University of Oxford
I am pleased to introduce the March 2022 issue of The Journal of Computational Finance.
This issue’s first paper, “Pricing barrier options with deep backward stochastic differential equation methods”, is in the active research area of derivative pricing with neural networks. Narayan Ganesan, Yajie Yu and Bernhard Hientzsch generalize the deep backward stochastic differential equation (BSDE) method previously used for vanilla options to contracts with barrier features by modifying the computational graph appropriately to account for barrier triggers.
In “Automatic differentiation for diffusion operator integral variance reduction”, our second paper, Johan Auster provides a generic implementation of the variance reduced estimator of value functions due to Heath and Platen that eliminates the need for detailed bespoke calculations. An extension to barrier contracts highlights the versatility of this approach.
The third paper in the issue, “Robust product Markovian quantization” by Ralph Rudd, Thomas A. McWalter, Jörg Kienitz and Eckhard Platen, provides a unified template for different quantization techniques for stochastic differential equations in the form of standard vector quantization. The paper proceeds to a generalization of a higher-order method that may be applied to stochastic volatility models, for which numerical examples are presented.
“Stability and convergence of Galerkin schemes for parabolic equations with application to Kolmogorov pricing equations in time-inhomogeneous Lévy models”, the issue’s final paper, finds Maximilian Gaß and Kathrin Glau analyzing numerical properties of generic Galerkin approximations to evolution equations with an emphasis on time-inhomogeneity, thus generalizing earlier works in this area in a practically important direction.
I want to end my letter by paying tribute to Peter Carr, who tragically passed away on March 1. Peter was a long-standing and dear friend, as well as being a member of our editorial board, for which I am deeply grateful. Peter shaped the field of mathematical finance over several decades as a quant and an academic scholar through his ingenuity and wit. His deep and numerous contributions were acknowledged through the Risk Magazine Quant of the Year Award in 2003. His paper “Option valuation using the fast Fourier transform”, published in The Journal of Computational Finance in 1999, has to date been cited more than 2700 times. It is impossible to do Peter’s impact on the community justice in these terms, though. He trained and mentored an extraordinary number of quantitative researchers with kindness and generosity, and he passed on his wealth of knowledge in countless lectures. Many of us had the privilege to witness Peter’s infectious enthusiasm and boundless talent for elegant mathematics. He will be painfully missed. Our thoughts are with his family
This paper presents a novel and direct approach to solving boundary- and final-value problems, corresponding to barrier options, using forward pathwise deep learning and forward–backward stochastic differential equations.
This paper demonstrates applications of automatic differentiation with nested dual numbers in the diffusion operator integral variance-reduction framework originally proposed by Heath and Platen.
In this paper the authors formulate the one-dimensional RMQ and d-dimensional PMQ algorithms as standard vector quantization problems by deriving the density, distribution and lower partial expectation functions of the random variables to be quantized at…
Stability and convergence of Galerkin schemes for parabolic equations with application to Kolmogorov pricing equations in time-inhomogeneous Lévy models
In this paper the authors derive stability and convergence of fully discrete approximation schemes of solutions to linear parabolic evolution equations governed by time-dependent coercive operators.