IDEAS home Printed from https://ideas.repec.org/a/gam/jstats/v8y2025i3p65-d1704566.html

Local Stochastic Correlation Models for Derivative Pricing

Author

Listed:
  • Marcos Escobar-Anel

    (Department of Statistical and Actuarial Sciences, Western University, 1151 Richmond Street, London, ON N6A 5B7, Canada)

Abstract

This paper reveals a simple methodology to create local-correlation models suitable for the closed-form pricing of two-asset financial derivatives. The multivariate models are built to ensure two conditions. First, marginals follow desirable processes, e.g., we choose the Geometric Brownian Motion (GBM), popular for stock prices. Second, the payoff of the derivative should follow a desired one-dimensional process. These conditions lead to a specific choice of the dependence structure in the form of a local-correlation model. Two popular multi-asset options are entertained: a spread option and a basket option.

Suggested Citation

  • Marcos Escobar-Anel, 2025. "Local Stochastic Correlation Models for Derivative Pricing," Stats, MDPI, vol. 8(3), pages 1-10, July.
    • Handle: RePEc:gam:jstats:v:8:y:2025:i:3:p:65-:d:1704566
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2571-905X/8/3/65/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2571-905X/8/3/65/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. JosE Da Fonseca & Martino Grasselli & Claudio Tebaldi, 2008. "A multifactor volatility Heston model," Quantitative Finance, Taylor & Francis Journals, vol. 8(6), pages 591-604.
    2. Marcos Escobar & Pablo Olivares, 2013. "Pricing of mountain range derivatives under a principal component stochastic volatility model," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 29(1), pages 31-44, January.
    3. Inci, A. Can & Li, H.C. & McCarthy, Joseph, 2011. "Financial contagion: A local correlation analysis," Research in International Business and Finance, Elsevier, vol. 25(1), pages 11-25, January.
    4. Beckers, Stan, 1980. "The Constant Elasticity of Variance Model and Its Implications for Option Pricing," Journal of Finance, American Finance Association, vol. 35(3), pages 661-673, June.
    5. 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.
    6. Escobar-Anel, Marcos, 2025. "A generalized constant elasticity of volatility and correlation ratio (CEVC) model: Empirical evidence and application for portfolio optimization," Economic Modelling, Elsevier, vol. 147(C).
    7. 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.
    8. Elie Bouri & Rangan Gupta & Shixuan Wang, 2022. "Nonlinear contagion between stock and real estate markets: International evidence from a local Gaussian correlation approach," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 27(2), pages 2089-2109, April.
    9. 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.
    10. Rama Cont & Romain Deguest, 2013. "Equity Correlations Implied By Index Options: Estimation And Model Uncertainty Analysis," Post-Print hal-00835272, HAL.
    11. Jun Liu, 2007. "Portfolio Selection in Stochastic Environments," The Review of Financial Studies, Society for Financial Studies, vol. 20(1), pages 1-39, January.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Marcos Escobar & Christoph Gschnaidtner, 2018. "A multivariate stochastic volatility model with applications in the foreign exchange market," Review of Derivatives Research, Springer, vol. 21(1), pages 1-43, April.
    2. Escobar-Anel, Marcos, 2025. "A generalized constant elasticity of volatility and correlation ratio (CEVC) model: Empirical evidence and application for portfolio optimization," Economic Modelling, Elsevier, vol. 147(C).
    3. 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.
    4. Wen Su, 2021. "Default Distances Based on the CEV-KMV Model," Papers 2107.10226, arXiv.org, revised May 2022.
    5. Gaetano Bua & Daniele Marazzina, 2021. "On the application of Wishart process to the pricing of equity derivatives: the multi-asset case," Computational Management Science, Springer, vol. 18(2), pages 149-176, June.
    6. Shuang Xiao & Guo Li & Yunjing Jia, 2017. "Estimating the Constant Elasticity of Variance Model with Data-Driven Markov Chain Monte Carlo Methods," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 34(01), pages 1-23, February.
    7. Fan, Chenxi & Luo, Xingguo & Wu, Qingbiao, 2017. "Stochastic volatility vs. jump diffusions: Evidence from the Chinese convertible bond market," International Review of Economics & Finance, Elsevier, vol. 49(C), pages 1-16.
    8. Takashi Kato & Jun Sekine & Kenichi Yoshikawa, 2013. "Order Estimates for the Exact Lugannani-Rice Expansion," Papers 1310.3347, arXiv.org, revised Jun 2014.
    9. Zheng, Xiaoxiao & Zhou, Jieming & Sun, Zhongyang, 2016. "Robust optimal portfolio and proportional reinsurance for an insurer under a CEV model," Insurance: Mathematics and Economics, Elsevier, vol. 67(C), pages 77-87.
    10. Zhang, Sumei & Gao, Xiong, 2019. "An asymptotic expansion method for geometric Asian options pricing under the double Heston model," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 1-9.
    11. Nicole Branger & Matthias Muck & Stefan Weisheit, 2019. "Correlation risk and international portfolio choice," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 39(1), pages 128-146, January.
    12. El-Khatib, Youssef & Goutte, Stephane & Makumbe, Zororo S. & Vives, Josep, 2023. "A hybrid stochastic volatility model in a Lévy market," International Review of Economics & Finance, Elsevier, vol. 85(C), pages 220-235.
    13. repec:uts:finphd:41 is not listed on IDEAS
    14. Alessandro Gnoatto & Martino Grasselli, 2011. "The explicit Laplace transform for the Wishart process," Papers 1107.2748, arXiv.org, revised Aug 2013.
    15. Marcos Escobar & Daniel Krause & Rudi Zagst, 2016. "Stochastic covariance and dimension reduction in the pricing of basket options," Review of Derivatives Research, Springer, vol. 19(3), pages 165-200, October.
    16. Kensuke Kato & Nobuhiro Nakamura, 2024. "PDE-Based Bayesian Inference of CEV Dynamics for Credit Risk in Stock Prices," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 31(2), pages 389-421, June.
    17. Olesia Verchenko, 2011. "Testing option pricing models: complete and incomplete markets," Discussion Papers 38, Kyiv School of Economics.
    18. David S. Bates, 1995. "Testing Option Pricing Models," NBER Working Papers 5129, National Bureau of Economic Research, Inc.
    19. Da Fonseca, José, 2016. "On moment non-explosions for Wishart-based stochastic volatility models," European Journal of Operational Research, Elsevier, vol. 254(3), pages 889-894.
    20. Jacinto Marabel Romo, 2016. "Is the information obtained from European options on equally weighted baskets enough to determine the prices of exotic derivatives such as worst-of options?," Review of Derivatives Research, Springer, vol. 19(1), pages 65-83, April.
    21. Simon Ellersgaard & Martin Tegnér, 2018. "Stochastic volatility for utility maximizers — A martingale approach," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 5(01), pages 1-39, March.

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jstats:v:8:y:2025:i:3:p:65-:d:1704566. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.