Displaced Jump-Diffusion Option Valuation

This article extends the jump-diffusion option pricing model of Merton and the displaced diffusion option pricing model of Rubinstein to price options on stock indices. First, the authors 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 equality 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 cannot be eliminated, the authors derive a displaced jump-diffusion (DJD) option valuation model to price options written on stock indices. Third, the authors test empirically our DJD option pricing model using S&P 500 Index options data from January 1996 through April 2006 and compare goodness of fit measures to those produced by the option pricing models of Merton and Rubinstein. The results of the tests strongly support the authors theories.