On the asymptotic free boundary for the American put option problem
2006 (English)In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 314, no 1, 345-362 p.Article in journal (Refereed) Published
In practical work with American put options, it is important to be able to know when to exercise the option, and when not to do so. In computer simulation based on the standard theory of geometric Brownian motion for simulating stock price movements, this problem is fairly easy to handle for options with a short lifespan, by analyzing binomial trees. It is considerably more challenging to make the decision for American put options with long lifespan. In order to provide a satisfactory analysis, we look at the corresponding free boundary problem, and show that the free boundary-which is the curve that separates the two decisions, to exercise or not to-has an asymptotic expansion, where the coefficient of the main term is expressed as an integral in terms of the free boundary. This raises the perspective that one could use numerical simulation to approximate the integral and thus get an effective way to make correct decisions for long life options.
Place, publisher, year, edition, pages
2006. Vol. 314, no 1, 345-362 p.
American put option, parabolic free boundary problem, obstacle problem, heat equation
IdentifiersURN: urn:nbn:se:kth:diva-15355DOI: 10.1016/j.jmaa.2005.03.082ISI: 000233882200024ScopusID: 2-s2.0-28844475579OAI: oai:DiVA.org:kth-15355DiVA: diva2:333396
QC 201005252010-08-052010-08-05Bibliographically approved