Forward or backward simulation? A comparative study

Abstract

The aim of this study is to present algorithms for the backward simulation of standard processes that are commonly used in financial applications. We extend the works of Ribeiro and Webber and Avramidis and L'Ecuyer on gamma bridge and obtain the backward construction of a gamma process. In addition, we are able to write a novel acceptance–rejection algorithm to simulate the Inverse Gaussian (IG) bridge and consequently, the IG process backward in time. Therefore, using the time-change approach, we can easily derive the backward generation of the compound Poisson with infinitely divisible jumps, the Variance-Gamma  the Normal-Inverse-Gaussian processes and subsequently the time-changed version of the Ornstein–Uhlenbeck process introduced by Li and Linesky. We then compare the performance of the forward and backward construction of all these processes and show that the latter one is the preferable solution in the context of pricing American options or energy facilities like gas storages.

Keywords:

• Backward Monte Carlo simulations
• Lévy processes
• Time-changed Ornstein–Uhlenbeck processes
• Energy derivatives

Acknowledgments

I would like to express my gratitude to one of two anonymous referees for her/his helpful and constructive comments, which led to a substantially improved version of this paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 Different equivalent expressions and parameterizations of the IG law are available in the literature, it is then critical to know which one the software in use is relying upon. For instance if one uses MATLAB routines she needs to set $\lambda =c^2$ and $\mu =c/\gamma$.