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Pricing Foreign Equity Options with Stochastic Correlation and Volatility

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  • Jun Ma

    (Temasek Laboratories, National University of Singapore)

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    Abstract

    A new class of foreign equity option pricing model is suggested that not only allows for the volatility but also for the correlation coefficient to vary stochastically over time. A modified Jacobi process is proposed to evaluate risk premium of the stochastic correlation, and a partial differential equation to price the correlation risk for the foreign equity has been set up, whose solution has been compared with the one with constant correlation. Since taking into account the stochastic volatility gives rise to more dimensions that produce more difficulty in numerical implementation of partial differential equation and Monte carlo, we figure out a series solution for pricing options under the correlation risk.

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    Bibliographic Info

    Article provided by Society for AEF in its journal Annals of Economics and Finance.

    Volume (Year): 10 (2009)
    Issue (Month): 2 (November)
    Pages: 303-327

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    Handle: RePEc:cuf:journl:y:2009:v:10:i:2:p:303-327

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    Related research

    Keywords: Exotic option; Option pricing; Correlation risk; Portfolio; Random walk;

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    1. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, Econometric Society, vol. 50(4), pages 987-1007, July.
    2. Robert C. Merton, 1973. "Theory of Rational Option Pricing," Bell Journal of Economics, The RAND Corporation, The RAND Corporation, vol. 4(1), pages 141-183, Spring.
    3. Joan Jasiak & R. Sufana & C. Gourieroux, 2005. "The Wishart Autoregressive Process of Multivariate Stochastic Volatility," Working Papers, York University, Department of Economics 2005_2, York University, Department of Economics.
    4. 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, Cambridge University Press, vol. 22(04), pages 419-438, December.
    5. Lawrence R. Glosten & Ravi Jagannathan & David E. Runkle, 1993. "On the relation between the expected value and the volatility of the nominal excess return on stocks," Staff Report, Federal Reserve Bank of Minneapolis 157, Federal Reserve Bank of Minneapolis.
    6. Andrea Buraschi & Paolo Porchia & Fabio Trojani, 2010. "Correlation Risk and Optimal Portfolio Choice," Journal of Finance, American Finance Association, American Finance Association, vol. 65(1), pages 393-420, 02.
    7. Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, American Finance Association, vol. 42(2), pages 281-300, June.
    8. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
    9. Ball, Clifford A. & Roma, Antonio, 1994. "Stochastic Volatility Option Pricing," Journal of Financial and Quantitative Analysis, Cambridge University Press, Cambridge University Press, vol. 29(04), pages 589-607, December.
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