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Weak approximation of averaged diffusion processes

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  • Gobet, Emmanuel
  • Miri, Mohammed

Abstract

We derive expansion results in order to approximate the law of the average of the marginal of diffusion processes. The average is computed w.r.t. a general parameter that is involved in the diffusion dynamics. Our approximation is based on the use of proxys with normal distribution or log-normal distribution, so that the expansion terms are explicit. We provide non asymptotic error bounds, which justifies the expansion accuracy as the time or the diffusion coefficients are small in a suitable sense.

Suggested Citation

  • Gobet, Emmanuel & Miri, Mohammed, 2014. "Weak approximation of averaged diffusion processes," Stochastic Processes and their Applications, Elsevier, vol. 124(1), pages 475-504.
    • Handle: RePEc:eee:spapps:v:124:y:2014:i:1:p:475-504
    DOI: 10.1016/j.spa.2013.08.007
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    References listed on IDEAS

    as
    1. Pierre Etoré & Emmanuel Gobet, 2012. "Stochastic expansion for the pricing of call options with discrete dividends," Post-Print hal-00507787, HAL.
    2. E. Benhamou & E. Gobet & M. Miri, 2010. "Expansion Formulas For European Options In A Local Volatility Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 13(04), pages 603-634.
    3. Rainer Avikainen, 2009. "On irregular functionals of SDEs and the Euler scheme," Finance and Stochastics, Springer, vol. 13(3), pages 381-401, September.
    4. Romain Bompis & Emmanuel Gobet, 2012. "Asymptotic and non asymptotic approximations for option valuation," Post-Print hal-00720650, HAL.
    5. Pierre Étor� & Emmanuel Gobet, 2012. "Stochastic Expansion for the Pricing of Call Options with Discrete Dividends," Applied Mathematical Finance, Taylor & Francis Journals, vol. 19(3), pages 233-264, August.
    6. Naoto Kunitomo & Akihiko Takahashi, 2001. "The Asymptotic Expansion Approach to the Valuation of Interest Rate Contingent Claims," Mathematical Finance, Wiley Blackwell, vol. 11(1), pages 117-151, January.
    7. E. Benhamou & E. Gobet & M. Miri, 2012. "Analytical formulas for a local volatility model with stochastic rates," Quantitative Finance, Taylor & Francis Journals, vol. 12(2), pages 185-198, September.
    8. Bernard Lapeyre & Emmanuel Temam, 2001. "Competitive Monte Carlo methods for the pricing of Asian options," Post-Print hal-01667057, HAL.
    9. Hélyette Geman & Marc Yor, 1993. "Bessel Processes, Asian Options, And Perpetuities," Mathematical Finance, Wiley Blackwell, vol. 3(4), pages 349-375, October.
    10. Kemna, A. G. Z. & Vorst, A. C. F., 1990. "A pricing method for options based on average asset values," Journal of Banking & Finance, Elsevier, vol. 14(1), pages 113-129, March.
    11. E. Benhamou & E. Gobet & M. Miri, 2009. "Smart expansion and fast calibration for jump diffusions," Finance and Stochastics, Springer, vol. 13(4), pages 563-589, September.
    12. Turnbull, Stuart M. & Wakeman, Lee Macdonald, 1991. "A Quick Algorithm for Pricing European Average Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 26(3), pages 377-389, September.
    13. Paolo Foschi & Stefano Pagliarani & Andrea Pascucci, 2011. "Black-Scholes formulae for Asian options in local volatility models," Quaderni di Dipartimento 7, Department of Statistics, University of Bologna.
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    Cited by:

    1. Florian Bourgey & Stefano De Marco & Emmanuel Gobet, 2022. "Weak approximations and VIX option price expansions in forward variance curve models," Papers 2202.10413, arXiv.org, revised May 2022.
    2. Julien Hok & Philip Ngare & Antonis Papapantoleon, 2018. "Expansion formulas for European quanto options in a local volatility FX-LIBOR model," Papers 1801.01205, arXiv.org, revised Apr 2018.
    3. Jaehyun Kim & Hyungbin Park & Jonghwa Park, 2019. "Pricing and hedging short-maturity Asian options in local volatility models," Papers 1911.12944, arXiv.org, revised Apr 2024.
    4. Cai, Ning & Li, Chenxu & Shi, Chao, 2021. "Pricing discretely monitored barrier options: When Malliavin calculus expansions meet Hilbert transforms," Journal of Economic Dynamics and Control, Elsevier, vol. 127(C).
    5. 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.
    6. Dan Pirjol & Lingjiong Zhu, 2016. "Short Maturity Asian Options in Local Volatility Models," Papers 1609.07559, arXiv.org.
    7. Romain Bompis, 2017. "Weak approximations for arithmetic means of geometric Brownian motions and applications to Basket options," Working Papers hal-01502886, HAL.
    8. Dan Pirjol & Lingjiong Zhu, 2017. "Short Maturity Asian Options for the CEV Model," Papers 1702.03382, arXiv.org.
    9. Julien Hok & Philip Ngare & Antonis Papapantoleon, 2018. "Expansion Formulas For European Quanto Options In A Local Volatility Fx-Libor Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(02), pages 1-43, March.

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