On Black-Scholes Equation

Abstract

In the last three decades increased attention has been paid to the valuation of the contingent claims whose value depend on underlying financial instruments, called securities. One of the most significant achievements in modern investment sciences is the Black-Scholes option pricing model. This model represents the value option should sell for, a fact that makes them attractive to individual and institutional investors. The model outcome is the famous equation that was introduced by F.Black and M. Scholes in 1973. Now, a large number of different contingent claims, referred to as derivatives, are trading on exchanges all over the world. Though the Black Scholes equation solution initially was used for the evaluation of the European option but soon this idea was generalized and applied to more complex and exotic types of derivatives instruments. Today there are other pricing models in use, and most of them are modest variations of original Black Scholes. The plan of this paper is following. First we will discuss the benchmark 'classic' models and then the other model of the option pricing will be introduced. Option price valuation depends on several parameters such as price of underlying security, interest rate, volatility, and time to expiration. An option contract is defined by specified payoff at maturity.