PRICING AMERICAN OPTIONS UNDER STOCHASTIC VOLATILITY

In this Master thesis a study of the valuation of American options under stochastic volatility is performed. While in literature the problem of pricing an American option written on an underlying asset with constant volatility has been extensively studied, the relative case for stochastic volatility models is not equally treated. Real world data demonstrate that the simplification of a constant volatility lead to a lack of trustworthiness. It is tested, in fact, that volatility is not constant, and stochastic volatility models are capable to capture dynamic volatility changes. Most of the option pricing methods that have been developed in literature for pricing under stochastic volatility focused their attention on Vanilla options and closed form solutions. Only in recent years with the implementation of the Linear Complementarity Problem ap- proach, more and more studies have been published considering the American case. Here the problem is tackled according to two different approaches, the ADI-IT methods, with a particular focus on the Modified Craig-Sneyd scheme, and the more common Explicit method. Firstly, general pricing approaches, considering stochastic volatility, are presented. Then, using the above quoted computational tools, an in-depth analysis of the American option problem is performed presenting, in addition, numerical results.