Speaker
Description
Many problems in Physics involve recovering unknown parameters or potentials from observed data. Quantitative Finance faces a similar challenge: given a set of observed option prices, we need to recover the local volatility function that drives the dynamics of the underlying asset. In this study, we explore the calibration of the local volatility surface by inverting the Dupire forward equation. The local volatility function is represented by an artificial neural network and is recovered by minimizing the difference between the observed option prices and those generated by numerically solving the Dupire partial differential equation. This approach yields a PDE-constrained optimization problem in which the volatility surface is inferred from market data. Because this problem is inherently ill-posed, we investigate the role of regularization in achieving stable and meaningful reconstructions.