Bulletin of the
Korean Mathematical Society BKMS

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

MSC numbers: 91G20, 91G30

Supported by: Bae is supported by the Basic Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education and Technology (NRF-2018R1D1A1A09082848), Lim by (NRF-2019R1I1A3A03059382), and BK21 FOUR (Fostering Outstanding Universities for Research, NO.5120200913674) funded by the Ministry of Education(MOE, Korea) and National Research Foundation of Korea(NRF).