Estimation of Value at Risk for the Indian capital market: Filtered Historical Simulation approach using GARCH model with suitable mean specification

The paper estimate 1-day Value at Risk (VaR) taking into consideration the financial integration of Indian capital market (BSE-SENSEX and NSE-NIFTY) with other global indicators and its own volatility using daily returns covering the period January 2003 to December 2009. The paper specifies a generalized autoregressive conditional heteroscedasticity (GARCH) framework to model the phenomena of volatility clustering on returns and examines the usefulness of considering lag values of return on (S&P 500, INR-EURO & INR-USD exchange rate, Gold price) as proxies to global financial condition in the specification of the mean equation. In general VaR is calculated either based on Historical Simulation (HS) approach which imposes practically no structure on the distribution of returns except stationarity or using Monte Carlo simulation (MCS) approach which assumes parametric models for variance and subsequently large number of random numbers is drawn from this specific distribution to calculate the desired risk measure. Filtered Historical Simulation (FHS) approach attempts to combine the best of the model-based approach with the best of the model-free approaches in a very intuitive fashion. The paper estimates VaR of return in the Indian capital market based on two composite methods i.e. (a) using univariate GARCH model where in the mean equation we have used lag values of return on S&P 500, INR-EURO & INR-USD exchange rate and Gold price; and following FHS approach; (b) using ARMA for mean equation, GARCH for volatility and FHS for VaR estimation i.e. ARMA-GARCH-FHS. The performances of the VaR estimates from both the methods were compared and it was found that VaR of return in the Indian capital market estimated based on method (a) i.e. GARCH with suitable mean specification outperforms method (b) i.e. the ARMA-GARCH method.