Pricing American contingent claims by stochastic linear programming

Abstract

We consider pricing of American contingent claims (ACC) as well as their special cases, in a multi-period, discrete time, discrete state space setting. Until now, determining the buyer's price for ACCs required solving an integer programme unlike European contingent claims for which solving a linear programme is sufficient. However, we show that a relaxation of the integer programming problem that is a linear programme, can be used to get the same lower bound for the price of the ACC.

Keywords:

• American contingent claim
• pricing
• hedging
• martingales
• stochastic linear programming

AMS Subject Classifications::

• 90C11
• 90C90
• 91B28

Acknowledgement

This research is partially supported by TUBITAK Grant 107K250 and a scholarship from the Fulbright Commission.