Bibliographic Details
| Title: |
RKHS regularization of singular local stochastic volatility McKean-Vlasov models |
| Authors: |
Bayer, Christian, Belomestny, Denis, Butkovsky, Oleg, Schoenmakers, John |
| Publication Year: |
2022 |
| Collection: |
ArXiv.org (Cornell University Library) |
| Subject Terms: |
Quantitative Finance - Computational Finance, Mathematics - Probability |
| Description: |
Motivated by the challenges related to the calibration of financial models, we consider the problem of solving numerically a singular McKean-Vlasov equation $$ d S_t= \sigma(t,S_t) S_t \frac{\sqrt v_t}{\sqrt {E[v_t|S_t]}}dW_t, $$ where $W$ is a Brownian motion and $v$ is an adapted diffusion process. This equation can be considered as a singular local stochastic volatility model. Whilst such models are quite popular among practitioners, unfortunately, its well-posedness has not been fully understood yet and, in general, is possibly not guaranteed at all. We develop a novel regularization approach based on the reproducing kernel Hilbert space (RKHS) technique and show that the regularized model is well-posed. Furthermore, we prove propagation of chaos. We demonstrate numerically that a thus regularized model is able to perfectly replicate option prices due to typical local volatility models. Our results are also applicable to more general McKean--Vlasov equations. |
| Document Type: |
text |
| Language: |
unknown |
| Relation: |
http://arxiv.org/abs/2203.01160 |
| Availability: |
http://arxiv.org/abs/2203.01160 |
| Accession Number: |
edsbas.277E9535 |
| Database: |
BASE |
