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SABR TYPE STOCHASTIC VOLATILITY OPERATOR IN HILBERT SPACE

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Zeyu Cao
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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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Dates and versions

hal-03018478 , version 1 (22-11-2020)

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  • HAL Id : hal-03018478 , version 1

Cite

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