Displaced Jump-Diffusion Option Valuation

Abstract

This paper extends the jump-diffusion option pricing model of Merton (1976) and the displaced diffusion option pricing model of Rubinstein (1983) to price options on stock indices. First, we provide a theory showing that the stock index value has a positive threshold or positive lower bound if the constituent firms of the index, when their equity falls below a given value, are replaced by new firms with higher equity. Second, using equilibrium arguments in an economy where the systematic jump risk of the stock index can not be eliminated, we derive a displaced jump-diffusion (DJD) option valuation model to price options written on stock indices. Third, we test empirically our DJD option pricing model using S&P 500 index options data from January 1996 through April 2006. The results of the tests strongly support our theories.