Non--regular McKean--Vlasov equations and calibration problem in local stochastic volatility models - Archive ouverte HAL
Article Dans Une Revue ArXiv e-prints Année : 2022

Non--regular McKean--Vlasov equations and calibration problem in local stochastic volatility models

Résumé

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.

Dates et versions

hal-04565543 , version 1 (02-05-2024)

Identifiants

Citer

Mao Fabrice Djete. Non--regular McKean--Vlasov equations and calibration problem in local stochastic volatility models. ArXiv e-prints, 2022. ⟨hal-04565543⟩
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