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SABR TYPE STOCHASTIC VOLATILITY OPERATOR IN HILBERT SPACE

Raphael Douady (rdouady@gmail.com) and Zeyu Cao (zeyu.cao@stonybrook.edu)
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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: Interest Rate Modeling; Stochastic Volatility Operator; Hilbert Space (search for similar items in EconPapers)
Date: 2020-11-22
Note: View the original document on HAL open archive server: https://paris1.hal.science/hal-03018478
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