On an automatic and optimal importance sampling approach with applications in finance
提出一种基于方差最小化的指数倾斜重要性抽样方法，保证最优倾斜参数的存在性与唯一性，并通过自动牛顿法求解，同时给出简化公式以降低高维计算成本，适用于路径依赖衍生品和篮子违约互换的定价。
Calculating high-dimensional integrals efficiently is essential and challenging in many scientific disciplines, such as pricing financial derivatives. This paper proposes an exponentially tilted importance sampling based on the criterion of minimizing the variance of the importance sampling estimators, and its contribution is threefold: (1) A theoretical foundation to guarantee the existence, uniqueness, and characterization of the optimal tilting parameter is built. (2) The optimal tilting parameter can be searched via an automatic Newton’s method. (3) Simplified yet competitive tilting formulas are further proposed to reduce heavy computational cost and numerical instability in high-dimensional cases. Numerical examples in pricing path-dependent derivatives and basket default swaps are provided.