Journal of Computational Finance

Christoph Reisinger
University of Oxford

It is a pleasure to introduce the latest issue of The Journal of Computational Finance. The first two contributions focus on using novel neural network machinery to enhance classical financial calibration procedures for improved robustness and accuracy, while the final paper combines classical Monte Carlo and finite-difference methods to improve numerical efficiency.

In the issue’s first paper, “Deep self-consistent learning of local volatility”, Zhe Wang, Ameir Shaa, Nicolas Privault and Claude Guet provide simultaneous neural network approximations for a discretely quoted options surface and a consistent local volatility function. These are achieved by a learning process that avoids arbitrage through explicit construction of the architecture and penalization, and by utilizing the Dupire partial differential equation through physics-informed neural networks methods. The authors’ computational results support the hypothesis that benchmark modifications improve the regularity and accuracy of calibrated surfaces.

Our second paper, “Robust financial calibration: a Bayesian approach for neural stochastic differential equations” by Christa Cuchiero, Eva Flonner and Kevin Kurt, introduces a Bayesian framework for calibrating neural stochastic differential equation (SDE) models (that is, SDEs whose coefficients are (over)parameterized by artificial neural networks) to both time series of quoted option prices and the historical price paths of the underlying asset. The resulting posterior distribution allows the computation of an uncertainty measure of predicted option prices and can be seen as a Bayesian variant of the approach by Patrick Gierjatowicz et al, published in this journal in 2022. Cuchiero et al’s approach also improves the calibration robustness compared with Alok Gupta and Christoph Reisinger’s 2014 paper, “Robust calibration of financial models using Bayesian estimators”. The findings of Cuchiero et al show reduced uncertainty bounds for the Bayesian neural SDE model.

Finally, in “Finite-difference solution ansatz approach in least-squares Monte Carlo”, the third paper in this issue, Jiawei Huo proposes the use of finite-difference solutions to construct control variates in the least-squares regression Monte Carlo estimation of conditional expectation values of financial products. Applications to Bermudan option pricing and valuation adjustment computations demonstrate the achieved variance reduction.

I wish you an enjoyable read.