IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1404.4028.html

Stochastic Spot/Volatility Correlation in Stochastic Volatility Models and Barrier Option Pricing

Author

Listed:
  • Mark Higgins

Abstract

Most models for barrier pricing are designed to let a market maker tune the model-implied covariance between moves in the asset spot price and moves in the implied volatility skew. This is often implemented with a local volatility/stochastic volatility mixture model, where the mixture parameter tunes that covariance. This paper defines an alternate model where the spot/volatility correlation is a separate mean-reverting stochastic variable which is itself correlated with spot. We also develop an efficient approximation for barrier option and one touch pricing in the model based on semi-static vega replication and compare it with Monte Carlo pricing. The approximation works well in markets where the risk neutral drift is modest.

Suggested Citation

  • Mark Higgins, 2014. "Stochastic Spot/Volatility Correlation in Stochastic Volatility Models and Barrier Option Pricing," Papers 1404.4028, arXiv.org.
    • Handle: RePEc:arx:papers:1404.4028
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1404.4028
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. repec:bla:jfinan:v:53:y:1998:i:3:p:1165-1190 is not listed on IDEAS
    2. Peter G. Zhang, 1998. "Hedging Exotic Options," World Scientific Book Chapters, in: Exotic Options A Guide to Second Generation Options, chapter 35, pages 639-643, World Scientific Publishing Co. Pte. Ltd..
    3. 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.
    4. Carr, Peter & Wu, Liuren, 2007. "Stochastic skew in currency options," Journal of Financial Economics, Elsevier, vol. 86(1), pages 213-247, October.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.

    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. Christoffersen, Peter & Heston, Steven & Jacobs, Kris, 2010. "Option Anomalies and the Pricing Kernel," Working Papers 11-17, University of Pennsylvania, Wharton School, Weiss Center.
    2. Almut Veraart & Luitgard Veraart, 2012. "Stochastic volatility and stochastic leverage," Annals of Finance, Springer, vol. 8(2), pages 205-233, May.
    3. Ammann, Manuel & Buesser, Ralf, 2013. "Variance risk premiums in foreign exchange markets," Journal of Empirical Finance, Elsevier, vol. 23(C), pages 16-32.
    4. Park, Yang-Ho, 2016. "The effects of asymmetric volatility and jumps on the pricing of VIX derivatives," Journal of Econometrics, Elsevier, vol. 192(1), pages 313-328.
    5. Carpinteyro, Martha & Venegas-Martínez, Francisco & Martínez-García, Miguel Ángel, 2018. "Modeling Returns of Stock Indexes through Fractional Brownian Motion Combined with Jump Processes and Modulated by Markov Chains," MPRA Paper 90549, University Library of Munich, Germany.
    6. Bingxin Li, 2020. "Option-implied filtering: evidence from the GARCH option pricing model," Review of Quantitative Finance and Accounting, Springer, vol. 54(3), pages 1037-1057, April.
    7. 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.
    8. Kilic, Erdem, 2017. "Contagion effects of U.S. Dollar and Chinese Yuan in forward and spot foreign exchange markets," Economic Modelling, Elsevier, vol. 62(C), pages 51-67.
    9. Du Du & Dan Luo, 2019. "The Pricing of Jump Propagation: Evidence from Spot and Options Markets," Management Science, INFORMS, vol. 67(5), pages 2360-2387, May.
    10. Jie-Cao He & Hsing-Hua Chang & Ting-Fu Chen & Shih-Kuei Lin, 2023. "Upside and downside correlated jump risk premia of currency options and expected returns," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 9(1), pages 1-58, December.
    11. Imma Valentina Curato & Simona Sanfelici, 2019. "Stochastic leverage effect in high-frequency data: a Fourier based analysis," Papers 1910.06660, arXiv.org, revised Mar 2021.
    12. Kenichiro Shiraya & Cong Wang & Akira Yamazaki, 2021. "A general control variate method for time-changed Lévy processes: An application to options pricing," CARF F-Series CARF-F-499, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    13. Dammak, Wael & Hamad, Salah Ben & de Peretti, Christian & Eleuch, Hichem, 2023. "Pricing of European currency options considering the dynamic information costs," Global Finance Journal, Elsevier, vol. 58(C).
    14. Beber, Alessandro & Breedon, Francis & Buraschi, Andrea, 2010. "Differences in beliefs and currency risk premiums," Journal of Financial Economics, Elsevier, vol. 98(3), pages 415-438, December.
    15. Carpinteyro, Martha & Venegas Martínez, Francisco & Martínez García, Miguel Ángel, 2019. "Modelado de rendimientos de índices bursátiles mediante movimiento fraccional browniano combinado con procesos de saltos y modulado por cadenas de Markov / Modeling Returns of Stock Indexes through Fr," Estocástica: finanzas y riesgo, Departamento de Administración de la Universidad Autónoma Metropolitana Unidad Azcapotzalco, vol. 9(2), pages 163-180, julio-dic.
    16. Peter Christoffersen & Steven Heston & Kris Jacobs, 2009. "The Shape and Term Structure of the Index Option Smirk: Why Multifactor Stochastic Volatility Models Work So Well," Management Science, INFORMS, vol. 55(12), pages 1914-1932, December.
    17. José Da Fonseca & Edem Dawui, 2021. "Semivariance and semiskew risk premiums in currency markets," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 41(3), pages 290-324, March.
    18. Chulmin Kang & Wanmo Kang & Jong Mun Lee, 2017. "Exact Simulation of the Wishart Multidimensional Stochastic Volatility Model," Operations Research, INFORMS, vol. 65(5), pages 1190-1206, October.
    19. Jan Maruhn & Morten Nalholm & Matthias Fengler, 2011. "Static hedges for reverse barrier options with robustness against skew risk: an empirical analysis," Quantitative Finance, Taylor & Francis Journals, vol. 11(5), pages 711-727.
    20. Peter Christoffersen & Mathieu Fournier & Kris Jacobs, 2018. "The Factor Structure in Equity Options," The Review of Financial Studies, Society for Financial Studies, vol. 31(2), pages 595-637.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:arx:papers:1404.4028. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.