Performance Measure of Binomial Model for Pricing American and European Options

Abstract

Binomial model is a powerful technique that can be used to solve many complex option-pricing problems. In contrast to the Black-Scholes model and other option pricing models that require solutions to stochastic differential equations, the binomial option pricing model is mathematically simple. It is based on the assumption of no arbitrage. The assumption of no arbitrage implies that all risk-free investments earn the risk-free rate of return and no investment opportunities exists that requires zero amount of investment but yield positive returns. It is the activity of many individuals operating within the context of financial market that, in fact, upholds these conditions. The activities of the arbitrageurs or speculators are often maligned in the media, but their activities insure that financial markets work. They insure that financial assets such as options are priced within a narrow tolerance of their theoretical values. In this paper we use binomial model to derive the Black-Scholes equation using the risk-neutral expectation formula. We also use binomial model for the valuation of European and American options. Lastly, the primary reason why the binomial model is used is its flexibility compared to the Black-Scholes model and it is also used to price a wide variety of options.