Calculation of optimum VaR based on different stochastic volatility models

Abstract

The VaR is a statistical technique widely used by banks worldwide to quantify their exposures to various market variables. Regulators require senior management of financial institutions to report on VaR values for different time horizons. There are 3 methods to calculate the VaR value – historical simulation, the parametric approach and Monte Carlo Simulation. Each method has its advantages and disadvantages. Comparison of VaR values for each of these 3 methods can help us understand which of the three methodologies are conservative or optimistic with respect to the others. For Historical Simulation, actual market data are required to compute the VaR measure. Monte Carlo simulation relies on the generation of scenarios which give us a clear picture of the maximum loss in different market situations. Parametric approach requires us to input the volatility value for a time horizon and gives us the VaR value for this value of input. The volatility value that we provide can be stochastic or historical. If stochastic volatilities are used, stochastic volatility models can provide this volatility value. Examples are SABR model, Heston Model. Calculations are based on CNX Nifty futures and different VaR values are compared to see which is the most conservative. For backtesting, we use the actual volatility value from the market and compare it to the VaR value we get when we use the volatility value from a stochastic volatility model.