In this thesis, we study saddlepoint approximation in statistics, which is used for approximating the density function and the distribution function of random variables, and the relative error of the approximation expansion is of uniformly O(n −1 ) over the whole interval of definition, even in the tail domains. We give a detailed version of derivation of this method. Due to its great properties, saddlepoint approximation has a vast amount of applications not only in statistics, but also in finance, we review these applications in finance up untill now. As another application, we present a new method to exact simulation of stochastic volatility model by using saddlepoint approximation. This thesis ends up with a discussion about the advantages and disadvantages of saddlepoint approximation as the conclusion part.