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Pricing Foreign Equity Options with Stochastic Correlation and Volatility

Author

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  • Jun Ma

    (Temasek Laboratories, National University of Singapore)

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.

Suggested Citation

  • Jun Ma, 2009. "Pricing Foreign Equity Options with Stochastic Correlation and Volatility," Annals of Economics and Finance, Society for AEF, vol. 10(2), pages 303-327, November.
  • Handle: RePEc:cuf:journl:y:2009:v:10:i:2:p:303-327
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    References listed on IDEAS

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    1. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters,in: Theory Of Valuation, chapter 8, pages 229-288 World Scientific Publishing Co. Pte. Ltd..
    2. Baz,Jamil & Chacko,George, 2004. "Financial Derivatives," Cambridge Books, Cambridge University Press, number 9780521815109.
    3. Andrea Buraschi & Paolo Porchia & Fabio Trojani, 2010. "Correlation Risk and Optimal Portfolio Choice," Journal of Finance, American Finance Association, vol. 65(1), pages 393-420, February.
    4. 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.
    5. Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. " On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December.
    6. Ball, Clifford A. & Roma, Antonio, 1994. "Stochastic Volatility Option Pricing," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 29(04), pages 589-607, December.
    7. 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(04), pages 419-438, December.
    8. 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.
    9. 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.
    10. Gourieroux, C. & Jasiak, J. & Sufana, R., 2009. "The Wishart Autoregressive process of multivariate stochastic volatility," Journal of Econometrics, Elsevier, vol. 150(2), pages 167-181, June.
    11. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
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    Citations

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    Cited by:

    1. Long Teng & Matthias Ehrhardt & Michael Günther, 2016. "On The Heston Model With Stochastic Correlation," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(06), pages 1-25, September.
    2. repec:gam:jijfss:v:6:y:2017:i:1:p:3-:d:124327 is not listed on IDEAS
    3. Andrey Itkin, 2017. "Modeling stochastic skew of FX options using SLV models with stochastic spot/vol correlation and correlated jumps," Papers 1701.02821, arXiv.org, revised Jan 2017.
    4. repec:eee:phsmap:v:483:y:2017:i:c:p:83-93 is not listed on IDEAS
    5. Sun, Qi & Xu, Weidong, 2015. "Pricing foreign equity option with stochastic volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 437(C), pages 89-100.

    More about this item

    Keywords

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

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects

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