Option Pricing and Binomial Model

Abstract

The binomial option pricing is developed from first principles. The underlying security is assumed to evolve in discrete steps of time. An option is shown, using the principle of no arbitrage, to be equivalent to a dynamic portfolio composed of the underlying security and risk-free cash. The option price is shown to be equivalent to a random evolution of the option price provided the underlying security has a martingale evolution. In a simple and transparent discrete-time model, the under-pinning of option theory is seen to be based on the binomial probability distribution. The binomial option pricing model, which is based on the binomial random variable, shows the utility of probability theory in option pricing.