A second-order Nyström-type discretization for the early-exercise curve of American put options

Abstract

It is well known that the value of an American option can be expressed as the sum of the corresponding European option and a premium, which reflects the additional right of early exercise. Based on this expression, it is possible to derive an integral equation for the early-exercise curve. Because the early-exercise curve is not sufficiently smooth at expiry, an ad hoc Nyström discretization of high order for solving the integral equation is not guaranteed. In this paper, we present a Nyström-type discretization, which uses an adequate integral transformation to circumvent the non-sufficient smoothness at expiry and results in a method of second order.

Keywords:

• American options
• early-exercise curve
• integral equation
• trapezoidal rule
• second-order Nyström method

2000 AMS Subject Classifications :

• 65B99
• 65R20