Non--regular McKean--Vlasov equations and calibration problem in local stochastic volatility models
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arXiv
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866913554652725248 |
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| author | Djete, Mao Fabrice |
| author_facet | Djete, Mao Fabrice |
| contents | In order to deal with the question of the existence of a calibrated local stochastic volatility model in finance, we investigate a class of McKean--Vlasov equations where a minimal continuity assumption is imposed on the coefficients. Namely, the drift coefficient and, in particular, the volatility coefficient are not necessarily continuous in the measure variable for the Wasserstein topology. In this paper, we provide an existence result and show an approximation by $N$--particle system or propagation of chaos for this type of McKean--Vlasov equations. As a direct result, we are able to deduce the existence of a calibrated local stochastic volatility model for an appropriate choice of stochastic volatility parameters. The associated propagation of chaos result is also proved. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_09986 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Non--regular McKean--Vlasov equations and calibration problem in local stochastic volatility models Djete, Mao Fabrice Probability Analysis of PDEs Mathematical Finance In order to deal with the question of the existence of a calibrated local stochastic volatility model in finance, we investigate a class of McKean--Vlasov equations where a minimal continuity assumption is imposed on the coefficients. Namely, the drift coefficient and, in particular, the volatility coefficient are not necessarily continuous in the measure variable for the Wasserstein topology. In this paper, we provide an existence result and show an approximation by $N$--particle system or propagation of chaos for this type of McKean--Vlasov equations. As a direct result, we are able to deduce the existence of a calibrated local stochastic volatility model for an appropriate choice of stochastic volatility parameters. The associated propagation of chaos result is also proved. |
| title | Non--regular McKean--Vlasov equations and calibration problem in local stochastic volatility models |
| topic | Probability Analysis of PDEs Mathematical Finance |
| url | https://arxiv.org/abs/2208.09986 |