IDEAS home Printed from https://ideas.repec.org/a/wly/jnljam/v2013y2013i1n875606.html

Fast Fourier Transform Based Power Option Pricing with Stochastic Interest Rate, Volatility, and Jump Intensity

Author

Listed:
  • Jiexiang Huang
  • Wenli Zhu
  • Xinfeng Ruan

Abstract

Firstly, we present a more general and realistic double‐exponential jump model with stochastic volatility, interest rate, and jump intensity. Using Feynman‐Kac formula, we obtain a partial integrodifferential equation (PIDE), with respect to the moment generating function of log underlying asset price, which exists an affine solution. Then, we employ the fast Fourier Transform (FFT) method to obtain the approximate numerical solution of a power option which is conveniently designed with different risks or prices. Finally, we find the FFT method to compute that our option price has better stability, higher accuracy, and faster speed, compared to Monte Carlo approach.

Suggested Citation

  • Jiexiang Huang & Wenli Zhu & Xinfeng Ruan, 2013. "Fast Fourier Transform Based Power Option Pricing with Stochastic Interest Rate, Volatility, and Jump Intensity," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnljam:v:2013:y:2013:i:1:n:875606
    DOI: 10.1155/2013/875606
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2013/875606
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2013/875606?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
    ---><---

    References listed on IDEAS

    as
    1. Peter G. Zhang, 1995. "An introduction to exotic options," European Financial Management, European Financial Management Association, vol. 1(1), pages 87-95, March.
    2. Chang, Charles & Fuh, Cheng-Der & Lin, Shih-Kuei, 2013. "A tale of two regimes: Theory and empirical evidence for a Markov-modulated jump diffusion model of equity returns and derivative pricing implications," Journal of Banking & Finance, Elsevier, vol. 37(8), pages 3204-3217.
    3. Alan L. Lewis, 2000. "Option Valuation under Stochastic Volatility," Option Valuation under Stochastic Volatility, Finance Press, number ovsv.
    4. 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.
    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. 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. Manley, Bruce & Niquidet, Kurt, 2010. "What is the relevance of option pricing for forest valuation in New Zealand?," Forest Policy and Economics, Elsevier, vol. 12(4), pages 299-307, April.
    3. 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.
    4. repec:uts:finphd:40 is not listed on IDEAS
    5. Emmanuel Coffie, 2022. "Numerical Method for Highly Non-linear Mean-reverting Asset Price Model with CEV-type Process," Papers 2205.00634, arXiv.org.
    6. Silva-Correa, María de los Ángeles & Martínez-Marca, José Luís & Venegas-Martínez, Francisco, 2016. "Impacto del mercado de derivados en la política monetaria: un modelo de volatilidad estocástica [Impact of the Derivatives Market on Monetary Policy: A Stochastic Volatility Model]," MPRA Paper 75705, University Library of Munich, Germany.
    7. Darae Jeong & Minhyun Yoo & Changwoo Yoo & Junseok Kim, 2019. "A Hybrid Monte Carlo and Finite Difference Method for Option Pricing," Computational Economics, Springer;Society for Computational Economics, vol. 53(1), pages 111-124, January.
    8. Peter Carr & Jian Sun, 2007. "A new approach for option pricing under stochastic volatility," Review of Derivatives Research, Springer, vol. 10(2), pages 87-150, May.
    9. Alexander Lipton, 2024. "Hydrodynamics of Markets:Hidden Links Between Physics and Finance," Papers 2403.09761, arXiv.org.
    10. Shane Miller, 2007. "Pricing of Contingent Claims Under the Real-World Measure," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 2-2007, January-A.
    11. Alexander Lipton, 2023. "Kelvin Waves, Klein-Kramers and Kolmogorov Equations, Path-Dependent Financial Instruments: Survey and New Results," Papers 2309.04547, arXiv.org.
    12. Gabriel Drimus & Walter Farkas, 2013. "Local volatility of volatility for the VIX market," Review of Derivatives Research, Springer, vol. 16(3), pages 267-293, October.
    13. Kevin John Fergusson, 2018. "Less-Expensive Pricing and Hedging of Extreme-Maturity Interest Rate Derivatives and Equity Index Options Under the Real-World Measure," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 3-2018, January-A.
    14. Shane Miller, 2007. "Pricing of Contingent Claims Under the Real-World Measure," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 25, July-Dece.
    15. Alexander Lipton & Artur Sepp, 2022. "Toward an efficient hybrid method for pricing barrier options on assets with stochastic volatility," Papers 2202.07849, arXiv.org.
    16. Minqiang Li, 2010. "A quasi-analytical interpolation method for pricing American options under general multi-dimensional diffusion processes," Review of Derivatives Research, Springer, vol. 13(2), pages 177-217, July.
    17. Barone-Adesi, Giovanni & Rasmussen, Henrik & Ravanelli, Claudia, 2005. "An option pricing formula for the GARCH diffusion model," Computational Statistics & Data Analysis, Elsevier, vol. 49(2), pages 287-310, April.
    18. Ai[diaeresis]t-Sahalia, Yacine & Kimmel, Robert, 2007. "Maximum likelihood estimation of stochastic volatility models," Journal of Financial Economics, Elsevier, vol. 83(2), pages 413-452, February.
    19. Frédéric Abergel & Riadh Zaatour, 2012. "What drives option prices ?," Post-Print hal-00687675, HAL.
    20. Kim, Jerim & Kim, Bara & Moon, Kyoung-Sook & Wee, In-Suk, 2012. "Valuation of power options under Heston's stochastic volatility model," Journal of Economic Dynamics and Control, Elsevier, vol. 36(11), pages 1796-1813.
    21. repec:hal:wpaper:hal-00687675 is not listed on IDEAS
    22. 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.

    More about this item

    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:wly:jnljam:v:2013:y:2013:i:1:n:875606. 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: Wiley Content Delivery (email available below). General contact details of provider: https://onlinelibrary.wiley.com/journal/4185 .

    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.