An efficient exponential twisting importance sampling technique for pricing financial derivatives

This paper develops an efficient Exponential Twisting Importance Sampling technique for variance reduction when it is used to price financial derivatives. A general class of exponential change of measure is well explored. This is the generalization of the proportional exponential twisting function, φϑ(x)=ϑx, discussed as an Example 4.6.2 in Glasserman’s book (2004). Then a new framework to find the optimal importance sampling density function is proposed based on the Cauchy-Schwartz Inequality and the Least Square Approach. In the special Gaussian case, the theory of our general exponential change of measure means finding the new drift vector and covariance matrix simultaneously. The method proposed by the paper has little smoothness requirements for the payoff functions and doesn’t rely on the initial values. It is illustrated that this method is high efficient for pricing financial derivatives, such as Asian options, Straddle options, Volatility derivatives and the pricing under the stochastic volatility models. Furthermore, this method can be extended to more general importance sampling densities such as non-Gaussian or multi-modal distributions.