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Pricing Black-Scholes options with correlated interest rate risk and credit risk: an extension

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  • Szu-Lang Liao
  • Hsing-Hua Huang

Abstract

This article provides a closed-form valuation formula for the Black-Scholes options subject to interest rate risk and credit risk. Not only does our model allow for the possible default of the option issuer prior to the option's maturity, but also considers the correlations among the option issuer's total assets, the underlying stock, and the default-free zero coupon bond. We further tailor-make a specific credit-linked option for hedging the default risk of the option issuer. The numerical results show that the default risk of the option issuer significantly reduces the option values, and the vulnerable option values may be remarkably overestimated in the case where the default can occur only at the maturity of the option.

Suggested Citation

  • Szu-Lang Liao & Hsing-Hua Huang, 2005. "Pricing Black-Scholes options with correlated interest rate risk and credit risk: an extension," Quantitative Finance, Taylor & Francis Journals, vol. 5(5), pages 443-457.
    • Handle: RePEc:taf:quantf:v:5:y:2005:i:5:p:443-457
    DOI: 10.1080/14697680500362718
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    1. 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..
    2. Longstaff, Francis A & Schwartz, Eduardo S, 1995. "A Simple Approach to Valuing Risky Fixed and Floating Rate Debt," Journal of Finance, American Finance Association, vol. 50(3), pages 789-819, July.
    3. Johnson, Herb & Stulz, Rene, 1987. "The Pricing of Options with Default Risk," Journal of Finance, American Finance Association, vol. 42(2), pages 267-280, June.
    4. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    5. Hull, John & White, Alan, 1995. "The impact of default risk on the prices of options and other derivative securities," Journal of Banking & Finance, Elsevier, vol. 19(2), pages 299-322, May.
    6. 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..
    7. Briys, Eric & de Varenne, François, 1997. "Valuing Risky Fixed Rate Debt: An Extension," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 32(2), pages 239-248, June.
    8. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    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, vol. 25(5), pages 993-1012, May.
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    Cited by:

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    3. Chaoqun Ma & Shengjie Yue & Hui Wu & Yong Ma, 2020. "Pricing Vulnerable Options with Stochastic Volatility and Stochastic Interest Rate," Computational Economics, Springer;Society for Computational Economics, vol. 56(2), pages 391-429, August.
    4. Jeon, Junkee & Kim, Geonwoo, 2019. "Pricing of vulnerable options with early counterparty credit risk," The North American Journal of Economics and Finance, Elsevier, vol. 47(C), pages 645-656.
    5. Jiang, I-Ming & Yang, Sheng-Yung & Liu, Yu-Hong & Wang, Alan T., 2013. "Valuation of double trigger catastrophe options with counterparty risk," The North American Journal of Economics and Finance, Elsevier, vol. 25(C), pages 226-242.
    6. Xingchun Wang, 2020. "Analytical valuation of Asian options with counterparty risk under stochastic volatility models," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 40(3), pages 410-429, March.
    7. Gechun Liang & Xingchun Wang, 2021. "Pricing vulnerable options in a hybrid credit risk model driven by Heston–Nandi GARCH processes," Review of Derivatives Research, Springer, vol. 24(1), pages 1-30, April.
    8. Rossella Agliardi, 2011. "A comprehensive structural model for defaultable fixed-income bonds," Quantitative Finance, Taylor & Francis Journals, vol. 11(5), pages 749-762.
    9. Jinghai Shao & Sovan Mitra & Andreas Karathanasopoulos, 2022. "Optimal feedback control of stock prices under credit risk dynamics," Annals of Operations Research, Springer, vol. 313(2), pages 1285-1318, June.
    10. Panhong Cheng & Zhihong Xu & Zexing Dai, 2023. "Valuation of vulnerable options with stochastic corporate liabilities in a mixed fractional Brownian motion environment," Mathematics and Financial Economics, Springer, volume 17, number 3, December.
    11. Wang, Xingchun, 2021. "Valuation of options on the maximum of two prices with default risk under GARCH models," The North American Journal of Economics and Finance, Elsevier, vol. 57(C).
    12. Tristan Guillaume, 2022. "Closed form valuation of barrier options with stochastic barriers," Annals of Operations Research, Springer, vol. 313(2), pages 1021-1050, June.
    13. Xie, Yurong & Deng, Guohe, 2022. "Vulnerable European option pricing in a Markov regime-switching Heston model with stochastic interest rate," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    14. Xingchun Wang, 2016. "The Pricing of Catastrophe Equity Put Options with Default Risk," International Review of Finance, International Review of Finance Ltd., vol. 16(2), pages 181-201, June.
    15. Wang, Xingchun, 2022. "Pricing vulnerable options with stochastic liquidity risk," The North American Journal of Economics and Finance, Elsevier, vol. 60(C).
    16. Lie-Jane Kao, 2016. "Credit valuation adjustment of cap and floor with counterparty risk: a structural pricing model for vulnerable European options," Review of Derivatives Research, Springer, vol. 19(1), pages 41-64, April.
    17. Wang, Xingchun, 2020. "Catastrophe equity put options with floating strike prices," The North American Journal of Economics and Finance, Elsevier, vol. 54(C).
    18. Wang, Xingchun, 2020. "Valuation of Asian options with default risk under GARCH models," International Review of Economics & Finance, Elsevier, vol. 70(C), pages 27-40.

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