Summary
We study the effect of risk aversion on the valuation of credit derivatives. Using the technology of utility-indiffierence valuation in intensity-based models of default risk, we analyze resulting yield spreads for single-name defaultable bonds and a simple representative two-name credit derivative. The impact of risk averse valuation on prices and yield spreads is expressed in terms of “effective correlation.”
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References
P. Artzner and F. Delbaen. Default risk insurance and incomplete markets. Mathematical Finance, 5:187–195, 1995.
D. Becherer. Rational hedging and valuation of integrated risks underconstant absolute risk aversion. Insurance: Mathematics and Economics, 33(1):1–28, 2003.
T. Bielecki and M. Jeanblanc. Indifference pricing of defaultable claims.In R. Carmona, editor, Indifference Pricing. Princeton University Press, 2006.
T. Bielecki, M. Jeanblanc, and M. Rutkowski. Hedging of defaultableclaims. Paris-Princeton Lectures on Mathematical Finance, ed. R. Carmona, Springer, 2004.
T. Bielecki and M. Rutkowski. Credit Risk. Springer-Verlag, 2001.
H. Buhlmann. Mathematical Methods in Risk Theory. Springer-Verlag, 1970.
P. Collin-Dufresne and J. Hugonnier. Event risk, contingent claims andthe temporal resolution of uncertainty. Carnegie Mellon University Working Paper, 2001.
J. Cvitanić, W. Schachermayer, and H. Wang. Utility maximization inincomplete markets with random endowment. Finance and Stochastics, 5(2):259–272, 2001.
M. Davis and V. Lo. Infectious defaults. Quantitative Finance, 1(4):382-387, 2001.
M.H.A. Davis, V. Panas, and T. Zariphopoulou. European option pricingwith transaction costs. SIAM J. Control and Optimization, 31:470–93, 1993.
F. Delbaen, P. Grandits, T. Rheinländer, D. Samperi, M. Schweizer,and C. Stricker. Exponential hedging and entropic penalties. Mathematical Finance, 12(2):99–123, 2002.
D. Duffe. Credit risk modeling with affine processes. J. Banking and Finance, 29:2751–2802, 2005.
D. Duffe and K. Singleton. Credit Risk. Princeton University Press, 2003.
D.Duffe and T. Zariphopoulou. Optimal investment with undiversifiable incomerisk. Mathematical Finance, 3(2):135–148, 1993.
A. Elizalde. Credit risk models IV: Understanding and pricing CDOs.www.abelelizalde.com, 2005.
J.P. Fouque, R. Sircar, and K. Sølna. Stochastic volatility effects ondefaultable bonds. Applied Finance, 13(3), 215–244, 2006.
H. Gerber. An Introduction to Mathematical Risk Theory. Huebner Foundation for Insurance Education, Wharton School, University of Pennsylvania, 1979.
S.D. Hodges and A. Neuberger. Optimalreplication of contingent claims under transaction costs. Review of Futures Markets, 8:222–239, 1989.
R. Jarrow and S. Turnbull. Pricing options on financial securitiessubject to credit risk. J. Finance, 50:53–85, 1995.
Y. M. Kabanov and C. Stricker. On the optimal portfolio for theexponential utility maximization: Remarks to the six-author paper.Mathematical Finance, 12(2):125–34, 2002.
I. Karatzas and S. Shreve. Methods of Mathematical Finance. Springer-Verlag, 1998.
D. Kramkov and W. Schachermayer. The asymptotic elasticity of utilityfunctions and optimal investment in incomplete markets. Annals of Applied Probability, 9(3):904–950, 1999.
D. Lando. On Cox processes and credit risky securities. Review of Derivatives Research, 2:99–120, 1998.
D. Lando. Credit Risk Modeling: Theory and Applications. Princeton Series in Finance. Princeton University Press, 2004.
V. Linetsky. Pricing equity derivatives subject to bankruptcy. Mathematical Finance, 16(2):255–282, 2006.
D. Madan and H. Unal. Pricing the risks of default. Review of Derivatives Research, 2:121–160, 1998.
P. Schönbucher. Credit Derivatives Pricing Models. Wiley, 2003.
T. Shouda. The indifference price of defaultable bonds with unpredictable recovery and their risk premiums. Preprint, Hitosubashi University, Tokyo, 2005.
R. Sircar and T. Zariphopoulou. Utility valuation of creditderivatives and application to CDOs. Submitted, 2006.
C. Tiu. On the Merton Problem in Incomplete Markets. Ph.D. thesis, The University of Texas at Austin, 2002.
T. Zhou. Indifference valuation of mortgage-backed securities in the presence of payment risk. Preprint, The University of Texas at Austin, 2006.
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Sircar, R., Zariphopoulou, T. (2007). Utility Valuation of Credit Derivatives: Single and Two-Name Cases. In: Fu, M.C., Jarrow, R.A., Yen, JY.J., Elliott, R.J. (eds) Advances in Mathematical Finance. Applied and Numerical Harmonic Analysis. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4545-8_15
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DOI: https://doi.org/10.1007/978-0-8176-4545-8_15
Publisher Name: Birkhäuser Boston
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