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

Author

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  • 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
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    References listed on IDEAS

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    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.
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    Citations

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    Cited by:

    1. Chenyu Zhao & Misha Beek & Peter Spreij & Makhtar Ba, 2025. "Polynomial approximation of discounted moments," Finance and Stochastics, Springer, vol. 29(1), pages 63-95, January.
    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. 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.
    6. Andrzej Daniluk & Rafa{l} Muchorski, 2015. "Approximations of Bond and Swaption Prices in a Black-Karasi\'{n}ski Model," Papers 1506.00697, arXiv.org.

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