Numerical Solution of Pricing of European Put Option with Stochastic Volatility

In this paper, European option pricing with stochastic volatility forecasted by well known GARCH model is discussed in context of Indian financial market. The data of Reliance Ltd. stockprice from ۳/۰۱/۲۰۰۰ to ۳۰/۰۳/۲۰۰۹ is used and resulting partial differential equation is solved byCrank-Nicolson finite difference method for various interest rates and maturity in time. Thesensitivity measures “Greeks” are also determined to validate the model. It is observed that the valueof European put option increases with maturity time and decreases with interest rate.

Keywords:

European Option , Finite difference method , Stochastic Volatility , GARCH (۱ , ۱) , Greeks