TIME STEPWISE LOCAL VOLATILITY - Bae, Hyeong Ohk; Lim, Hyuncheul (Bulletin of the Korean Mathematical Society, 2022)
We propose a path integral method to construct a time step-wise 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 in-tegration. 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.