SABR TYPE STOCHASTIC VOLATILITY OPERATOR IN HILBERT SPACE

Raphaël Douady (1, 2) , Zeyu Cao (2)

1 CES - Centre d'économie de la Sorbonne
2 SUNY - State University of New York

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

Domains: Quantitative Finance [q-fin]; Computational Finance [q-fin.CP]; Statistics [stat]; Applications [stat.AP]; Quantitative Finance [q-fin]; General Finance [q-fin.GN]; Quantitative Finance [q-fin]; Portfolio Management [q-fin.PM]; Quantitative Finance [q-fin]; Pricing of Securities [q-fin.PR]; Quantitative Finance [q-fin]; Risk Management [q-fin.RM]; Quantitative Finance [q-fin]; Statistical Finance [q-fin.ST]

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