Wall Street Rocket Science: Black-Scholes and Beyond

An option is a nancial contract whose value depends on that of an underlying asset such as a company stock. The Black-Scholes model for option pricing, published in 1973, revolutionized the nancial industry by introducing a no-arbitrage paradigm for valuing uncertainty and hedging against risk. This simple model assumes that the underlying stock price follows a stochastic Brownian motion process with a constant variance rate, or volatility. This assumption restricts the stock price to follow a log-normal distribution. To allow for more exible stock price distributions observed in the real market, several new methods have been recently proposed. Jarrow and Rudd 6] proposed to price options based on an estimated future proole for the stock price distribution. Rubinstein 13] introduced a binomial tree model of possible stock price movements consistent with current market prices. Hutchinson, Lo, and Poggio 5] proposed to price options using non-linear regression. In this paper, we rst review the basic Black-Scholes model, and then examine the three cited methods. Special emphasis is placed on the diiculties in these new methods, and it is argued that a new paradigm truly superior to the basic Black-Scholes model has yet to emerge.