SABR TYPE STOCHASTIC VOLATILITY OPERATOR IN HILBERT SPACE

Raphaël Douady; Zeyu Cao

Preprints, Working Papers, ...

SABR TYPE STOCHASTIC VOLATILITY OPERATOR IN HILBERT SPACE

Raphaël Douady ^{1, 2} Zeyu Cao ²

1 CES - Centre d'économie de la Sorbonne

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

Document type :

Preprints, Working Papers, ...

Domain :

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]

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https://hal-paris1.archives-ouvertes.fr/hal-03018478
Contributor : Raphael DOUADY Connect in order to contact the contributor
Submitted on : Sunday, November 22, 2020 - 6:22:50 PM
Last modification on : Friday, April 29, 2022 - 10:12:43 AM
Long-term archiving on: : Tuesday, February 23, 2021 - 9:39:44 PM

SABR TYPE STOCHASTIC VOLATILITY OPERATOR IN HILBERT SPACE

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