Exact sampling with coupled Markov chains and applications to statistical mechanics
Proceedings of the seventh international conference on Random structures and algorithms
Exact simulation of option greeks under stochastic volatility and jump diffusion models
WSC '04 Proceedings of the 36th conference on Winter simulation
Simulation of Brownian motion at first-passage times
Mathematics and Computers in Simulation
Multilevel Monte Carlo Path Simulation
Operations Research
| Hi-index | 0.00 |
Generating sample paths of stochastic differential equations SDE using the Monte Carlo method finds wide applications in financial engineering. Discretization is a popular approximate approach to generating those paths: it is easy to implement but prone to simulation bias. This paper presents a new simulation scheme to exactly generate samples for SDEs. The key observation is that the law of a general SDE can be decomposed into a product of the law of standard Brownian motion and the law of a doubly stochastic Poisson process. An acceptance-rejection algorithm is devised based on the combination of this decomposition and a localization technique. The numerical results corroborates that the mean-square error of the proposed method is in the order of Ot-1/2, which is superior to the conventional discretization schemes. Furthermore, the proposed method also can generate exact samples for SDE with boundaries which the discretization schemes usually find difficulty in dealing with.