Critically discuss the suitability of using the Black & Scholes model for pricing derivatives

Institution Title Name Date The Black Scholes model Introduction The Black scholes model is a mathematical model developed to describe the financial market and derivative investments; it shows the price variations over time of the financial instruments such as stock that can be used to determine the price of European call option. Option are financial instrument giving the holder the right to buy or sell an underlying stock or commodity at a future point in time at an agreed upon price .The model is a tool of pricing the equity option thus; it is an approach of calculating the value of stock option be it call option or put up option. The main idea that lies behind this model is that the price of an option is determined implicitly by the price of underlying stock. This model is one of the most important concepts of financial theory; it was developed by Fisher Black and Myron Scholes in 1973 and it is used widely today since it is known to be the best in determining the fair prices of option as we are going to see. (/). The Black Scholes model was not developed overnight, but it took a considerable length of time for the two professors to come up with it. Fisher Black started working on it when calculating the price of the stock warrants and it involved computing mathematical derivatives to ascertain how the rate of the discount of a warrant varies with stock price with time. The results of his work held an alarming resemblance with a known heat transfer equation, later Myron Scholes joined him and they came up with this accurate option pricing model (/b-s_model.htm). The model is divided into two sections, the first part shows the expected benefits one gets when he acquires a stock outright, this is fond by multiplying the stock price by the change in premium call with respect to the underlying stock price. The second part shows the present value of paying the exercise price on the expiration date The good thing with Back Scholes model is that it fits better to the dynamics of historic prices and pricing formulas for European options and it performs better than the earlier models, more over, until recently, there are no analytical formulas presented to tackle the European pricing option which can out do this one of Black and scholes, thus it has become the standard measure of pricing option. (). For some one to value an investment he has to evaluate its probability distribution, and to evaluate probability distribution, hedge funds and other market participants use geometric Brownian motion models, binomial models and stochastic calculus. Black scholes pricing theory has provided a new way of valuing stock option and more importantly it started a revolution in how hedge funds and other market participants think about and value financial assets. In application of Black Scholes model, there are several assumptions that should be observed for one to achieve accurate results. These assumptions are; the stock pays no dividends during the option’s life, this is an alarming disadvantage to the model since most companies pay dividends to their share holders. The second assumption is that European terms are used ,European exercise terms demands that that option be exercised only at...