IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1908.09640.html
   My bibliography  Save this paper

Expansion method for pricing foreign exchange options under stochastic volatility and interest rates

Author

Listed:
  • Kenji Nagami

Abstract

Some expansion methods have been proposed for approximately pricing options which has no exact closed formula. Benhamou et al. (2010) presents the smart expansion method that directly expands the expectation value of payoff function with respect to the volatility of volatility, then uses it to price options in the stochastic volatility model. In this paper, we apply their method to the stochastic volatility model with stochastic interest rates, and present the expansion formula for pricing options up to the second order. Then the numerical studies are performed to compare our approximation formula with the Monte-Carlo simulation. It is found that our formula shows the numerically comparable results with the method proposed by Grzelak et al. (2012) which uses the approximation of characteristic function.

Suggested Citation

  • Kenji Nagami, 2019. "Expansion method for pricing foreign exchange options under stochastic volatility and interest rates," Papers 1908.09640, arXiv.org.
    • Handle: RePEc:arx:papers:1908.09640
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1908.09640
    File Function: Latest version
    Download Restriction: no
    ---><---

    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. Lech A. Grzelak & Cornelis W. Oosterlee, 2012. "On Cross-Currency Models with Stochastic Volatility and Correlated Interest Rates," Applied Mathematical Finance, Taylor & Francis Journals, vol. 19(1), pages 1-35, February.
    3. Akihiko Takahashi & Toshihiro Yamada, 2015. "On Error Estimates for Asymptotic Expansions with Malliavin Weights: Application to Stochastic Volatility Model," Mathematics of Operations Research, INFORMS, vol. 40(3), pages 513-541, March.
    4. Grzelak, Lech & Oosterlee, Kees, 2009. "On The Heston Model with Stochastic Interest Rates," MPRA Paper 20620, University Library of Munich, Germany, revised 18 Jan 2010.
    5. Alan L. Lewis, 2000. "Option Valuation under Stochastic Volatility," Option Valuation under Stochastic Volatility, Finance Press, number ovsv, December.
    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. Fazlollah Soleymani & Andrey Itkin, 2019. "Pricing foreign exchange options under stochastic volatility and interest rates using an RBF--FD method," Papers 1903.00937, arXiv.org.
    2. Yijuan Liang & Xiuchuan Xu, 2019. "Variance and Dimension Reduction Monte Carlo Method for Pricing European Multi-Asset Options with Stochastic Volatilities," Sustainability, MDPI, vol. 11(3), pages 1-21, February.
    3. Singor, Stefan N. & Grzelak, Lech A. & van Bragt, David D.B. & Oosterlee, Cornelis W., 2013. "Pricing inflation products with stochastic volatility and stochastic interest rates," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 286-299.
    4. Benjamin Tin Chun Cheng, 2017. "Pricing and Hedging of Long-Dated Commodity Derivatives," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 2-2017.
    5. Alessandro Gnoatto & Martino Grasselli, 2013. "An analytic multi-currency model with stochastic volatility and stochastic interest rates," Papers 1302.7246, arXiv.org, revised Mar 2013.
    6. repec:uts:finphd:37 is not listed on IDEAS
    7. Cui, Zhenyu & Lars Kirkby, J. & Nguyen, Duy, 2017. "A general framework for discretely sampled realized variance derivatives in stochastic volatility models with jumps," European Journal of Operational Research, Elsevier, vol. 262(1), pages 381-400.
    8. Grzelak, Lech & Oosterlee, Kees, 2010. "An Equity-Interest Rate Hybrid Model With Stochastic Volatility and the Interest Rate Smile," MPRA Paper 20574, University Library of Munich, Germany.
    9. Darren Shannon & Grigorios Fountas, 2021. "Extending the Heston Model to Forecast Motor Vehicle Collision Rates," Papers 2104.11461, arXiv.org, revised May 2021.
    10. Christoffersen, Peter & Heston, Steven & Jacobs, Kris, 2010. "Option Anomalies and the Pricing Kernel," Working Papers 11-17, University of Pennsylvania, Wharton School, Weiss Center.
    11. Nicolas Langrené & Geoffrey Lee & Zili Zhu, 2016. "Switching To Nonaffine Stochastic Volatility: A Closed-Form Expansion For The Inverse Gamma Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(05), pages 1-37, August.
    12. Misha Beek & Michel Mandjes & Peter Spreij & Erik Winands, 2020. "Regime switching affine processes with applications to finance," Finance and Stochastics, Springer, vol. 24(2), pages 309-333, April.
    13. Bertram During & Christian Hendricks & James Miles, 2016. "Sparse grid high-order ADI scheme for option pricing in stochastic volatility models," Papers 1611.01379, arXiv.org.
    14. Rehez Ahlip & Laurence A. F. Park & Ante Prodan, 2017. "Pricing currency options in the Heston/CIR double exponential jump-diffusion model," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 4(01), pages 1-30, March.
    15. Björn Lutz, 2010. "Pricing of Derivatives on Mean-Reverting Assets," Lecture Notes in Economics and Mathematical Systems, Springer, number 978-3-642-02909-7, December.
    16. Lay Harold A. & Colgin Zane & Reshniak Viktor & Khaliq Abdul Q. M., 2018. "On the implementation of multilevel Monte Carlo simulation of the stochastic volatility and interest rate model using multi-GPU clusters," Monte Carlo Methods and Applications, De Gruyter, vol. 24(4), pages 309-321, December.
    17. Kim, Seong-Tae & Kim, Jeong-Hoon, 2020. "Stochastic elasticity of vol-of-vol and pricing of variance swaps," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 177(C), pages 420-440.
    18. Andrey Itkin, 2023. "The ATM implied skew in the ADO-Heston model," Papers 2309.15044, arXiv.org.
    19. Falko Baustian & Katev{r}ina Filipov'a & Jan Posp'iv{s}il, 2019. "Solution of option pricing equations using orthogonal polynomial expansion," Papers 1912.06533, arXiv.org, revised Jun 2020.
    20. Minqiang Li, 2015. "Derivatives Pricing on Integrated Diffusion Processes: A General Perturbation Approach," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 35(6), pages 582-595, June.
    21. 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.

    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:1908.09640. 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.