Credit Securitisations and Derivatives: Challenges for the Global Markets

12

Dynamic Modeling of Credit Derivatives

Alfred Hamerle, Kilian Plank and Christian Scherr

University of Regensburg

12.1 INTRODUCTION

The integrative pricing of options and corresponding credit derivatives has recently been addressed extensively (see Carverhill and Luo (2011), Collin-Dufresne et al. (2012), Hamerle et al. (2012), Li and Zhao (2011)) in discussing the influential publication of Coval et al. (2009). In the present chapter, we do not want to restrict ourselves to the specific question of whether CDX tranches offered a risk premium comparable to S&P 500 index options. Rather, we provide a simple model with a small number of parameters and a high degree of analytical tractability for a general option-based pricing of credits derivatives. The comprehensive and (semi-)analytical1 description of credit-related assets (firm values), as well as corresponding portfolios, are therefore in the center of focus.

In a certain sense, this corresponds to the notion of the CreditGrades model, originally presented by Finger et al. (2002) and Stamicar and Finger (2005). Within the CreditGrades model, equity and asset processes are linked by a particular formula that expresses asset volatility in terms of equity volatility, as well as equity and debt level. To overcome the main disadvantages of this approach, Sepp (2006) introduced two robust model extensions, taking account of both stochastic volatility and jump behavior. Ozeki et al. (2010) adapted the latter concept and transfer ...