A Prospect Approach to Option Pricing

Abstract

It's a well known empirical fact that actual option prices show persistent and systematic deviations from Black-Scholes option values. While a substantial number of enhancements have been proposed in the literature, these approaches typically leave investor's preferences towards risk unmodified. Recently, empirical studies using option prices find support for non-concave utility functions proposed by Kahneman and Tversky. In this paper, we study option prices in an economy where investors are loss averse over fluctuations in the value of their financial wealth. The design of our pricing model is influenced by prospect theory, including behavioral aspects like risk attitude, mental accounting and probability perception. The theoretical marginal prospect option writer is risk averse in the domain of gains, risk taking in the domain of losses; (s)he overestimates small probabilities and underestimates large probabilities of the option being exercised in-the-money. The pricing framework can help to explain the implied volatility pattern typically observed from actual option prices. Empirical analysis on European call options on the S&P 500 index shows that prospect option pricing models significantly improve the fitting performance in in-sample, as well as in out-of-sample analysis. Further, the analysis shows that the marginal investor's behavior is different from the prospect theoretical observations. In stead of being risk averse in the domain of gains, risk taking in the domain of losses, and overestimate small and underestimate large probabilities of the option expiring in-the-money, marginal writers of call options on the S&P 500 index display the reverse behavior.