IDEAS home Printed from https://ideas.repec.org/a/wsi/ijtafx/v15y2012i05ns0219024912500379.html
   My bibliography  Save this article

Fourier Transform Methods For Regime-Switching Jump-Diffusions And The Pricing Of Forward Starting Options

Author

Listed:
  • ALESSANDRO RAMPONI

    (Department of Economics and Finance, University of Rome, Tor Vergata, via Columbia, 2, 00133, Rome, Italy)

Abstract

In this paper we consider a jump-diffusion dynamic whose parameters are driven by a continuous time and stationary Markov Chain on a finite state space as a model for the underlying of European contingent claims. For this class of processes we firstly outline the Fourier transform method both in log-price and log-strike to efficiently calculate the value of various types of options and as a concrete example of application, we present some numerical results within a two-state regime switching version of the Merton jump-diffusion model. Then we develop a closed-form solution to the problem of pricing a Forward Starting Option and use this result to approximate the value of such a derivative in a general stochastic volatility framework.

Suggested Citation

  • Alessandro Ramponi, 2012. "Fourier Transform Methods For Regime-Switching Jump-Diffusions And The Pricing Of Forward Starting Options," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(05), pages 1-26.
    • Handle: RePEc:wsi:ijtafx:v:15:y:2012:i:05:n:s0219024912500379
    DOI: 10.1142/S0219024912500379
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0219024912500379
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0219024912500379?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 look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Giuseppe Di Graziano & L. C. G. Rogers, 2009. "Equity with Markov-modulated dividends," Quantitative Finance, Taylor & Francis Journals, vol. 9(1), pages 19-26.
    2. Friedrich Hubalek & Jan Kallsen & Leszek Krawczyk, 2006. "Variance-optimal hedging for processes with stationary independent increments," Papers math/0607112, arXiv.org.
    3. Ernst Eberlein & Kathrin Glau & Antonis Papapantoleon, 2010. "Analysis of Fourier Transform Valuation Formulas and Applications," Applied Mathematical Finance, Taylor & Francis Journals, vol. 17(3), pages 211-240.
    4. Daniel Dufresne & Jose Garrido & Manuel Morales, 2009. "Fourier Inversion Formulas in Option Pricing and Insurance," Methodology and Computing in Applied Probability, Springer, vol. 11(3), pages 359-383, September.
    5. Biagini, Francesca & Bregman, Yuliya & Meyer-Brandis, Thilo, 2008. "Pricing of catastrophe insurance options written on a loss index with reestimation," Insurance: Mathematics and Economics, Elsevier, vol. 43(2), pages 214-222, 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. Cui, Zhenyu & Kirkby, J. Lars & Nguyen, Duy, 2017. "Equity-linked annuity pricing with cliquet-style guarantees in regime-switching and stochastic volatility models with jumps," Insurance: Mathematics and Economics, Elsevier, vol. 74(C), pages 46-62.
    2. Alessandro Ramponi, 2016. "On a Transform Method for the Efficient Computation of Conditional V@R (and V@R) with Application to Loss Models with Jumps and Stochastic Volatility," Methodology and Computing in Applied Probability, Springer, vol. 18(2), pages 575-596, June.
    3. Alessandro Ramponi, 2022. "Spread Option Pricing in Regime-Switching Jump Diffusion Models," Mathematics, MDPI, vol. 10(9), pages 1-15, May.
    4. F. Antonelli & A. Ramponi & S. Scarlatti, 2016. "Random Time Forward-Starting Options," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(08), pages 1-25, December.
    5. Yu Yang & Yonghong Wu & Benchawan Wiwatanapataphee, 2020. "Time-consistent mean–variance asset-liability management in a regime-switching jump-diffusion market," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 34(4), pages 401-427, December.
    6. J. Lars Kirkby & Duy Nguyen, 2020. "Efficient Asian option pricing under regime switching jump diffusions and stochastic volatility models," Annals of Finance, Springer, vol. 16(3), pages 307-351, September.

    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. Ernst Eberlein & Kathrin Glau & Antonis Papapantoleon, 2008. "Analysis of Fourier transform valuation formulas and applications," Papers 0809.3405, arXiv.org, revised Sep 2009.
    2. St'ephane Goutte & Nadia Oudjane & Francesco Russo, 2013. "Variance optimal hedging for continuous time additive processes and applications," Papers 1302.1965, arXiv.org.
    3. Wang, Xingchun, 2020. "Catastrophe equity put options with floating strike prices," The North American Journal of Economics and Finance, Elsevier, vol. 54(C).
    4. Marco Nicolosi & Flavio Angelini & Stefano Herzel, 2018. "Portfolio management with benchmark related incentives under mean reverting processes," Annals of Operations Research, Springer, vol. 266(1), pages 373-394, July.
    5. Ismail Laachir & Francesco Russo, 2016. "BSDEs, càdlàg martingale problems and orthogonalisation under basis risk," Post-Print hal-01086227, HAL.
    6. Asai, Manabu & McAleer, Michael, 2015. "Leverage and feedback effects on multifactor Wishart stochastic volatility for option pricing," Journal of Econometrics, Elsevier, vol. 187(2), pages 436-446.
    7. Tankov, Peter & Voltchkova, Ekaterina, 2009. "Asymptotic analysis of hedging errors in models with jumps," Stochastic Processes and their Applications, Elsevier, vol. 119(6), pages 2004-2027, June.
    8. Aleksandar Mijatovi'c & Martijn Pistorius, 2009. "Exotic derivatives under stochastic volatility models with jumps," Papers 0912.2595, arXiv.org, revised Oct 2010.
    9. Mitra, Sovan, 2013. "Operational risk of option hedging," Economic Modelling, Elsevier, vol. 33(C), pages 194-203.
    10. Martijn Pistorius & Johannes Stolte, 2012. "Fast computation of vanilla prices in time-changed models and implied volatilities using rational approximations," Papers 1203.6899, arXiv.org.
    11. Michael Schmutz & Thomas Zürcher, 2014. "Static Hedging with Traffic Light Options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 34(7), pages 690-702, July.
    12. Thilini Mahanama & Abootaleb Shirvani & Svetlozar Rachev, 2022. "A Natural Disasters Index," Environmental Economics and Policy Studies, Springer;Society for Environmental Economics and Policy Studies - SEEPS, vol. 24(2), pages 263-284, April.
    13. Jan Kallsen & Richard Vierthauer, 2009. "Quadratic hedging in affine stochastic volatility models," Review of Derivatives Research, Springer, vol. 12(1), pages 3-27, April.
    14. Alev{s} v{C}ern'y & Jan Kallsen, 2007. "On the Structure of General Mean-Variance Hedging Strategies," Papers 0708.1715, arXiv.org, revised Jul 2017.
    15. Stefan Waldenberger, 2015. "The affine inflation market models," Papers 1503.04979, arXiv.org.
    16. Alev{s} v{C}ern'y & Johannes Ruf, 2019. "Simplified stochastic calculus with applications in Economics and Finance," Papers 1912.03651, arXiv.org, revised Jan 2021.
    17. Fontana, Claudio & Gnoatto, Alessandro & Szulda, Guillaume, 2023. "CBI-time-changed Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 163(C), pages 323-349.
    18. Fred Espen Benth & Giulia Di Nunno & Asma Khedher & Maren Diane Schmeck, 2015. "Pricing of Spread Options on a Bivariate Jump Market and Stability to Model Risk," Applied Mathematical Finance, Taylor & Francis Journals, vol. 22(1), pages 28-62, March.
    19. Christian Bayer & John Schoenmakers, 2015. "Option pricing in affine generalized Merton models," Papers 1512.03677, arXiv.org.
    20. Feunou Bruno & Tafolong Ernest, 2015. "Fourier inversion formulas for multiple-asset option pricing," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 19(5), pages 531-559, December.

    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:wsi:ijtafx:v:15:y:2012:i:05:n:s0219024912500379. 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: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/ijtaf/ijtaf.shtml .

    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.