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Non--regular McKean--Vlasov equations and calibration problem in local stochastic volatility models
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abstract
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.
Forward citations
Cited by 2 Pith papers
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On the Weak Error for Local Stochastic Volatility Models
Weak order one is proven for a half-step Euler discretization of local stochastic volatility dynamics, with the particle approximation error quantified in terms of step size, regularization, and number of particles.
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McKean-Vlasov equations with singular coefficients - a review of recent results
This paper is a structured review of singular McKean-Vlasov SDEs, unifying the Lp-Lq and distributional drift frameworks and their main solution tools.
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