IDEAS home Printed from https://ideas.repec.org/a/wsi/ijtafx/v09y2006i07ns0219024906003925.html
   My bibliography  Save this article

The Exponent Expansion: An Effective Approximation Of Transition Probabilities Of Diffusion Processes And Pricing Kernels Of Financial Derivatives

Author

Listed:
  • LUCA CAPRIOTTI

    (Global Modelling and Analytics Group, Credit Suisse, One Cabot Square, London, E14 4QJ, UK)

Abstract

A computational technique borrowed from the physical sciences is introduced to obtain accurate closed-form approximations for the transition probability of arbitrary diffusion processes. Within the path integral framework the same technique allows one to obtain remarkably good approximations of the pricing kernels of financial derivatives. Several examples are presented, and the application of these results to increase the efficiency of numerical approaches to derivative pricing is discussed.

Suggested Citation

  • Luca Capriotti, 2006. "The Exponent Expansion: An Effective Approximation Of Transition Probabilities Of Diffusion Processes And Pricing Kernels Of Financial Derivatives," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 9(07), pages 1179-1199.
    • Handle: RePEc:wsi:ijtafx:v:09:y:2006:i:07:n:s0219024906003925
    DOI: 10.1142/S0219024906003925
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0219024906003925
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0219024906003925?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. Jan W Dash, 2004. "Quantitative Finance and Risk Management:A Physicist's Approach," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 5436, February.
    2. Andrew Matacz, 2000. "Path Dependent Option Pricing: the path integral partial averaging method," Papers cond-mat/0005319, arXiv.org.
    3. Andrew Matacz, 2000. "Path dependent option pricing: the path integral partial averaging method," Science & Finance (CFM) working paper archive 500034, Science & Finance, Capital Fund Management.
    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. Zuzana Buckova & Beata Stehlikova & Daniel Sevcovic, 2016. "Numerical and analytical methods for bond pricing in short rate convergence models of interest rates," Papers 1607.04968, arXiv.org.
    2. Andrzej Daniluk & Rafał Muchorski, 2016. "Approximations Of Bond And Swaption Prices In A Black–Karasiński Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(03), pages 1-32, May.
    3. Pagliarani, Stefano & Pascucci, Andrea, 2011. "Analytical approximation of the transition density in a local volatility model," MPRA Paper 31107, University Library of Munich, Germany.
    4. Luca Capriotti & Yupeng Jiang & Gaukhar Shaimerdenova, 2019. "Approximation Methods For Inhomogeneous Geometric Brownian Motion," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(02), pages 1-16, March.
    5. Andrzej Daniluk & Rafa{l} Muchorski, 2015. "Approximations of Bond and Swaption Prices in a Black-Karasi\'{n}ski Model," Papers 1506.00697, arXiv.org.

    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. G. Bormetti & G. Montagna & N. Moreni & O. Nicrosini, 2006. "Pricing exotic options in a path integral approach," Quantitative Finance, Taylor & Francis Journals, vol. 6(1), pages 55-66.
    2. Zura Kakushadze, 2014. "Path Integral and Asset Pricing," Papers 1410.1611, arXiv.org, revised Aug 2016.
    3. G. Bormetti & G. Montagna & N. Moreni & O. Nicrosini, 2004. "Pricing Exotic Options in a Path Integral Approach," Papers cond-mat/0407321, arXiv.org, revised May 2006.
    4. Mark Flood, 2009. "Embracing change: financial informatics and risk analytics," Quantitative Finance, Taylor & Francis Journals, vol. 9(3), pages 243-256.
    5. Igor Halperin & Matthew Dixon, 2018. ""Quantum Equilibrium-Disequilibrium": Asset Price Dynamics, Symmetry Breaking, and Defaults as Dissipative Instantons," Papers 1808.03607, arXiv.org, revised May 2019.
    6. Capuozzo, Pietro & Panella, Emanuele & Schettini Gherardini, Tancredi & Vvedensky, Dimitri D., 2021. "Path integral Monte Carlo method for option pricing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 581(C).
    7. Halperin, Igor & Dixon, Matthew, 2020. "“Quantum Equilibrium-Disequilibrium”: Asset price dynamics, symmetry breaking, and defaults as dissipative instantons," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).
    8. Anantya Bhatnagar & Dimitri D. Vvedensky, 2022. "Quantum effects in an expanded Black–Scholes model," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 95(8), pages 1-12, August.

    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:09:y:2006:i:07:n:s0219024906003925. 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.