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Intrinsic expansions for averaged diffusion processes

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  • Pagliarani, S.
  • Pascucci, A.
  • Pignotti, M.

Abstract

We show that the convergence rate of asymptotic expansions for solutions of SDEs is higher in the case of degenerate diffusion compared to the elliptic case, i.e. it is higher when the Brownian motion directly acts only along some directions. In the scalar case, this phenomenon was already observed in Gobet and Miri 2014 using Malliavin calculus techniques. Here, we provide a general and detailed analysis by employing the recent study of intrinsic functional spaces related to hypoelliptic Kolmogorov operators in Pagliarani et al. 2016. Applications to finance are discussed, in the study of path-dependent derivatives (e.g. Asian options) and in models incorporating dependence on past information.

Suggested Citation

  • Pagliarani, S. & Pascucci, A. & Pignotti, M., 2017. "Intrinsic expansions for averaged diffusion processes," Stochastic Processes and their Applications, Elsevier, vol. 127(8), pages 2560-2585.
    • Handle: RePEc:eee:spapps:v:127:y:2017:i:8:p:2560-2585
    DOI: 10.1016/j.spa.2016.12.002
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    References listed on IDEAS

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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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    6. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
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    8. Chueh‐Yung Tsao & Chuang‐Chang Chang & Chung‐Gee Lin, 2003. "Analytic approximation formulae for pricing forward‐starting Asian options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 23(5), pages 487-516, May.
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    Cited by:

    1. Weston Barger & Matthew Lorig, 2019. "Optimal Liquidation Under Stochastic Price Impact," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(02), pages 1-28, March.
    2. Louis-Pierre Arguin & Nien-Lin Liu & Tai-Ho Wang, 2018. "Most-Likely-Path In Asian Option Pricing Under Local Volatility Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(05), pages 1-32, August.
    3. Pascucci, Andrea & Pesce, Antonello, 2020. "The parametrix method for parabolic SPDEs," Stochastic Processes and their Applications, Elsevier, vol. 130(10), pages 6226-6245.

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