TAILIEUCHUNG - Credit Default Swaps Calibration and Option Pricing with the SSRD Stochastic Intensity and Interest-Rate Model

Worse, because the consumer fails to see that she will pay a large penalty and back-load repayment—and not because she has a taste for immediate gratification with respect to consumption— she underestimates the cost of credit and borrows too much. Due to this combination of decisions, a nonsophisticated consumer, no matter how close to sophisticated, has discontinuously lower welfare than a sophisticated consumer. This discontinuity demonstrates in an extreme form our main point regarding contracts and welfare in the credit market: that because the credit contracts firms design in response postulate large penalties for deferring repayment, even relatively minor mispredictions of preferences by borrowers can have large. | Reduced version in Proceedings of the 6-th Columbia JAFEE Conference Tokyo March 15-16 2003 pages 563-585. Updated version published in Finance Stochastics Vol. IX 1 2005 This paper is available at Credit Default Swaps Calibration and Option Pricing with the SSRD Stochastic Intensity and Interest-Rate Model Damiano Brigo Aurelien Alfonsi Credit Models Banca IMI San Paolo IMI Group Corso Matteotti 6 - 20121 Milano Italy Fax 39 02 7601 9324 First Version February 1 2003. This version February 18 2004 Abstract In the present paper we introduce a two-dimensional shifted square-root diffusion SSRD model for interest rate derivatives and single-name credit derivatives in a stochastic intensity framework. The SSRD is the unique model to the best of our knowledge allowing for an automatic calibration of the term structure of interest rates and of credit default swaps CDS s . Moreover the model retains free dynamics parameters that can be used to calibrate option data such as caps for the interest rate market and options on CDS s in the credit market. The calibrations to the interest-rate market and to the credit market can be kept separate thus realizing a superposition that is of practical value. We discuss the impact of interest-rate and default-intensity correlation on calibration and pricing and test it by means of Monte Carlo simulation. We use a variant of Jamshidian s decomposition to derive an analytical formula for CDS options under CIR stochastic intensity. Finally we develop an analytical approximation based on a Gaussian dependence mapping for some basic credit derivatives terms involving correlated CIR processes. JEL classification code G13. AMS classification codes 60H10 60J60 60J75 91B70 1 D. Brigo A. Alfonsi Credit derivatives with shifted square root diffusion models 2 1 Credit Default Swaps A credit default swap is a contract ensuring protection against default. This contract

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