University of Oxford
It is a pleasure to introduce the latest issue of The Journal of Computational Finance, which contains the usual inspiring mix of novel modeling and computation, as well as foundational numerical analysis.
In the issue’s first paper, “Modeling the bid and ask prices of options”, Dilip B. Madan, Wim Schoutens and King Wang investigate convex ordering of densities derived jointly from the bid and ask prices of calls and puts, and they discuss the consequences for joint models.
The second paper in the issue, “An optimal control strategy for execution of large stock orders using long short-term memory networks” by A. Papanicolaou, H. Fu, P. Krishnamurthy, B. Healy and F. Khorrami, demonstrates how long short-term memory (LSTM) neural networks can utilize cross-sectional information from different stocks in the Standard & Poor’s 100 to improve the performance of intraday single-asset execution strategies.
In our third paper, “Sharp L1-approximation of the log-Heston stochastic differential equation by Euler-type methods”, Annalena Mickel and Andreas Neuenkirch prove that various adaptations of the Euler–Maruyama scheme for the Heston model converge with strong order arbitrarily close to 1/2, the best achievable order in the standard regular case, as long as the model satisfies the so-called Feller condition. This fills a long-standing gap in the analysis of this popular model. In other cases, a parameter-dependent rate, which is conjectured not to be sharp in numerical tests, is given.
The issue’s last paper, “Efficient numerical valuation of European options under the two-asset Kou jump-diffusion model” by Karel J. in ’t Hout and Pieter Lamotte, provides an algorithm that allows the computation of splitting schemes for Kou’s jump model for derivatives on two assets with an optimal computational cost. A careful stability analysis and detailed numerical tests are carried out, including for the option’s sensitivities.
I hope that you will find the papers in this issue interesting.
The authors investigate and partially solve theoretical and empirical problems for the joint modelling of bid and ask prices.
An optimal control strategy for execution of large stock orders using long short-term memory networks
Using a general power law in the Almgren and Chriss model and real data, the authors simulate the execution of a large stock order with an appropriately trained LSTM network.
The authors employ Euler-type methods to study the L¹ approximation of the log-Heston stochastic differential equation at equidistant time points.
The authors extend a technique proposed by Toivanen (2008), arriving at an algorithm evaluating the nonlocal double integral appearing in the two-dimensional Kou PIDE and perform several numerical experiments to demonstrate actual convergence behavior…