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A Multidimensional Exponential Utility Indifference Pricing Model with Applications to Counterparty Risk

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  • Vicky Henderson
  • Gechun Liang

Abstract

This paper considers exponential utility indifference pricing for a multidimensional non-traded assets model subject to inter-temporal default risk, and provides a semigroup approximation for the utility indifference price. The key tool is the splitting method. We apply our methodology to study the counterparty risk of derivatives in incomplete markets.

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File URL: http://arxiv.org/pdf/1111.3856
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Bibliographic Info

Paper provided by arXiv.org in its series Papers with number 1111.3856.

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Date of creation: Nov 2011
Date of revision: May 2014
Handle: RePEc:arx:papers:1111.3856

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Web page: http://arxiv.org/

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References

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  1. A. Oberman & T. Zariphopoulou, 2003. "Pricing early exercise contracts in incomplete markets," Computational Management Science, Springer, Springer, vol. 1(1), pages 75-107, December.
  2. Ying Hu & Peter Imkeller & Matthias Muller, 2005. "Utility maximization in incomplete markets," Papers math/0508448, arXiv.org.
  3. Hull, John & White, Alan, 1995. "The impact of default risk on the prices of options and other derivative securities," Journal of Banking & Finance, Elsevier, Elsevier, vol. 19(2), pages 299-322, May.
  4. G. Liang & T. Lyons & Z. Qian, 2010. "A Functional Approach to FBSDEs and Its Application in Optimal Portfolios," Papers 1011.4499, arXiv.org.
  5. Vicky Henderson, 2005. "The impact of the market portfolio on the valuation, incentives and optimality of executive stock options," Quantitative Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 5(1), pages 35-47.
  6. Johnson, Herb & Stulz, Rene, 1987. " The Pricing of Options with Default Risk," Journal of Finance, American Finance Association, American Finance Association, vol. 42(2), pages 267-80, June.
  7. Merton, Robert C, 1974. "On the Pricing of Corporate Debt: The Risk Structure of Interest Rates," Journal of Finance, American Finance Association, American Finance Association, vol. 29(2), pages 449-70, May.
  8. Jarrow, Robert A & Turnbull, Stuart M, 1995. " Pricing Derivatives on Financial Securities Subject to Credit Risk," Journal of Finance, American Finance Association, American Finance Association, vol. 50(1), pages 53-85, March.
  9. Klein, Peter & Inglis, Michael, 2001. "Pricing vulnerable European options when the option's payoff can increase the risk of financial distress," Journal of Banking & Finance, Elsevier, Elsevier, vol. 25(5), pages 993-1012, May.
  10. Grasselli, Matheus & Henderson, Vicky, 2009. "Risk aversion and block exercise of executive stock options," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 33(1), pages 109-127, January.
  11. Michael Monoyios, 2004. "Performance of utility-based strategies for hedging basis risk," Quantitative Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 4(3), pages 245-255.
  12. Klein, Peter, 1996. "Pricing Black-Scholes options with correlated credit risk," Journal of Banking & Finance, Elsevier, Elsevier, vol. 20(7), pages 1211-1229, August.
  13. Vicky Henderson, 2002. "Valuation Of Claims On Nontraded Assets Using Utility Maximization," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 12(4), pages 351-373.
  14. Ronnie Sircar & Thaleia Zariphopoulou, 2010. "Utility valuation of multi-name credit derivatives and application to CDOs," Quantitative Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 10(2), pages 195-208.
  15. Kramkov, D. & Sîrbu, M., 2007. "Asymptotic analysis of utility-based hedging strategies for small number of contingent claims," Stochastic Processes and their Applications, Elsevier, Elsevier, vol. 117(11), pages 1606-1620, November.
  16. Damiano Brigo & Kyriakos Chourdakis, 2009. "Counterparty Risk For Credit Default Swaps: Impact Of Spread Volatility And Default Correlation," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., World Scientific Publishing Co. Pte. Ltd., vol. 12(07), pages 1007-1026.
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Cited by:
  1. I. Halperin & A. Itkin, 2012. "Pricing Illiquid Options with $N+1$ Liquid Proxies Using Mixed Dynamic-Static Hedging," Papers 1209.3503, arXiv.org.
  2. Michael Monoyios, 2012. "Malliavin calculus method for asymptotic expansion of dual control problems," Papers 1209.6497, arXiv.org, revised Oct 2013.

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