A subdiffusive Lévy model for pricing power options in illiquid markets

Abstract

We extend the existing subdiffusive jump-diffusion model to a more general subdiffusive Levy model where the underlying Levy process is time changed by a general inverse Lévy subordinator. We are able to obtain the characteristic function of log asset price by exploiting the fact that the Laplace transform of the inverse subordinator can be computed through an inverse Laplace transform in general and is given in explicit form for commonly encountered inverse subordinators. Different from previous studies where numerical methods such as Monte Carlo or PDE are used to calculate the option prices, we employ Fourier transform to derive the analytical solutions to power option prices.