Jump-Diffusion Option Valuation Without a Representative Investor: A Stochastic Dominance Approach

Abstract

We present a new method of pricing plain vanilla call and put options when the underlying asset returns follow a jump-diffusion process. The method is based on stochastic dominance insofar as it does not need any assumption on the utility function of a representative investor apart from risk aversion. It develops discrete time multiperiod reservation write and reservation purchase bounds on option prices. The bounds are valid for any asset dynamics and are such that any risk averse investor improves her expected utility by introducing a short (long) option in her portfolio if the upper (lower) bound is violated by the observed market price. The bounds are evaluated recursively for a general discretization of the continuous time jump-diffusion returns. The limiting forms of the bounds are then found as the time partition becomes continuous. It is found that the two bounds tend to the common limit equal to the Black-Scholes-Merton price when there is no jump component, but to two different limits when the jump component is present. The interval between the two bounds depends on the size of the risk premium on the underlying asset and is around 8% for the empirically relevant sizes of the parameters.

Keywords: option pricing, incomplete markets, stochastic dominance, jump-diffusion

JEL Classification: G13