Mathematical modelling and analysis of Asian options with stochastic strike price

Abstract

The goal of this article is to introduce strike Asian options on stochastic average and to price them using a variable reduction technique. The problem of solving the associated Black–Scholes equation is reduced to finding the heat kernel of the operator . This is done by two approaches: using a geometrical method and then applying the van Vleck formula; using a moments method to get a double infinite series formula involving Hermite polynomials.

Keywords:

• Asian option
• stochastic integral
• Black–Scholes equation
• Brownian motion
• option pricing

AMS Subject Classifications::

• 62P05
• 91G80

Acknowledgements

Ovidiu Calin was partially supported by the NSF Grant #0631541 and by a sabbatical leave from the Eastern Michigan University during the academic year 2009–2010. Der-Chen Chang was partially supported by Hong Kong RGC competitive earmarked research grants #600607, #601410 and a competitive research grant at Georgetown University.