University of Oxford
I am pleased to introduce the September 2021 issue of The Journal of Computational Finance.
This issue has two themes running through it: machine learning and fixed income. This is exemplified by our first paper, “An artificial neural network representation of the SABR stochastic volatility model”, in which William A. McGhee demonstrates how artificial neural networks can be trained to accurately reproduce option prices under the SABR stochastic volatility model. The online evaluation of the trained surrogate model takes a small fraction of the time of a state-of-the-art partial differential equation solver and has negligible bias compared with the standard SABR expansion formula.
An accurate approximation formula for the Heston–Hull–White foreign exchange model is then proposed by Kenji Nagami in “Expansion method for pricing foreign exchange options under stochastic volatility and interest rates”, the issue’s second paper. Exploiting small volatility-of-volatility, a second-order analytical expansion is shown to match numerical benchmark solutions well even in regimes where other methods fail.
Simon Fecamp, Joseph Mikael and Xavier Warin propose machine learning approaches to optimal hedging under market frictions in the third paper in this issue: “Deep learning for discrete-time hedging in incomplete markets”. The authors compare a global optimization technique with a local dynamic programming technique, and their numerical studies find that the former approach gives a superior performance, which ultimately enables the authors to construct optimal frontiers.
In our final paper, “Quantization-based Bermudan option pricing in the foreign exchange world”, Jean-Michel Fayolle, Vincent Lemaire, Thibaut Montes and Gilles Pagès construct optimal quantizations of exchange rate processes with stochastic rates, which facilitate a dynamic programming argument for Bermudan-style contracts. Numerical tests validate the method and show its efficiency.
I hope you will enjoy learning about these exciting new research directions as much as I have
In this paper the universal approximation theorem of artificial neural networks (ANNs) is applied to the stochastic alpha beta rho (SABR) stochastic volatility model in order to construct highly efficient representations.
Expansion method for pricing foreign exchange options under stochastic volatility and interest rates
This paper applies the smart expansion method to the Heston–Hull–White model, which admits stochastic interest rates to enhance the model, and obtains the expansion formula for pricing options in the model up to second order.
This paper presents several algorithms based on machine learning to solve hedging problems in incomplete markets.
This paper proposes two numerical solutions based on product optimal quantization for the pricing of Bermudan options on foreign exchange rates.