Credit Risk Modeling and Credit Derivatives Valuation in Intensity-based Models

Bomi Kim, Purdue University

Abstract

Our research focuses on pricing credit derivatives, including single-name credit default swaps (CDSs), Bermudan CDS options, and basket CDSs with and without counterparty risk adjustment. Unlike European CDS option pricing, which admits closed-form solutions, Bermudan CDS option pricing does not have a closed-form solution. In this work, approximate dynamic programming (ADP) and duality methods are applied to find lower and upper bounds of Bermudan CDS option prices where the default intensity of the underlying reference company is modeled with the Cox, Ingersoll and Ross (CIR) process. While lower bounds of the option prices are obtained from the primal ADP problem with the exercise strategy we approximate, upper bounds of the option prices are computed using a martingale in the duality method. Unlike European CDS option values, Bermudan CDS option values are less sensitive to the default risk of the reference firm. To model the default dependence among entities, we introduce interacting intensities with exogenous jump diffusion processes. For a single-name CDS with bilateral counterparty risk adjustment, the default intensity of each entity (investor, counterparty or reference firm) is modeled as a two-state Markov chain where a jump to the other state is driven by external economy shock following jump diffusion stochastic processes. With transition probabilities obtained from the Kolmogorov equation, bilateral counterparty risk adjusted CDS and CDS option prices can be computed. Our result shows swap rates with bilateral counterparty risk adjustment are sensitive not only to the default risk of the reference firm, but also to the default risks of the investor and the counterparty. We extend our default contagion model with interacting intensities to price a basket CDS with a homogeneous group of reference firms where risks are exchangeable among firms. We implement three different intensity models: a simple linear model, a time dependent exponential decay model, and a two-state Markov chain model with jump diffusion processes. We investigate swap rates of a basket CDS with the three intensity models, and show the sensitivity of swap rates to the default intensities of the investor and the counterparty, and to external shock.

Degree

Ph.D.

Advisors

Morin, Purdue University.

Subject Area

Finance|Industrial engineering

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