Time stepwise local volatility - 배형옥; 임현철 (대한수학회보, 2022)
We propose a path integral method to construct a time stepwise local volatility for the stock index market under Dupire's model. Our method is focused on the pricing with the Monte Carlo Method (MCM). We solve the problem of randomness of MCM by applying numerical integration. We reconstruct this task as a matrix equation. Our method provides the analytic Jacobian and Hessian required by the nonlinear optimization solver, resulting in stable and fast calculations.
Keywords: Time stepwise local volatility; Dupire's model; Monte Carlo; transition density function; path integral method