Pricing and Hedging of Rating-Sensitive Claims Modeled by $\mathbb{F}$-doubly Stochastic Markov Chains

Abstract

In this paper, we achieve two goals. First we give a formula describing prices of defaultable rating-sensitive claims of general type. Secondly, we solve the problem of replication of an arbitrary rating-sensitive claim on a market on which we can trade in default free assets and a fixed number of defaultable general rating-sensitive claims. The credit rating migration process is modeled by F-doubly stochastic Markov chains, a broad class of processes which contains Markov chains and is fully characterized by some martingale property.