Alternative Randomization for Valuing American Options

This paper provides a fast and accurate randomization algorithm for valuing American puts and calls on dividend-paying stocks and their early exercise boundaries. The primal focus is on the American put, because the associated call can be analyzed through the use of put-call symmetry relations. The algorithm is strongly inspired by the randomization of Carr (1998) where he considered the American put with a random maturity distributed as the Erlangian distribution. In our randomization, however, we instead use an alternative random maturity distributed as an order static from a population of iid exponential random variables. This idea enables us to derive a much simpler recursion scheme starting from the Canadian case with the exponentially random maturity. Numerical experiments indicate that our randomization algorithm together with Richardson extrapolation works well to generate accurate approximations for the early exercise boundary as well as the option value.

• Type: Journal
• Year: 2010
• Where: APJOR
• Authors: Toshikazu Kimura
• Keywords: APJOR 2007, APJOR 2010, Early Exercise, Random Maturity, Randomization