tailieunhanh - COUNTERPARTY RISK FOR CREDIT DEFAULT SWAPS

Consistent with real-life credit-card and subprime mortgage contracts but (we argue) inconsistent with natural specifications of rational time-consistent theories, in the competitive equilibrium of our model firms offer seemingly cheap credit to be repaid quickly, but introduce large penalties for falling behind this front-loaded repayment schedule. The contracts are designed so that borrowers who underestimate their taste for immediate gratification both pay the penalties and repay in an ex ante suboptimal back-loaded manner more often than they predict or prefer. To make matters worse, the same misprediction leads nonsophisticated consumers to underestimate the cost of credit and borrow too much—despite borrowing being for future consumption | Updated version forthcoming in the International Journal of Theoretical and Applied Finance COUNTERPARTY RISK FOR CREDIT DEFAULT SWAPS IMPACT OF SPREAD VOLATILITy AND DEFAULT CORRELATION Damiano Brigo Fitch Solutions and Dept. of Mathematics Imperial College 101 Finsbury Pavement EC2A 1RS London. E-mail dami ano .brigo@fitchsolutions. com Kyriakos Chourdakis Fitch Solutions and CCFEA University of Essex 101 Finsbury Pavement EC2A 1RS London. E-mail kyriakos. chourdakis@fitchsolutions. com Abstract We consider counterparty risk for Credit Default Swaps CDS in presence of correlation between default of the counterparty and default of the CDS reference credit. Our approach is innovative in that besides default correlation which was taken into account in earlier approaches we also model credit spread volatility. Stochastic intensity models are adopted for the default events and defaults are connected through a copula function. We find that both default correlation and credit spread volatility have a relevant impact on the positive counterparty-risk credit valuation adjustment to be subtracted from the counterparty-risk free price. We analyze the pattern of such impacts as correlation and volatility change through some fundamental numerical examples analyzing wrong-way risk in particular. Given the theoretical equivalence of the credit valuation adjustment with a contingent CDS we are also proposing a methodology for valuation of contingent CDS on CDS. AMS Classification Codes 60H10 60J60 60J75 62H20 91B70 JEL Classification Codes C15 C63 C65 G12 G13 Keywords Counterparty Risk Credit Valuation adjustment Credit Default Swaps Contingent Credit Default Swaps Credit Spread Volatility Default Correlation Stochastic Intensity Copula Functions Wrong Way Risk. First version May 16 2008. This version October 3 2008 D. Brigo K. Chourdakis FitchSolutions Counterparty risk valuation adjustment for CDS 2 1 Introduction We consider counterparty risk for Credit Default Swaps CDS in .

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