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.

Mots clés: Interest Rate Modeling; Stochastic Volatility Operator; Hilbert Space

Domaines: Finance quantitative [q-fin.CP]; Applications [stat.AP]; Finance [q-fin.GN]; Gestion de portefeuilles [q-fin.PM]; Pricing [q-fin.PR]; Gestion des risques [q-fin.RM]; Econométrie de la finance [q-fin.ST]

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