Pricing American Strangle Options

This thesis focuses on the valuation of American strangle options with one or more underlying assets under constant or stochastic volatility. European strangle options can be regarded as the combination of a European call option with a European put option. But American Strangle options, due to the early exercise feature, essentially differ from the strangle combination. The valuation of American strangles has been a challenging problem and is far from fully understood. As American options can be exercised at any time before maturity, the valuation does not have explicit formulas. Hence it is necessary to develop numerical methods to solve the problems. This thesis develops tree-based methods and least squares Monte Carlo methods (LSM) to calculate the constant and stochastic volatility pricing models for American Strangle options with one-dimensional and multi-dimensional underlying assets and to identify the optimal exercise boundaries.Firstly, this thesis provides the background and significance of target problems. Due to the early exercise feature, American options become the most active types of products in the market of financial derivatives. There are a large number of trading types among the American options, such as Asian options, looking-back options, butterfly options, and so on. Since American strangle options have not been started trading yet, relevant research is not much. But the American strangle options performed well in emerging financial market, and therefore it is expected to be as popular as European strangle options in the financial market in the near future. Overall the study of American strangle option pricing problems is important in both real and academic worlds.Secondly, the core part of the thesis is divided into three sections:The first section is about the constant volatility pricing model for American strangle options; The second section focuses on American strangle options with stochastic volatility; The third section studies American strangle options with multidimensional underlying assets.Conclusion and discussions on the future work are given in the final section.