A Comparative Study of American Option Valuation and Computation

For many practitioners and market participants, the valuation of financialderivatives is considered of very high importance as its uses range from arisk management tool, to a speculative investment strategy or capital enhancement. A developing market requires efficient but accurate methods forvaluing financial derivatives such as American options.A closed form analytical solution for American options has been very difficultto obtain due to the different boundary conditions imposed on the valuationproblem. Following the method of solving the American option as a freeboundary problem in the spirit of the "no-arbitrage" pricing framework ofBlack-Scholes, the option price and hedging parameters can be representedas an integral equation consisting of the European option value and an earlyexercise value dependent upon the optimal free boundary.Such methods exist in the literature and along with risk-neutral pricing methods have been implemented in practice. Yet existing methods are accuratebut inefficient, or accuracy has been compensated for computational speed.A new numerical approach to the valuation of American options by cubicsplines is proposed which is proven to be accurate and efficient when compared to existing option pricing methods. Further comparison is made tothe behaviour of the American option's early exercise boundary with otherpricing models.