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Derivatives Pricing on Integrated Diffusion Processes: A General Perturbation Approach

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  • Minqiang Li

Abstract

Many derivatives products are directly or indirectly associated with integrated diffusion processes. We develop a general perturbation method to price those derivatives. We show that for any positive diffusion process, the hitting time of its integrated process is approximately normally distributed when the diffusion coefficient is small. This result of approximate normality enables us to reduce many derivative pricing problems to simple expectations. We illustrate the generality and accuracy of this probabilistic approach with several examples in the Heston model. Major advantages of the proposed technique include extremely fast computational speed, ease of implementation, and analytic tractability. © 2014 Wiley Periodicals, Inc. Jrl Fut Mark 35:582–595, 2015

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  • 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.
    • Handle: RePEc:wly:jfutmk:v:35:y:2015:i:6:p:582-595
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    1. Martin Forde & Antoine Jacquier, 2010. "Robust Approximations for Pricing Asian Options and Volatility Swaps Under Stochastic Volatility," Applied Mathematical Finance, Taylor & Francis Journals, vol. 17(3), pages 241-259.
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    Cited by:

    1. Zhenyu Cui & J. Lars Kirkby & Guanghua Lian & Duy Nguyen, 2017. "Integral Representation Of Probability Density Of Stochastic Volatility Models And Timer Options," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(08), pages 1-32, December.
    2. Minqiang Li & Fabio Mercurio, 2014. "Closed-Form Approximation Of Perpetual Timer Option Prices," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 17(04), pages 1-34.

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    More about this item

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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