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.
Received May 17, 2021; Accepted July 28, 2021. 2010 Mathematics Subject Classification. 91G20, 91G30. Key words and phrases. Time stepwise local volatility, Dupire\u2019s model, Monte Carlo, transition density function, path integral method. 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).
