A Libor Market Model with Default Risk
In this paper a new credit risk model for credit derivatives is presented. The model is based upon the ‘Libor market’ modelling framework for default-free interest rates. We model effective default-free forward rates and effective forward credit spreads as lognormal diffusion processes, and recovery is modelled as a fraction of the par value of the defaulted claim. The newly introduced survival-based pricing measures are a valuable tool in the pricing of defaultable payoffs and allow a straightforward derivation of the no-arbitrage dynamics of forward rates and forward credit spreads. The model can be calibrated to the prices of defaultable coupon bonds, asset swap rates and default swap rates for which closed-form solutions are given. For options on default swaps and caps on credit spreads, approximate solutions of high accuracy exist. This pricing formula for options on default swaps is made exact in a modified modelling framework using an analogy to the swap measure, the default swap measure.
|Date of creation:||Dec 2000|
|Date of revision:|
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- Erik Schlögl, 1999.
"A Multicurrency Extension of the Lognormal Interest Rate Market Models,"
Research Paper Series
20, Quantitative Finance Research Centre, University of Technology, Sydney.
- Erik Schlögl, 2002. "A multicurrency extension of the lognormal interest rate Market Models," Finance and Stochastics, Springer, vol. 6(2), pages 173-196.
- Jarrow, Robert A & Lando, David & Turnbull, Stuart M, 1997.
"A Markov Model for the Term Structure of Credit Risk Spreads,"
Review of Financial Studies,
Society for Financial Studies, vol. 10(2), pages 481-523.
- Robert A. Jarrow & David Lando & Stuart M. Turnbull, 2008. "A Markov Model for the Term Structure of Credit Risk Spreads," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 18, pages 411-453 World Scientific Publishing Co. Pte. Ltd..
- Miltersen, K. & K. Sandmann & D. Sondermann, 1994.
"Closed Form Solutions for Term Structure Derivatives with Log-Normal Interest Rates,"
Discussion Paper Serie B
308, University of Bonn, Germany.
- Miltersen, Kristian R & Sandmann, Klaus & Sondermann, Dieter, 1997. " Closed Form Solutions for Term Structure Derivatives with Log-Normal Interest Rates," Journal of Finance, American Finance Association, vol. 52(1), pages 409-30, March.
- Xiaoliang Zhao & Paul Glasserman, 2000. "Arbitrage-free discretization of lognormal forward Libor and swap rate models," Finance and Stochastics, Springer, vol. 4(1), pages 35-68.
- Farshid Jamshidian, 1997. "LIBOR and swap market models and measures (*)," Finance and Stochastics, Springer, vol. 1(4), pages 293-330.
- Jarrow, Robert A & Turnbull, Stuart M, 1995.
" Pricing Derivatives on Financial Securities Subject to Credit Risk,"
Journal of Finance,
American Finance Association, vol. 50(1), pages 53-85, March.
- Robert A. Jarrow & Stuart M. Turnbull, 2008. "Pricing Derivatives on Financial Securities Subject to Credit Risk," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 17, pages 377-409 World Scientific Publishing Co. Pte. Ltd..
- David Heath & Robert Jarrow & Andrew Morton, 2008.
"Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation,"
World Scientific Book Chapters,
in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305
World Scientific Publishing Co. Pte. Ltd..
- Heath, David & Jarrow, Robert & Morton, Andrew, 1992. "Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation," Econometrica, Econometric Society, vol. 60(1), pages 77-105, January.
- Lotz, Christopher & Schlogl, Lutz, 2000. "Default risk in a market model," Journal of Banking & Finance, Elsevier, vol. 24(1-2), pages 301-327, January.
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