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Sabr Type Stochastic Volatility Operator In Hilbert Space

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  • Raphaël Douady

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, SUNY - State University of New York)

  • Zeyu Cao

    (SUNY - State University of New York)

Abstract

In this paper, we define stochastic volatility operators in Hilbert space which are analogs to the widely-used SABR model [14] in finite dimensional case. We show the existence of the mild solution and some related regularity properties. Our proof is based on Leray-Schauder fixed point theorem and some priori inequalities on the stochastic operator processes we construct.

Suggested Citation

  • Raphaël Douady & Zeyu Cao, 2020. "Sabr Type Stochastic Volatility Operator In Hilbert Space," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-03018478, HAL.
    • Handle: RePEc:hal:cesptp:hal-03018478
    Note: View the original document on HAL open archive server: https://paris1.hal.science/hal-03018478
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    References listed on IDEAS

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    1. Raphaël Douady, 2013. "Yield Curve Smoothing and Residual Variance of Fixed Income Positions," Post-Print hal-00666751, HAL.
    2. D. P. Kennedy, 1994. "The Term Structure Of Interest Rates As A Gaussian Random Field," Mathematical Finance, Wiley Blackwell, vol. 4(3), pages 247-258, July.
    3. Rama Cont, 2005. "Modeling Term Structure Dynamics: An Infinite Dimensional Approach," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 8(03), pages 357-380.
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