Numerical solution of an integral equation for perpetual Bermudan options

Abstract

We consider perpetual Bermudan options, which have no expiration and can be exercised every T time units. We use the Green's function approach to write down an integral equation for the value of a perpetual Bermudan call option on an expiration date; this integral equation leads to a Wiener–Hopf problem. We discretize the integral in the integral equation to convert the problem to a linear algebra problem, which is straightforward to solve, and this enables us to find the location of the free boundary and the value of the perpetual Bermudan call. We compare our results to earlier studies which used other numerical methods.

Keywords:

• Bermudan options
• integral equations
• Green's functions
• Wiener–Hopf problems

2010 AMS Subject Classifications:

• 91G20
• 65R20