56.
Bauwens, L, and J.P. Vandeuren (1997), ‘Modeling Interest Rates With A Cointegrated VarGarch Model’, Core Discussion Paper, 9780.
Bauwens, L., S. Laurent and J.V.K. Rombouts (2005) ‘Multivariate GARCH Models: A Survey’, CORE Discussion Papers 2003/31
Beirne, J., G. Maria C., and N. Spagnolo (2008), ‘Interest and Exchange Rate Risk and Stock Returns: A Multivariate GARCHM Modelling Approach’, Centre for Empirical Finance, Brunel University, London
Berument, H. (1999), ‘The Impact of Inflation Uncertainty on Interest Rates in UK’, Scottish Journal of Political Economy, Vol.46, No.2
Bhar, R., C. Chiarella and T.M. Pham (2007) ‘Modeling the Currency Forward Risk Premium: Theory and Evidence’.
Bhoi, B.K. and S. Dhal (1999), ‘ Integration of Financial Markets in India: An Empirical Analysis’, Reserve Bank Of India Occasional Papers, Vol.19, and No.4,1998
Bidarkota, P.V. (2004), ‘Risk Premia in Forward Foreign Exchange Markets: A Comparison of Signal Extraction and Regression’, Department Of Economics, Florida International University
Black, F. (1972), ‘Capital Market Equilibrium with Restricted Borrowing’, Journal of Business. 45.
Black, Fischer (1976), ‘Studies Of Stock Market Volatility Changes’, Proceedings of The 1976 Meetings Of The American Statistical Association, Business And Economic Statistics Section, 177181.
Black, F. and M. Scholer (1973), ‘The Pricing of options and Corporate Liabilities', Journal of Political Economy, Vol. 81, No. 3.
Bollerslev, Tim (1986), ‘Generalized Autoregressive Conditional Heteroskedasticity’, Journal of Econometrics, 31, 307327.
Bollerlsev, T, Chou, Ray Y. and Kroner, K. F. (1992), ‘ARCH Modeling in Finance: A Review of Theory and Empirical Evidence’, Journal of Econometrics, 52, 559.
Bollerslev, T, Engle, R. F., and Nelson, D.B.,(1994), ‘ARCH Models’, in The Handbook of Econometrics, Vol IV, Ed. R. F. Engle And D. Mcfadden, Amsterdam: North Holland, 29593038.
Bollerslev, T. and Melvin, M. (1994), ‘BidAsk Spreads and the Volatility in the Foreign Exchange Market: An Empirical Analysis’, Journal of International Economics, 36, 355372.
Bollerslev, T. and Wooldridge, J. M. (1992), ‘QuasiMaximum Likelihood Estimation and Inference in Dynamic Models with TimeVarying Covariance’, Econometric Reviews, 11(2), 143172.
Brailsford, T.J. and K. Maheswaran (1998), ‘The Dynamics of the Australian ShortTerm Interest Rate’, Australian Journal Of Management, Vol. 23, No. 2, December 1998,
Brenner, R. J., Harjes, R. H., and Kroner, K.F. (1996), ‘Another Look at Models of the ShortTerm Interest Rate’, Journal of Financial and Quantitative Analysis, 31(1), 85107.
Brennan, M. J. and E. S. Schwatz (1980), 'Analysing Convertible Bonds', Journal of Financial and Quantitative Analysis', Vol. 15.
Chan, K.C., Karolyi, G. A., Longstaff, F. A., and Sanders, A. B. (1992), ‘An Empirical Comparison of Alternative Models of the ShortTerm Interest Rate’, Journal Of Finance, 47(3), 12091227.
Chou, Ray Y., (1988), ‘Volatility Persistence and Stock Valuations: Some Empirical Evidence Using GARCH, Journal of Applied Econometrics, 3, 279294.
Christiansen, C. (2005), ‘Multivariate Term Structure Models with Level and Heteroskedasticity Effects’. Journal of Banking and Finance 29 (5), 1037– 1055.
Christiansen, C (2008), ‘LevelARCH Short Rate Models with Regime Switching: Bivariate Modeling of US and European Short Rates’, International Review of Financial Analysis 17 (2008) 925–948
Cox, J. C., J. E. Ingersoll and S. a. Ross (1985), 'A Theory of the Term Structure of Interest Rates', Econometrica, Vol. 53.
Christie, A, (1982), ‘The Stochastic Behavior Of Common Stock Variances: Value, Leverage And Interest Rate Effects’, Journal of Financial Economics, 10, 407432.
Della Corte, P., Lucio Sarno, and Ilias Tsiakas (2007), ‘An Economic Evaluation of Empirical Exchange Rate Models: Robust Evidence Of Predictability and Volatility Timing’.
Das, S. R. (2002), 'The Surprise element : Jumps in Interest Rates', Journal of Econometrics, Vol. 106.
Drost, F. C. and Nijman, T. E., (1993), ‘Temporal Aggregation of GARCH Processes’, Econometrica, 61(4), 909927.
Durand, R.B and Douglas Scott(2003) ‘Ishares Australia: A Clinical Study In International Behavioral Finance, International Review Of Financial Analysis 143 (2003) 1–17
Duan, J.C. and K. Jacobs (2001) ‘Short And Long Memory In Equilibrium Interest Rate Dynamics, Scientific Series, Cirano
JinChuan Duan, Kris Jacobs(2007) ‘Is Long Memory Necessary? An Empirical Investigation Of Nonnegative Interest Rate Processes, Journal Of Empirical Finance
Edwards, S. (1998), ‘Interest Rate Volatility, Capital Controls, and Contagion, Nber Working Papers W6756.
Edwards, Sebastian and Raul Susmel (2003), ‘InterestRate Volatility in Emerging Markets’, The Review of Economics and Statistics, May 2003, 85(2): 328–348
Engle, R. F. (2001), ‘GARCH 101: the Use of ARCH/GARCH Models in Applied Econometrics’, Journal of Economic Perspectives, 15 (4), 157–168
Engle, R. F. and Andrew J. Patton (2001),’What Good is A Volatility Model?
Engle, Robert F., (1982), ‘Autoregressive Conditional Heteroskedasticity with Estimates of the Variance of United Kingdom Inflation’, Econometrica, 50(4), 9871007.
Engle, R. F., Ito, T., and Lin WenLing, (1990), ‘Meteor Showers or Heat Waves? Heteroskedastic IntraDaily Volatility in the Foreign Exchange Market’, Econometrica, 58(3), 525542.
Engle, R. F., D. M. Lilien and R. P. Rabbins (1987), 'Estimating Time Varying Risk Premium in the Term Structure : the ARCHM Model', Econometrica, Vol. 55.
Engle, R.F., L. David, and R, Russell, (1987), ‘Estimation of Time Varying Risk Premia on the Term Structure: The ARCHM Model’, Econometrica, 55, 391407.
Engle, R.F., and M. Simone, (1999), ‘CAVIAR: Conditional Autoregressive Value At Risk by Regression Quantiles’, University Of California, San Diego, Department Of Economics Working Paper 9920.
Engle, Robert F., and M. Joseph, (1996), ‘GARCH for Groups’, Risk, 9(8), 3640.
Engle, Robert F., and Ng, Victor, (1993), ‘Measuring and Testing the Impact of News on Volatility’, Journal Of Finance, 48, 17491778.
Engle, Robert F., Ng, V. K. and Rothschild, M. (1990), ‘Asset Pricing with a FactorARCH Covariance Structure’, Journal Of Econometrics, 45(2), 235237.
Fama, Eugene F., (1965), ‘The Behavior of StockMarket Prices, Journal of Business, 38(1), 34105.
Ferreira, M.A. and J.A. Lopez, (2004), ‘Evaluating Interest Rate Covariance Models within ValueatRisk Framework’, FRBSF Working Paper, 200403.
Flad, M. (2006), ‘Do Macrofactors help Forecasting Stock Market Volatility?’.
French, K.R, G. W. Schwert and R.F. Stambaugh (1986), ‘Expected Stock Returns and Volatility’, William E. Simon Graduate School of Business Administration, Univershy of Rochester Working Paper No.Mere8510
Galac, T, Lana Ivièiæ and Mirna Dumièiæ (2007) ‘A Simple Model of Interest Rates in the Croatian Money Market’, Paper Presented in the 13th Dubrovnik Economic Conference .
Galagedera, D. ‘A Review of Capital Asset Pricing Models’, Department of Econometrics and Business Statistics, Monash University
Glosten, Lawrence R., Jagannathan, Ravi and Runkle, David E. (1993), ‘On the Relation Between the Expected Value And the Volatility of the Nominal Excess Returns on Stocks’, Journal of Finance, 48(5), 17791801.
Gray, S. F. (1996), ‘Modeling the Conditional Distribution of Interest Rates as a RegimeSwitching Process’, Journal of Financial Economics, 42(1), 2762.
Hamilton, J.D., and Susmel, Raul, (1994), ‘Autoregressive Conditional Heteroskedasticity and Changes in Regime’, Journal Of Econometrics, 64(1), 307333.
Hansen, B.E.(1994), ‘Autoregressive Conditional Density Estimation’, International Economic Review, 35.
Hansen, P.R and A. Lunde, ‘A Comparison of Volatility Models: Does anything Beat a GARCH(1,1)?, Working Paper Series No. 84, Center for Analytical Finance, University Of Aarhus
Harvey, Campbell R., and Siddique, Akhtar (1999), ‘Autoregressive Conditional Skewness’, Journal of Financial and Quantitative Analysis, 34(4), 465487.
Johannes, M. (2004), 'The Statistical and Economic Role of Jumps in Continuous Time interest Rate Models', Journal of Finance, Vol. 59.
Kalimipalli, M and Raul Susmel (2003) ‘RegimeSwitching Stochastic Volatility And ShortTerm Interest Rates Paper Presented at University of Houston, McGill University and the NFA 2000 Meetings in Waterloo.
Kiani, K.M (2006) ‘Predictability in Stock Returns in an Emerging Market: Evidence from KSE 100 Stock Price Index’, The Pakistan Development Review 45 : 3 (Autumn 2006) Pp. 369–381
Kim, S.J and Jeffrey Sheen (1998), ‘International Linkages and Macroeconomic News Effects on Interest Rate Volatility – Australia and the US’, Pacific Basin Finance Journal.
Koedijk, K.C., Nissen, F., Schotman, P.C., and Wolf., C.C., (1997), ‘The Dynamics of ShortTerm Interest Rate Volatility Revisited’, European Finance Review 1, 105–130.
Lamoureux, C.L. And W.D. Lastrapes (1990), ‘Persistence in Variance, Structural Change and GARCH Model’, Journal Of Business And Economic Statistics, Vol.8, No.2
Li, XiaoMing, and LiPing Zou (2008), ‘How do Policy and Information Shocks Impact CoMovements of China’s TBond and Stock Markets? , Journal of Banking and Finance 32 (2008) 347–359
Lintner, J. (1965), 'The Valuation of Risk Assets and the Selection of Risky Investments in Stock portfolios and Capital Budgets' The Review of Economics and Statistics, Vol. 47, No. 1.
Longstaff, F.A., and Schwartz, E., (1992), ‘InterestRate Volatility and the Term Structure: A Two Factor General Equilibrium Model’, Journal of Finance 47 (4), 1259–1282.
Mandelbrot, Benoit, (1963), ‘The Variation of Certain Speculative Prices’, Journal of Business, 36(4), 394419.
Markowitz, Harry M. (1952) ‘Portfolio Selection’, Journal of Finance 7 (1)
Mccurdy, T.H. And I.G. Morgan (1991), ‘Tests for a Systematic Risk Component in Deviations From Uncovered Interest Rate Parity’, Review of Economic Studies, Vol.58.
Mossiru, J. (1966), 'Equilibrium in a Capital Asset Market', Econometrica, Vol. 34, No. 4.
Murta, Fátima S. (2007) ‘The Money Market Daily Session: An UHFGARCH Model Applied to the Portuguese Case Before and after EMU’.
Nama, K., Chong Soo Pyun B, and Augustine C. Arize (2002) ‘Asymmetric MeanReversion and Contrarian Profits: AnstGarch Approach, Journal of Empirical Finance 9, 563– 588
Nelson, Daniel B., (1991), ‘Conditional Heteroscedasticity in Asset Returns: A New Approach’, Econometrica, 59(2), 347370.
Nelson, Daniel B., and Foster, Dean P., (1994), ‘Asymptotic Filtering Theory for Univariate ARCH Models’, Econometrica, 62(1), 141.
Nowman. K.B, and B.H. Yahia (2008) ‘Euro and FIBOR Interest Rates: A Continuous Time Modelling Analysis’ International Review of Financial Analysis 17 (2008) 1029–1035
Piazessi, M. (2005), 'Bond yields and Federal Reserve', Journal of Political Economy, Vol. 113.
Podobnik, B, Plamen, C.I., I. Grosse, K. Matia, And H.Eugene Stanley (2004) ‘ARCHGARCH’ Approach to Modeling High Frequency Financial Data’, Physica A, 344.
Ozun, A (2007) ‘International Transmission of Volatility in the Us Interest Rates into the Stock Returns: Some Comparative Evidence from World Equity Markets’, International Research Journal of Finance And Economics, 10 (2007)
Raj, Janak and Sarat Dhal (2008), ‘ Financial Integration of India’s Stock Market with Global and Major Regional Markets’, BIS Papers 42, Bank for International Settlements, Basel.
Raunig, B and Johann Scharler (2006) Money Market Uncertainty and Retail Interest Rate Fluctuations: A CrossCountry Comparison, Http:// Ssrn.Com/Abstract=964609
Report on Currency and Finance (RCF) 200506, Reserve Bank of India
Richardson, M. P. and Stock, J. H., (1989), ‘Drawing Inferences from Statistics Based on MultiYear Asset Returns’, Journal of Financial Economics, 25, 323348.
Schwert, G. William, 1989, ‘Why Does Stock Market Volatility Change over Time?’, Journal Of Finance, 44, 11151153.
Sharpe, W.F. (1964) “Capital Asset Prices: A Theory of Market Equilibrium under Consideration of Risk.” Journal of Finance, Vol. Xix.
Shahiduzzaman M. and Mahmud Salahuddin Naser (2007) ‘Volatility in the Overnight MoneyMarket Rate in Bangladesh: Recent Experiences’, Pn0707
Siklos, P., and L.F. Skoczylas (2002) ‘Volatility Clustering in Real Interest Rates: International Evidence’ Journal of Macroeconomics 24 (2002) 193–209
Singh, B. and S. Dhal (1999), ‘Repo Auction Formats, Bidders Behaviour and Money Market Response in India’, Reserve Bank of India Occasional Papers, Vol.19, No.3, 1998.
Smith, D (2002), ‘MarkovSwitching and Stochastic Volatility Diffusion Models of ShortTerm Interest Rates’, Journal of Economics and Business, Vol.20, No.2.
Suardi, Sandy (2008) ‘Are Levels Effects Important in OutofSample Performance of Short Rate Models?’ Economics Letters 99 (2008) 181–184
Treynor, J. L. (1962), 'Toward a Theory of Market Value of Risky Assets', reprinted in 'Risky Booxs', (Ects) R. A. Korajezyk, London.
Trichet, JeanClaude (2009), ‘Underpricing of risks in the financial sector’, Speech by President of the ECB delivered at the Coface Country Risk Conference 2009, Carrousel du Louvre, Paris, 19 January 2009
United States Congressional Budget Office (2000) ‘A Framework For Projecting Interest Rate Spreads and Volatilities’. Washington.
Zakoian, J. M. (1994), ‘Threshold Heteroskedastic Models’, Journal of Economic Dynamics and Control, 18, 931955.
Vasicek, O. (1977), 'An Equilibrium characterisation of the Term Structure', Journal of Financial Economics, Vol. 5.
* B.M. Misra is Adviser and Sarat Dhal is Assistant Adviser, Department of Economic Analysis and Policy, Reserve Bank of India, Central Office at Mumbai. The views expressed in the paper are of the authors only.
^{ 1} Statement made by Dr. Rakesh Mohan, Deputy Governor of the Reserve Bank of India and Leader of the Indian Delegation to the International Monetary and Financial Committee, Washington DC on April 14, 2007.
^{4} If P is the stock price index, the annualised return from daily data is derived as R=(P_{t}/P_{t252}1)*100 as there are about 252 business days in a year. On the basis of natural logarithm transformed stock price index (p), the annualised return is derived as R = (p_{t}p_{t252})*100 . It may be noted here that our analysis is not based on total equity return and therefore, we do not take into account the dividend yield.
^{5} The repo rate used in the study is the middle of repo and reverse repo rate. 