Test of Log-Normal Process with Importance Sampling for Options Pricing

Log-normal process and martingale restriction bring some bias on the premium for option pricing models. It is possible to reduce the bias by adding more parameters like jump diffusion, stochastic volatility or regime switching. In this case closed form solutions and numerical approximations suffer from the dimension of the problem. Monte Carlo integration then appears to be unique solution for high dimensional calculations. However variance of the output of interest should be decreased in Monte Carlo applications in order to have confident results. The method of Importance Sampling can be used in an attempt to reduce variance. In this study we test the log-normal process for options pricing via Importance Sampling Monte Carlo. Our analysis is based on the theory of variance reduction and we don’t have any empirical data. Numerical results indicate that the risk neutral density should be substituted in the range of moneyness.