Simulation of Tempered Stable Lévy Bridges and Its Applications
针对温和稳定莱维子序，提出一种桥采样方法，利用双鞍点近似推导条件概率密度，并基于伽马桥和逆高斯桥设计接受-拒绝算法，在有限方差CGMY过程的期权定价中结合自适应采样和分层采样实现方差缩减。
We consider tempered stable Lévy subordinators and develop a bridge sampling method. An approximate conditional probability density function (PDF) given the terminal values is derived with stable index less than one, using the double saddlepoint approximation. We then propose an acceptance-rejection algorithm based on the existing gamma bridge and the inverse Gaussian bridge as proposal densities. Its performance is comparable to existing sequential sampling methods such as Devroye (2009) [Devroye L (2009) Random variate generation for exponentially and ploynomially tilted stable distributions. ACM Trans. Modeling Comput. Simulation 19(4):18:1–20.] and Hofert (2011) [Hofert M (2011) Sampling exponentially tilted stable distributions. ACM Trans. Modeling Comput. Simulation 22(1):3:1–11.] when generating a fixed number of observations. As applications, we consider option pricing problems in Lévy models. First, we demonstrate the effectiveness of bridge sampling when combined with adaptive sampling under finite-variance CGMY processes. Second, further efficiency gain is achieved in terms of variance reduction via stratified sampling.