Comparison and survey of finite difference methods for pricing American options under finite activity jump-diffusion models

Abstract

Partial integro-differential formulations are often used for pricing American options under jump-diffusion models. A survey on such formulations and their numerical methods is presented. A detailed description of six efficient methods based on a linear complementarity formulation and finite difference discretizations is given. Numerical experiments compare the performance of these methods for pricing American put options under finite activity jump models.

Keywords:

• jump-diffusion model
• American option
• linear complementarity problem
• finite difference method
• iterative method

2010 AMS Subject Classifications::

• 35K85
• 65M06
• 65Y20
• 91G20
• 91G60