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Derivative Pricing with Multivariate Stochastic Volatility : Application to Credit Risk

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  • Christian Gourieroux

    (Crest)

  • Razvan Sufana

    (Crest)

Abstract

This paper extends to the multiasset framework the closed-form solution for options withstochastic volatility derived in Heston (1993) and Ball and Roma (1994). This extensionintroduces a risk premium in the return equation and considers Wishart dynamics for theprocess of the stochastic volatility matrix, which is the multiasset analogue of the model ofCox, Ingersoll, and Ross (1985). This approach is used to extend Merton’s model (Merton(1974)) for corporate default to a framework with stochastic liability, stochastic volatilityand several firms.

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  • Christian Gourieroux & Razvan Sufana, 2004. "Derivative Pricing with Multivariate Stochastic Volatility : Application to Credit Risk," Working Papers 2004-31, Center for Research in Economics and Statistics.
    • Handle: RePEc:crs:wpaper:2004-31
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    References listed on IDEAS

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    1. Chen, Ren-Raw & Chung, San-Lin & Yang, Tyler T., 2002. "Option Pricing in a Multi-Asset, Complete Market Economy," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 37(4), pages 649-666, December.
    2. Boyle, Phelim P., 1988. "A Lattice Framework for Option Pricing with Two State Variables," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 23(1), pages 1-12, March.
    3. Johnson, Herb & Shanno, David, 1987. "Option Pricing when the Variance Is Changing," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 22(2), pages 143-151, June.
    4. Nicole El Karoui & Monique Jeanblanc‐Picquè & Steven E. Shreve, 1998. "Robustness of the Black and Scholes Formula," Mathematical Finance, Wiley Blackwell, vol. 8(2), pages 93-126, April.
    5. Mark. B. Garman., 1976. "A General Theory of Asset Valuation under Diffusion State Processes," Research Program in Finance Working Papers 50, University of California at Berkeley.
    6. Merton, Robert C, 1974. "On the Pricing of Corporate Debt: The Risk Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 29(2), pages 449-470, May.
    7. Christian Gourieroux & Joann Jasiak & Razvan Sufana, 2004. "The Wishart Autoregressive of Multivariate Stochastic Volatility," Working Papers 2004-32, Center for Research in Economics and Statistics.
    8. Stein, Elias M & Stein, Jeremy C, 1991. "Stock Price Distributions with Stochastic Volatility: An Analytic Approach," The Review of Financial Studies, Society for Financial Studies, vol. 4(4), pages 727-752.
    9. Naik, Vasanttilak, 1994. "Asset Prices in Dynamic Production Economies with Time-Varying Risk," The Review of Financial Studies, Society for Financial Studies, vol. 7(4), pages 781-801.
    10. Melino, Angelo & Turnbull, Stuart M., 1990. "Pricing foreign currency options with stochastic volatility," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 239-265.
    11. Stapleton, Richard C & Subrahmanyam, Marti G, 1984. "The Valuation of Multivariate Contingent Claims in Discrete Time Models," Journal of Finance, American Finance Association, vol. 39(1), pages 207-228, March.
    12. Blattberg, Robert C & Gonedes, Nicholas J, 1974. "A Comparison of the Stable and Student Distributions as Statistical Models for Stock Prices," The Journal of Business, University of Chicago Press, vol. 47(2), pages 244-280, April.
    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. Darrell Duffie & Jun Pan & Kenneth Singleton, 2000. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," Econometrica, Econometric Society, vol. 68(6), pages 1343-1376, November.
    15. David G. Hobson & L. C. G. Rogers, 1998. "Complete Models with Stochastic Volatility," Mathematical Finance, Wiley Blackwell, vol. 8(1), pages 27-48, January.
    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. Boyle, Phelim P & Evnine, Jeremy & Gibbs, Stephen, 1989. "Numerical Evaluation of Multivariate Contingent Claims," The Review of Financial Studies, Society for Financial Studies, vol. 2(2), pages 241-250.
    18. Clark, Peter K, 1973. "A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices," Econometrica, Econometric Society, vol. 41(1), pages 135-155, January.
    19. Wiggins, James B., 1987. "Option values under stochastic volatility: Theory and empirical estimates," Journal of Financial Economics, Elsevier, vol. 19(2), pages 351-372, December.
    20. Ball, Clifford A. & Roma, Antonio, 1994. "Stochastic Volatility Option Pricing," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 29(4), pages 589-607, December.
    21. Scott, Louis O., 1987. "Option Pricing when the Variance Changes Randomly: Theory, Estimation, and an Application," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 22(4), pages 419-438, December.
    22. Praetz, Peter D, 1972. "The Distribution of Share Price Changes," The Journal of Business, University of Chicago Press, vol. 45(1), pages 49-55, January.
    23. Hull, John C & White, Alan D, 1987. "The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
    24. Ho, Teng-Suan & Stapleton, Richard C & Subrahmanyam, Marti G, 1995. "Multivariate Binomial Approximations for Asset Prices with Nonstationary Variance and Covariance Characteristics," The Review of Financial Studies, Society for Financial Studies, vol. 8(4), pages 1125-1152.
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    Cited by:

    1. Richter, Anja, 2014. "Explicit solutions to quadratic BSDEs and applications to utility maximization in multivariate affine stochastic volatility models," Stochastic Processes and their Applications, Elsevier, vol. 124(11), pages 3578-3611.
    2. José Fonseca & Martino Grasselli & Claudio Tebaldi, 2007. "Option pricing when correlations are stochastic: an analytical framework," Review of Derivatives Research, Springer, vol. 10(2), pages 151-180, May.
    3. Gourieroux, C. & Monfort, A. & Sufana, R., 2010. "International money and stock market contingent claims," Journal of International Money and Finance, Elsevier, vol. 29(8), pages 1727-1751, December.
    4. C. Gourieroux, 2006. "Continuous Time Wishart Process for Stochastic Risk," Econometric Reviews, Taylor & Francis Journals, vol. 25(2-3), pages 177-217.
    5. JosE Da Fonseca & Martino Grasselli & Claudio Tebaldi, 2008. "A multifactor volatility Heston model," Quantitative Finance, Taylor & Francis Journals, vol. 8(6), pages 591-604.
    6. Branger, Nicole & Muck, Matthias & Seifried, Frank Thomas & Weisheit, Stefan, 2017. "Optimal portfolios when variances and covariances can jump," Journal of Economic Dynamics and Control, Elsevier, vol. 85(C), pages 59-89.
    7. Jacinto Marabel Romo, 2012. "Worst-Of Options And Correlation Skew Under A Stochastic Correlation Framework," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(07), pages 1-32.
    8. He, Yunhao & Leippold, Markus, 2020. "Short-run risk, business cycle, and the value premium," Journal of Economic Dynamics and Control, Elsevier, vol. 120(C).
    9. Georges Dionne & Genevieve Gauthier & Nadia Ouertani & Nabil Tahani, 2011. "Heterogeneous Basket Options Pricing Using Analytical Approximations," Multinational Finance Journal, Multinational Finance Journal, vol. 15(1-2), pages 47-85, March - J.
    10. Jun Ma, 2009. "A Stochastic Correlation Model with Mean Reversion for Pricing Multi-Asset Options," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 16(2), pages 97-109, June.
    11. Andreas Mühlbacher & Thomas Guhr, 2018. "Credit Risk Meets Random Matrices: Coping with Non-Stationary Asset Correlations," Risks, MDPI, vol. 6(2), pages 1-25, April.

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