We consider a class of stochastic path-dependent volatility models where the stochastic volatility, whose square follows the Cox-Ingersoll-Ross model, is multiplied by a (leverage) function of the spot price, its running maximum, and time. We propose a Monte Carlo simulation scheme which combines a log-Euler scheme for the spot process with the full truncation Euler scheme or the backward Euler-Maruyama scheme for the squared stochastic volatility component. Under some mild regularity assumptions and a condition on the Feller ratio, we establish the strong convergence with order 1/2 (up to a logarithmic factor) of the approximation process up to a critical time. The model studied in this paper contains as special cases Heston-type stochastic-local volatility models, the state-of-the-art in derivative pricing, and a relatively new class of path-dependent volatility models. The present paper is the first to prove the convergence of the popular Euler schemes with a positive rate, which is moreover consistent with that for Lipschitz coefficients and hence optimal.
Convergence of the Euler--Maruyama particle scheme for a regularised McKean--Vlasov equation arising from the calibration of local-stochastic volatility models
Simulation of stochastic volatility models via operator splitting schemes
University of Waterloo（滑铁卢大学）；Hong Kong University of Science and Technology (Guangzhou)（香港科技大学（广州））；Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））
Strong Convergence for Euler-Maruyama and Milstein Schemes with Asymptotic Method
Graduate School of Science and Engineering, Ritsumeikan University（立命馆大学理工学研究科）；Graduate School of Economics, The University of Tokyo（东京大学经济学研究科）；Mitsubishi UFJ Trust Investment Technology Institute Co., Ltd. (MTEC)（三菱UFJ信托投资技术研究所有限公司）
