IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v251y2015icp1-13.html
   My bibliography  Save this article

FX options pricing in logarithmic mean-reversion jump-diffusion model with stochastic volatility

Author

Listed:
  • Zhong, Yinhui
  • Bao, Qunfang
  • Li, Shenghong

Abstract

As a tradable asset, foreign currency has the particular property of mean-reversion, which should be reasonably included in FX dynamic modeling. From observation of FX historical data, jump takes frequently and it should be considered as modeling factor as well. The implied volatility smile/skew in FX options market is very significant, thus stochastic volatility is necessary in FX options models. Combining the three factors together, a new model named logarithmic mean-reversion jump-diffusion model with stochastic volatility is constructed. Conditional characteristic function under this model is derived by expectation approach, and Attari’s pricing formula is further attained. At last, we give some empirical results to show the good performance of our model.

Suggested Citation

  • Zhong, Yinhui & Bao, Qunfang & Li, Shenghong, 2015. "FX options pricing in logarithmic mean-reversion jump-diffusion model with stochastic volatility," Applied Mathematics and Computation, Elsevier, vol. 251(C), pages 1-13.
    • Handle: RePEc:eee:apmaco:v:251:y:2015:i:c:p:1-13
    DOI: 10.1016/j.amc.2014.11.040
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S009630031401563X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2014.11.040?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. S. G. Kou & Hui Wang, 2004. "Option Pricing Under a Double Exponential Jump Diffusion Model," Management Science, INFORMS, vol. 50(9), pages 1178-1192, September.
    3. Jorion, Philippe & Sweeney, Richard J., 1996. "Mean reversion in real exchange rates: evidence and implications for forecasting," Journal of International Money and Finance, Elsevier, vol. 15(4), pages 535-550, August.
    4. Bates, David S, 1996. "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options," The Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 69-107.
    5. Bjørn Eraker & Michael Johannes & Nicholas Polson, 2003. "The Impact of Jumps in Volatility and Returns," Journal of Finance, American Finance Association, vol. 58(3), pages 1269-1300, June.
    6. C. H. Hui & C. F. Lo, 2006. "Currency barrier option pricing with mean reversion," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 26(10), pages 939-958, October.
    7. Ekvall, Niklas & Peter Jennergren, L. & Naslund, Bertil, 1997. "Currency option pricing with mean reversion and uncovered interest parity: A revision of the Garman-Kohlhagen model," European Journal of Operational Research, Elsevier, vol. 100(1), pages 41-59, July.
    8. repec:bla:jfinan:v:59:y:2004:i:3:p:1367-1404 is not listed on IDEAS
    9. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    10. Garman, Mark B. & Kohlhagen, Steven W., 1983. "Foreign currency option values," Journal of International Money and Finance, Elsevier, vol. 2(3), pages 231-237, December.
    11. Cho-hoi Hui, 2006. "Currency Barrier Option Pricing with Mean Reversion," Working Papers 0605, Hong Kong Monetary Authority.
    12. Hoi Ying Wong & Chun Man Chan, 2008. "Turbo warrants under stochastic volatility," Quantitative Finance, Taylor & Francis Journals, vol. 8(7), pages 739-751.
    13. Sweeney, Richard J., 2006. "Mean Reversion in G-10 Nominal Exchange Rates," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 41(3), pages 685-708, September.
    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. Ying Chang & Yiming Wang & Sumei Zhang, 2021. "Option Pricing under Double Heston Jump-Diffusion Model with Approximative Fractional Stochastic Volatility," Mathematics, MDPI, vol. 9(2), pages 1-10, January.

    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. Chiu, Hsin-Yu & Chen, Ting-Fu, 2020. "Impact of volatility jumps in a mean-reverting model: Derivative pricing and empirical evidence," The North American Journal of Economics and Finance, Elsevier, vol. 52(C).
    2. Wong, Hoi Ying & Lo, Yu Wai, 2009. "Option pricing with mean reversion and stochastic volatility," European Journal of Operational Research, Elsevier, vol. 197(1), pages 179-187, August.
    3. 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.
    4. Michael C. Fu & Bingqing Li & Rongwen Wu & Tianqi Zhang, 2020. "Option Pricing Under a Discrete-Time Markov Switching Stochastic Volatility with Co-Jump Model," Papers 2006.15054, arXiv.org.
    5. Carr, Peter & Wu, Liuren, 2007. "Stochastic skew in currency options," Journal of Financial Economics, Elsevier, vol. 86(1), pages 213-247, October.
    6. Liming Feng & Vadim Linetsky, 2008. "Pricing Options in Jump-Diffusion Models: An Extrapolation Approach," Operations Research, INFORMS, vol. 56(2), pages 304-325, April.
    7. Chen, Jian & Qi, Shuyuan, 2024. "Limit-hitting exciting effects: Modeling jump dependencies in stock markets adhering to daily price-limit rules," Journal of Banking & Finance, Elsevier, vol. 163(C).
    8. Frances Shaw & Finbarr Murphy & Fergal G. O’Brien, 2016. "Jumps in Euribor and the effect of ECB monetary policy announcements," Environment Systems and Decisions, Springer, vol. 36(2), pages 142-157, June.
    9. Björn Lutz, 2010. "Pricing of Derivatives on Mean-Reverting Assets," Lecture Notes in Economics and Mathematical Systems, Springer, number 978-3-642-02909-7, October.
    10. Ako Doffou & Jimmy E. Hilliard, 2001. "Pricing Currency Options Under Stochastic Interest Rates And Jump-Diffusion Processes," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 24(4), pages 565-585, December.
    11. Maciej Kostrzewski & Jadwiga Kostrzewska, 2021. "The Impact of Forecasting Jumps on Forecasting Electricity Prices," Energies, MDPI, vol. 14(2), pages 1-17, January.
    12. Shin-Yun Wang & Ming-Che Chuang & Shih-Kuei Lin & So-De Shyu, 2021. "Option pricing under stock market cycles with jump risks: evidence from the S&P 500 index," Review of Quantitative Finance and Accounting, Springer, vol. 56(1), pages 25-51, January.
    13. Cosma, Antonio & Galluccio, Stefano & Pederzoli, Paola & Scaillet, Olivier, 2020. "Early Exercise Decision in American Options with Dividends, Stochastic Volatility, and Jumps," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 55(1), pages 331-356, February.
    14. Antonio Cosma & Stefano Galluccio & Paola Pederzoli & O. Scaillet, 2012. "Valuing American Options Using Fast Recursive Projections," Swiss Finance Institute Research Paper Series 12-26, Swiss Finance Institute.
    15. Neumann, Maximilian & Prokopczuk, Marcel & Wese Simen, Chardin, 2016. "Jump and variance risk premia in the S&P 500," Journal of Banking & Finance, Elsevier, vol. 69(C), pages 72-83.
    16. Chris Brooks & Marcel Prokopczuk, 2013. "The dynamics of commodity prices," Quantitative Finance, Taylor & Francis Journals, vol. 13(4), pages 527-542, March.
    17. Ostap Okhrin & Michael Rockinger & Manuel Schmid, 2023. "Distributional properties of continuous time processes: from CIR to bates," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 107(3), pages 397-419, September.
    18. Lian, Yu-Min & Chen, Jun-Home, 2022. "Foreign exchange option pricing under regime switching with asymmetrical jumps," Finance Research Letters, Elsevier, vol. 46(PA).
    19. Jondeau, Eric & Rockinger, Michael, 2000. "Reading the smile: the message conveyed by methods which infer risk neutral densities," Journal of International Money and Finance, Elsevier, vol. 19(6), pages 885-915, December.
    20. Feng, Chengxiao & Tan, Jie & Jiang, Zhenyu & Chen, Shuang, 2020. "A generalized European option pricing model with risk management," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).

    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:eee:apmaco:v:251:y:2015:i:c:p:1-13. 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.