Nonregular McKean-Vlasov Equations and Calibration Problem in Local Stochastic Volatility Models

• 成果类型: Article; Early Access
• 署名作者: Djete, Mao Fabrice
• 署名单位: Institut Polytechnique de Paris; Ecole Polytechnique; ENSTA Paris
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X; 1526-5471
• DOI: 10.1287/moor.2023.0326
• 发表日期: 2026-03-17
• 关键词: McKean-Vlasov stochastic differential equation; no Wasserstein continuity; local stochastic volatility model; particle system; bounds

摘要

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 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 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.