Multi-factor VaR models under Black-Scholes pricing for Indian equity index (S & P CNX Nifty) options

Abstract

The aim of the paper is to evaluate different models for calculating the value at Risk for a position in an option. Various correction factors need to be applied to the basic VaR model which bases itself on the linearity of payoffs and assumption of normality of the returns distribution. The change in the position of the option is not linearly dependent on the changes in the stock prices, and hence the normal VaR models must be modified. The performance of three models is studied taking data on the NIFTY index option which is Delta-Normal Model, Monte Carlo Simulation using only the stock price as a risk factor and Monte Carlo Simulation using both stock price and volatility as risk factors were the two risk factors are assumed to be uncorrelated. The pricing model used to price the option is the Black-Scholes option pricing formula. It is observed that the Delta-Normal Method gives the most accurate using proportion of failures test. The two-factor model performs best in the case of At the money and Out of the money options. The single factor model performs the worst in all situations. All the models fail in the case of in the money options.