A spectral approach to pricing of forward starting options

Abstract

We propose a new class of models for pricing forward starting options. We assume that the asset price is a nonlinear function of a CIR process, time changed by a composition of a Levy subordinator and an absolutely ´ continuous process. The new models introduce the nonlinearity in both drift and diffusion components of the underlying process and can capture jumps and stochastic volatility in a flexible way. By employing the spectral expansion technique, we are able to derive the analytical formulas for the forward starting option prices. We also implement a specific model numerically and test its sensitivity to some of the key parameters of the model.