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SABR TYPE STOCHASTIC VOLATILITY OPERATOR IN HILBERT SPACE

Raphaël Douady () and Zeyu Cao ()
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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

Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) from HAL

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.

Keywords: Stochastic Volatility Operator; Hilbert Space; Interest Rate Modeling (search for similar items in EconPapers)
Date: 2020-11-22
Note: View the original document on HAL open archive server: https://hal-paris1.archives-ouvertes.fr/hal-03018478
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