Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/315067 
Year of Publication: 
2024
Citation: 
[Journal:] Finance and Stochastics [ISSN:] 1432-1122 [Volume:] 28 [Issue:] 4 [Publisher:] Springer Berlin Heidelberg [Place:] Berlin/Heidelberg [Year:] 2024 [Pages:] 1147-1178
Publisher: 
Springer Berlin Heidelberg, Berlin/Heidelberg
Abstract: 
Abstract Motivated by the challenges related to the calibration of financial models, we consider the problem of numerically solving a singular McKean–Vlasov equation dXt=σ(t,Xt)XtvtE[vtt]dWt,where Wis a Brownian motion and vis an adapted diffusion process. This equation can be considered as a singular local stochastic volatility model. While such models are quite popular among practitioners, its well-posedness has unfortunately not yet been fully understood and in general is possibly not guaranteed at all. We develop a novel regularisation approach based on the reproducing kernel Hilbert space (RKHS) technique and show that the regularised model is well posed. Furthermore, we prove propagation of chaos. We demonstrate numerically that a thus regularised model is able to perfectly replicate option prices coming from typical local volatility models. Our results are also applicable to more general McKean–Vlasov equations.
Subjects: 
Stochastic volatility models
Singular McKean–Vlasov equations
Reproducing kernel Hilbert space
Persistent Identifier of the first edition: 
Additional Information: 
C63;G17
Creative Commons License: 
cc-by Logo
Document Type: 
Article
Document Version: 
Published Version
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