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http://dx.doi.org/10.4134/BKMS.b210391

TIME STEPWISE LOCAL VOLATILITY  

Bae, Hyeong-Ohk (Department of Financial Engineering Ajou University)
Lim, Hyuncheul (Department of Mathematics Chonnam National University)
Publication Information
Bulletin of the Korean Mathematical Society / v.59, no.2, 2022 , pp. 507-528 More about this Journal
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). 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;
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Times Cited By KSCI : 1  (Citation Analysis)
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