Modern pricing models - Essay Example

This work involved calculating a derivative to measure how the discount rate of a warrant varies with time and stock price. The result of this calculation held a striking resemblance to a well-known heat transfer equation. Soon after this discovery, Myron Scholes joined Black and the result of their work is a startlingly accurate option pricing model. The Black–Scholes model was first published in their 1973 paper, "The Pricing of Options and Corporate Liabilities", published in the Journal of Political Economy (Black & Scholes, 1973).

Robert Merton was the first to publish a paper expanding the mathematical understanding of the options pricing model, and coined the term "Black–Scholes options pricing model" (Merton, 1973). Merton and Scholes received the 1997 Nobel Prise in Economics for their work. Black was mentioned as a contributor by the Swedish Academy though ineligible for the prize because of his death in 1995. Black and Scholes cant take all credit for their work, in fact their model is actually an improved version of a previous model developed by A.

James Boness in his Ph.D. dissertation at the University of Chicago (). Black and Scholes improvements on the Boness model come in the form of a proof that the risk-free interest rate is the correct discount factor, and with the absence of assumptions regarding investors risk preferences. The Black–Scholes model assumes that the market consists of at least one risky asset, usually called the stock, and one riskless asset, usually called the money market, cash, or bond. The key idea is to hedge the option by buying and selling the underlying asset in just the right way and, as a consequence, to eliminate risk.

(random walk) The instantaneous log returns of the stock price is an infinitesimal random walk with drift; more precisely, it is a geometric Brown motion, and we will assume its drift and volatility