Comparing Merton model and Gram-Charlier model to capture skewness and kurtosis on bond performance

Abstract

The existence of skewness and kurtosis in finance data distribution is as a generalization of the normal density. Non-normal skewness and kurtosis of underlying asset of bond issuer significantly contribute to the phenomenon of volatility smile. Merton jump diffusion model is one of the first beyond Black-Scholes model in the sense that it tries to capture the effect of skewness and kurtosis of the asset prices density by a simple addition of a compound Poisson jump process. Another approach to consider the effect of skewness and kurtosis in asset prices for bond valuation is the Gram-Charlier (G-C) expansion. Hermite polynomial is used to get an expansion of the probability distribution in G-C method. In this paper we compare Merton Jump Diffusion (MJD) Model and G-C model in the term of equity and default probability. The result showed that G-C model is more consistent than MJD model when the skewness and kurtosis are taken into account.