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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)

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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    Cited by:

    1. Pierre-Edouard Arrouy & Sophian Mehalla & Bernard Lapeyre & Alexandre Boumezoued, 2020. "Jacobi Stochastic Volatility factor for the Libor Market Model," Working Papers hal-02468583, HAL.
    2. 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.
    3. Long Teng & Matthias Ehrhardt & Michael Günther, 2017. "Numerical Simulation of the Heston Model under Stochastic Correlation," IJFS, MDPI, vol. 6(1), pages 1-16, December.
    4. Pierre-Edouard Arrouy & Alexandre Boumezoued & Bernard Lapeyre & Sophian Mehalla, 2022. "Jacobi stochastic volatility factor for the LIBOR market model," Finance and Stochastics, Springer, vol. 26(4), pages 771-823, October.
    5. Andrey Itkin, 2017. "Modelling stochastic skew of FX options using SLV models with stochastic spot/vol correlation and correlated jumps," Applied Mathematical Finance, Taylor & Francis Journals, vol. 24(6), pages 485-519, November.
    6. Ardian, Aldin & Kumral, Mustafa, 2020. "Incorporating stochastic correlations into mining project evaluation using the Jacobi process," Resources Policy, Elsevier, vol. 65(C).
    7. Gong, Xiaoli & Zhuang, Xintian, 2017. "Pricing foreign equity option under stochastic volatility tempered stable Lévy processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 483(C), pages 83-93.
    8. 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.
    9. Long Teng & Matthias Ehrhardt & Michael Günther, 2018. "Quanto Pricing In Stochastic Correlation Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(05), pages 1-20, August.
    10. László Márkus & Ashish Kumar, 2021. "Modelling Joint Behaviour of Asset Prices Using Stochastic Correlation," Methodology and Computing in Applied Probability, Springer, vol. 23(1), pages 341-354, March.
    11. Li, Zhe & Zhang, Wei-Guo & Liu, Yong-Jun, 2018. "European quanto option pricing in presence of liquidity risk," The North American Journal of Economics and Finance, Elsevier, vol. 45(C), pages 230-244.
    12. Tianyao Chen & Xue Cheng & Jingping Yang, 2019. "Common Decomposition of Correlated Brownian Motions and its Financial Applications," Papers 1907.03295, arXiv.org, revised Nov 2020.

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    More about this item

    Keywords

    Exotic option; Option pricing; Correlation risk; Portfolio; Random walk;
    All these keywords.

    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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