Journal of Computational Finance

Christoph Reisinger
University of Oxford

I am delighted to introduce this issue of The Journal of Computational Finance. The three papers herein have a theme of derivative pricing, with one paper on deep learning of European option prices in incomplete markets under a risk-sharing paradigm, and two papers on numerical methods for American options under nonstandard models, using Monte Carlo and finite-difference methodology, respectively.

In our first paper, “Deep equal risk pricing of illiquid derivatives with multiple hedging instruments”, Alexandre Carbonneau and Frédéric Godin outline the principle of equal risk pricing, whereby holders of long and short positions of an illiquid derivative reduce their exposure by trading in multiple liquid hedging instruments. They fix the illiquid derivative’s price such that the resulting residual risk of the hedged position, quantified by a convex risk measure, is shared equally. The authors’ computational approach to the combined pricing and hedging problem leverages the seminal work on deep hedging. Carbonneau and Godin also demonstrate, by way of numerical experiments, how the inclusion of multiple hedging instruments reduces risk effectively.

The issue’s second paper, “Pricing time-capped American options using a least squares Monte Carlo method” by Paweł Stȩpniak and Zbigniew Palmowski, revisits Longstaff and Schwartz’s classical method for early exercise options and extends it to the setting where the maturity of the option is capped if an event occurs during the lifetime of the contract. They rigorously show the convergence of their generalized estimators in this setting, under the dynamics of the underlying asset given by an exponential Lévy process. Their numerical tests illustrate the efficacy and robustness of this approach.

In the last paper in the issue, “Pricing American options under irrational behavior in a Markov regime-switching model with a finite-element method”, Mohammad Saber Rohi, Saghar Heidari and Hossein Azari consider a model for an American option where the holder exercises irrationally, leading to a modified quasi-variational inequality as an alternative to the optimal exercise case. They prove the stability of a finite-element approximation and demonstrate convergence of the scheme in numerical experiments.

These three papers provide a snapshot of the impressive variety of methodologies adopted in the derivatives industry today. I hope you find them interesting.

Finally, I would like to draw your attention to the 12th General Advanced Mathematical Methods for Finance (AMaMeF) conference in Verona on June 23–27, which is co-organized by Athena Picarelli, one of this journal’s associate editors. The conference has a first-rate lineup of plenary speakers, as well as mini-symposiums addressing a wide range of topics in mathematical finance and its applications. I hope to see you there.

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