Abstract
Importance sampling the approach of variance reduction is one of the most important methods to estimate the probability of rare events. By properly changing of measure, this method can reduce the variance of new estimator. However, there are several ways of choosing the appropriate probability measure to implement importance sampling. The “Minimal Entropy Measure” is chosen as suitable probability measure, which is entropy-based importance sampling. This article takes the Lévy Processes as examples, such as jump diffusion process, variance gamma process and normal inverse Gaussian process. Moreover, our method works on stochastic volatility jump model. We compare the numerical results with basic Monte Carlo and other distance function to demonstrate that this method is effective. Finally, we estimate the parameters by method of moment on examples of Lévy Process, and briefly describe estimation of parameters of stochastic volatility jump model by Markov chain Monte Carlo method.