tailieunhanh - Pricing and Hedging of Credit Derivatives via the Innovations Approach to Nonlinear Filtering

In this paper we propose a new, information-based approach for modelling the dynamic evolution of a portfolio of credit risky securities. In our setup market prices of traded credit derivatives are given by the solution of a nonlinear filtering problem. The innovations approach to nonlinear filtering is used to solve this problem and to derive the dynamics of market prices. Moreover, the practical application of the model is discussed: we analyse calibration, the pricing of exotic credit derivatives and the computation of risk-minimizing hedging strategies. The paper closes with a few numerical case studies | Pricing and Hedging of Credit Derivatives via the Innovations Approach to Nonlinear Filtering Rudiger Frey and Thorsten Schmidt June 2010 Abstract In this paper we propose a new information-based approach for modelling the dynamic evolution of a portfolio of credit risky securities. In our setup market prices of traded credit derivatives are given by the solution of a nonlinear filtering problem. The innovations approach to nonlinear filtering is used to solve this problem and to derive the dynamics of market prices. Moreover the practical application of the model is discussed we analyse calibration the pricing of exotic credit derivatives and the computation of risk-minimizing hedging strategies. The paper closes with a few numerical case studies. Keywords Credit derivatives incomplete information nonlinear filtering hedging 1 Introduction Credit derivatives - derivative securities whose payoff is linked to default events in a given portfolio - are an important tool in managing credit risk. However the subprime crisis and the subsequent turmoil in credit markets highlights the need for a sound methodology for the pricing and the risk management of these securities. Portfolio products pose a particular challenge in this regard the main difficulty is to capture the dependence structure of the defaults and the dynamic evolution of the credit spreads in a realistic and tractable way. The authors wish to thank A. Gabih A. Herbertsson and R. Wendler for their assistance and comments and two anonymous referees for their useful suggestions. A previous unpublished version of this paper is Frey Gabih and Schmidt 2007 . Department of Mathematics University of Leipzig D-04009 Leipzig Germany. Email Department of Mathematics Chemnitz University of Technology Reichenhainer Str. 41 D-09126 Chemnitz Germany. Email 2 In this paper we propose a new information-based approach to this problem. We consider a