OPTION PRICING

The derivation and solution of the celebrated Black-Scholes OptionPricing Formula is set out in rather more detail than has appeared in the literature so far. One problem with the Black-Scholes analysis is that the mathematical skills required in the derivation and particularly in the solution of the model are fairly advanced and probably unfamiliar to most economists. In this project, we will derive the Black-Scholes pricing model of a European option by calculating the expected value of the option. We will assume that the stock price is log-normally distributed and that the universe is risk neutral. Then, using Ito’s Lemma, we will justif5’ the use of the risk-neutral rate in these initial calculations. Finally, we will prove put-call parity in order to price European put options, and apply the concepts of the Black-Scholes formula to value an option with pricing equity