Journal of Mathematical Analysis and Applications | 2019
Pricing and hedging of general rating-sensitive claims in a jump-diffusion market model in the presence of stochastic factors
Abstract
Abstract In this paper we solve a problem of finding a risk minimizing hedging strategy on a general Markovian market with ratings on which prices are influenced by additional factors and rating. The market is described by a system of SDEs driven by a Wiener process and a compensated Poisson random measure. Rating-sensitive claims are considered. We relate the problem of pricing and hedging the contracts described by a general cash-flow process to solving Cauchy/Dirichlet problems and subsequently to solving some linear system of equations. We illustrate our theory on two examples of different nature. The first is a general exponential Levy model with stochastic volatility, and the second is a generalization of an exponential Levy model with regime switching.