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.
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.