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An asymptotic expansion approach to the valuation of vulnerable options under a multiscale stochastic volatility model

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  • Jeon, Jaegi
  • Kim, Geonwoo
  • Huh, Jeonggyu

Abstract

In this study, we examine the pricing of vulnerable options under a stochastic volatility model based on the partial differential equation approach. Specifically, we consider a multiscale stochastic volatility model that is assumed to be driven by two diffusions (fast-scale and slow-scale) and use an asymptotic expansion approach to drive the approximate pricing formulas of vulnerable options, which allows the counterparty credit risk at maturity. Furthermore, we provide the Greek Delta of vulnerable options for the dynamic hedge and present the numerical results to examine the effect of the multiscale stochastic volatility model and to show the accuracy of our formula.

Suggested Citation

  • Jeon, Jaegi & Kim, Geonwoo & Huh, Jeonggyu, 2021. "An asymptotic expansion approach to the valuation of vulnerable options under a multiscale stochastic volatility model," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    • Handle: RePEc:eee:chsofr:v:144:y:2021:i:c:s0960077920310328
    DOI: 10.1016/j.chaos.2020.110641
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    1. A. Ronald Gallant & Chien-Te Hsu & George Tauchen, 1999. "Using Daily Range Data To Calibrate Volatility Diffusions And Extract The Forward Integrated Variance," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 617-631, November.
    2. Koo, Eunho & Kim, Geonwoo, 2017. "Explicit formula for the valuation of catastrophe put option with exponential jump and default risk," Chaos, Solitons & Fractals, Elsevier, vol. 101(C), pages 1-7.
    3. Fouque,Jean-Pierre & Papanicolaou,George & Sircar,Ronnie & Sølna,Knut, 2011. "Multiscale Stochastic Volatility for Equity, Interest Rate, and Credit Derivatives," Cambridge Books, Cambridge University Press, number 9780521843584, January.
    4. Jean-Pierre Fouque & Ronnie Sircar & Knut Sølna, 2006. "Stochastic Volatility Effects on Defaultable Bonds," Applied Mathematical Finance, Taylor & Francis Journals, vol. 13(3), pages 215-244.
    5. 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.
    6. Ma, Chaoqun & Ma, Zonggang & Xiao, Shisong, 2019. "A closed-form pricing formula for vulnerable European options under stochastic yield spreads and interest rates," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 59-68.
    7. Kim, Geonwoo & Koo, Eunho, 2016. "Closed-form pricing formula for exchange option with credit risk," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 221-227.
    8. Fard, Farzad Alavi, 2015. "Analytical pricing of vulnerable options under a generalized jump–diffusion model," Insurance: Mathematics and Economics, Elsevier, vol. 60(C), pages 19-28.
    9. 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.
    10. Sassan Alizadeh & Michael W. Brandt & Francis X. Diebold, 2002. "Range‐Based Estimation of Stochastic Volatility Models," Journal of Finance, American Finance Association, vol. 57(3), pages 1047-1091, June.
    11. 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.
    12. Klein, Peter, 1996. "Pricing Black-Scholes options with correlated credit risk," Journal of Banking & Finance, Elsevier, vol. 20(7), pages 1211-1229, August.
    13. 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.
    14. Wang, Guanying & Wang, Xingchun & Zhou, Ke, 2017. "Pricing vulnerable options with stochastic volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 485(C), pages 91-103.
    15. Lee, Min-Ku & Kim, Jeong-Hoon, 2018. "Pricing of defaultable options with multiscale generalized Heston’s stochastic volatility," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 144(C), pages 235-246.
    16. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    17. 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.
    18. Chernov, Mikhail & Ronald Gallant, A. & Ghysels, Eric & Tauchen, George, 2003. "Alternative models for stock price dynamics," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 225-257.
    19. 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.
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