American Option Valuation and Computation

The pricing of American options has been one of the most popular research areas in quantitative finance. Finding solutions to the Ameri-can option valuation problem is a difficult task compared to its European counterpart because of the added feature of early exercise. The American option valuation is commonly known as a free boundary value problem. This book features the methodology of option pricing from the derivation of the standard European option formula and then explores the American option pricing techniques introduced by researchers and academics. The methods range from semi-analytical, approximation and numerical approaches all seeking to improve accuracy and efficiency. A new type of numerical method is also introduced to price American options in this book. The critical exercise boundary which is a priori required to be solved for some of the valuation methods is efficiently approximated using cubic splines. The application of cubic splines reduces computational time without sacrificing accuracy. The results of this new method is compared against other pricing methods.