Bull. Korean Math. Soc. Published online October 14, 2021
Hyeong Ohk Bae and Hyuncheul Lim
Ajou University; Chonnam National University
Abstract : 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) and taking the idea in [5]. 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 : Local Volatility, Dupire Model, Arrow Debreu, Transition Density
