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SABR TYPE STOCHASTIC VOLATILITY OPERATOR IN HILBERT SPACE

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.
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https://hal-paris1.archives-ouvertes.fr/hal-03018478
Contributor : Raphael Douady <>
Submitted on : Sunday, November 22, 2020 - 6:22:50 PM
Last modification on : Tuesday, January 19, 2021 - 11:08:38 AM

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  • HAL Id : hal-03018478, version 1

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Raphaël Douady, Zeyu Cao. SABR TYPE STOCHASTIC VOLATILITY OPERATOR IN HILBERT SPACE. 2020. ⟨hal-03018478⟩

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