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CDS and Option on CDS
  • CDS with Counterparty Risk in a Markov Chain Copula Model with Joint Defaults In this paper we study the counterparty risk on a payer CDS in a Markov chain model of two reference credits, the firm underlying the CDS and the protection seller in the CDS. We first state few preliminary results about pricing and CVA of a CDS with counterparty risk in a general set-up. We then introduce a Markov chain copula model in which wrong way risk is represented by the possibility of joint defaults between the counterpart and the firm underlying the CDS. In the set-up thus specified we have semi-explicit formulas for most quantities of interest with regard to CDS counterparty risk like price, CVA, EPE or hedging strategies. Model calibration is made simple by the copula property of the model. Numerical results show adequation of the behavior of EPE and CVA in the model with stylized features. , S.Crepey, M.Jeanblanc, B.Zargari (2009)
  • Bilateral Counterparty Risk Valuation with Stochastic Dynamical Models and Application to Credit Default Swaps We introduce the general arbitrage-free valuation framework for counterparty risk adjustments in presence of bilateral default risk, including default of the investor. We illustrate the symmetry in the valuation and show that the adjustment involves a long position in a put option plus a short position in a call option, both with zero strike and written on the residual net value of the contract at the relevant default times. We allow for correlation between the default times of the investor, counterparty and underlying portfolio risk factors. We use arbitrage-free stochastic dynamical models. We then specialize our analysis to Credit Default Swaps (CDS) as underlying portfolio, generalizing the work of Brigo and Chourdakis (2008) [5] who deal with unilateral and asymmetric counterparty risk. We introduce stochastic intensity models and a trivariate copula function on the default times exponential variables to model default dependence. Similarly to [5], we ?nd that both default correlation and credit spread volatilities have a relevant and structured impact on the adjustment. Di?erently from [5], the two parties will now agree on the credit valuation adjustment. We study a case involving British Airways, Lehman Brothers and Royal Dutch Shell, illustrating the bilateral adjustments in concrete crisis situations. , D.Brigo, A.Capponi (2009)
  • Counterparty Risk for Credit Default Swaps: Impact of spread volatility and default correlation , D.Brigo, K.Chourdakis (2008)
  • Pricing Constant Maturity Credit Default Swaps Under Jump Dynamics , H.Jonsson, W.Schoutens (2008)
  • Arbitrage-free pricing of Credit Index Options. The no-armageddon pricing measure and the role of correlation after the subprime crisis In this work we consider three problems of the standard market approach to pricing of credit index options: the definition of the index spread is not valid in general, the usually considered payoff leads to a pricing which is not always defined, and the candidate numeraire one would use to define a pricing measure is not strictly positive, which would lead to a non-equivalent pricing measure. We give a general mathematical solution to the three problems, based on a novel way of modelling the flow of information through the definition of a new subfiltration. Using this subfiltration, we take into account consistently the possibility of default of all names in the portfolio, that is neglected in the standard market approach. We show that, while the related mispricing can be negligible for standard options in normal market conditions, it can become highly relevant for different options or in stressed market conditions. In particular, we show on 2007 market data that after the subprime credit crisis the mispricing of the market formula compared to the no arbitrage formula we propose has become financially relevant even for the liquid Crossover Index Options. , D. Brigo, M. Morini (2007)
  • Credit Derivatives Pricing with a Smile-Extended Jump Stochastic Intensity Model , D. Brigo, N. El-Bachir (2006)
  • CDS Market Formulas and Models , D. Brigo, M. Morini (2005)
  • Credit Default Swap Calibration and Equity Swap Valuation under Counterparty Risk with a Tractable Structural Model , D. Brigo, M. Tarenghi (2005)
  • Candidate Market Models and the Calibrated CIR++ Stochastic Intensity Model for Credit Default Swap Options and Callable Floaters , D. Brigo (2005)
  • A Comparison between the stochastic intensity SSRD Model and the Market Model for CDS Options Pricing , D. Brigo, L. Cousot (2004)
  • Credit Default Swaps Calibration and Option Pricing with the SSRD Stochastic Intensity and Interest-Rate Model , D. Brigo, A. Alfonsi (2004)
  • The Valuation of Credit Default Swap Options , J.Hull, A.White (2003)
  • VALUATION OF CREDIT DEFAULT SWAPS AND SWAPTIONS This paper presents a conceptual framework for valuation of single-name credit derivatives, and recuperates, in some cases generalizing, a few of known results in credit risk theory. Valuation is viewed with respect to a given state price and relative to a general numeraire. Survival probabilities and default recoveries are considered as processes adapted to a subfiltration, following Jeanblanc and Rutosksy [JR], or, in the special case of Cox processes, Lando [L]. A result of Duffie and Singleton [DS] on pricing bonds with recovery in terms of loss ratio is reproduced. The notion of coadapted change of numeraire is introduced, and its invariants identified and studied. The concept of a credit claim is formalized by introducing notions of T-claims,  -claims, and T -streams. Application is made to credit default swaps and swaption, and a known Black-Scholes approximation for the latter is derived. , F.Jamshidian (2002)
  • Valuing Credit Defaut Swaps I: No Counterparty Default Risk , J.Hull, A.White (2000)
  • Valuing Credit Defaut Swaps II: Modelling Default Correlations , J.Hull, A.White (2000)

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