A Cumulative Prospect Theory Approach to Option Pricing

Abstract

It is a well known from the empirical option pricing literature, that actual option prices show persistent and systematic deviations from theoretical values under standard pricing assumptions. While a substantial number of enhancements have been proposed, these approaches typically leave investor’s preferences towards risk unmodified. In this paper, we study option prices under cumulative prospect theory. We distinguish two prospect option pricing models, based on whether cash flows are either considered to be segregated or aggregated over time. A numerical example is provided to highlight the effect of different degrees of prospect behavior on option prices. In an empirical application to S&P 500 index options, our models are compared with benchmark models that are frequently used in the option pricing literature. Results suggest that our prospect option pricing models significantly improve the fitting performance over the Black-Scholes model and that especially the aggregated version’s performance is at least equivalent to the stochastic volatility model of Heston.

Keywords: Prospect Theory, Framing, Mental Accounting, Risk Attitude, Loss Aversion, Probability Perception, Weighting Function, Stochastic Volatility, Option Pricing

JEL Classification: D01, G11, G12