I am delighted to introduce to you the first issue of The Journal of Computational Finance for 2020.
This issue highlights the progress being made in scenario-driven approaches to computational finance, where traditionally models formulated as partial differential equations (for example) would have been used. These new approaches not only alleviate potentially problematic modeling assumptions, but also – perhaps surprisingly – show advantages in terms of computational complexity, even in cases where model-based approaches are applicable.
In this issue’s first paper, “A shrinking horizon optimal liquidation framework with lower partial moments criteria”, Hassan Anis and Roy H. Kwon introduce a novel method for solving optimal liquidation problems. The key elements of their algorithm are scenario-based optimization, which bypasses the curse of dimensionality observed in alternative approaches such as decision trees, and a shrinking time horizon, to respect the dynamic nature of the problem.
Marta Małecka explores a new way of verifying models for expected shortfall using bootstrapping in “Extremal risk management: expected shortfall value verification using the bootstrap method”, our second paper. Here, the computation is based purely on samples, without making distributional assumptions, and it outperforms model-based methods in the author’s numerical experiments.
Changing topics, “Second-order Monte Carlo sensitivities in linear or constant time”, the third paper in the issue, finds Roberto Daluiso analyzing Monte Carlo estimators for second-order sensitivities of model derivative values with respect to a large number of inputs. This approach is novel in that the computational complexity is within a constant factor of the cost of computing the price, independent of the number of inputs.
In our final article, “Pricing American call options using the Black–Scholes equation with a nonlinear volatility function”, Maria do Rosario Grossinho, Yaser Faghan
Kord and Daniel Sevcovic study the computation of derivative prices under classical transaction cost models. In their resulting mathematical framework of Black– Scholes-type problems with a nonlinear volatility function depending on the option’s Gamma, the authors present a novel transformation of the original equations into a new linear complementarity problem that is amenable to standard finite difference and nonlinear iteration methods.
I wish you a stimulating read.
University of Oxford
In this paper, a novel quasi-multiperiod model for optimal position liquidation in the presence of both temporary and permanent market impact is proposed. Two main features distinguish the proposed approach from its alternatives.
This paper considers the problem of efficiently computing the full matrix of second-order sensitivities of a Monte Carlo price when the number of inputs is large.
In this paper, we refer to the axiomatic theory of risk and investigate the problem of formal verification of the expected shortfall (ES) model based on a sample ES. Recognizing the infeasibility of parametric methods, they explore the bootstrap…
In this paper, the authors investigate a nonlinear generalization of the Black–Scholes equation for pricing American-style call options, where the volatility term may depend on both the underlying asset price and the Gamma of the option.