Pricing Credit Derivatives under Incomplete Information: a Nonlinear-Filtering Approach

This paper considers a general reduced form pricing model for
credit derivatives where default intensities are driven by some factor process
X. The process X is not directly observable for investors in secondary markets;
rather, their information set consists of the default history and of noisy price
observation for traded credit products. In this context the pricing of credit
derivatives leads to a challenging nonlinear filtering problem. We provide recursive
updating rules for the filter, derive a finite dimensional filter for the
case where X follows a finite state Markov chain and propose a novel particle filtering algorithm. A numerical case study illustrates the properties of the
proposed algorithms.