Unifying the Three Volatility Models

ABSTRACT. This article describes a method for building analytically tractable option pricing models which combine state dependent volatility, stochastic volatility and jumps. Starting from a Laguerre representation of the pricing kernel, we show how to account for jumps and stochastic volatility by altering the time de-pendent coefficients of a series expansion. This operation is easy to implement analytically and gives rise to numerically efficient formulas for the pricing kernel. This technique stemmed from a line of research on barrier models for credit derivatives, but the method is of broader relevance to option pricing theory. 1