University of Oxford
I am pleased to introduce the December 2021 issue of The Journal of Computational Finance.
In the issue’s first paper, “Probabilistic machine learning for local volatility”, Martin Tegnér and Stephen Roberts give a contemporary Gaussian processes take on local volatility calibration. Building on ideas from “Robust calibration of financial models using Bayesian estimators” by Alok Gupta and myself (which appeared in this journal in 2014) as well as earlier works by Stéphane Crépey, Rama Cont, Adil Reghaï and others from the inverse problems community, Tegnér and Roberts provide a fully nonparametric approach to the fitting problem and they are able to perform dynamic inference.
Christoph Belak, Daniel Hoffmann and Frank T. Seifried develop a Monte Carlo method for nonlinear and nonlocal pricing problems in our second paper: “Branching diffusions with jumps, and valuation with systemic counterparties”. They are able to show the equivalence between two representations of value functions by a partial integro-differential equation and by branching diffusion processes with jumps. This leads to an elegant simulation scheme, which is illustrated by the pricing of trades with a defaultable, systemically important bank.
“Rainbows and transforms: semi-analytic formulas”, the third paper in this issue, finds Norberto Laghi revisiting the classical problem of analytical or semi-analytical solutions for exotic options. Requiring only knowledge of the characteristic function, the paper derives such formulas for best-of and worst-of basket options using Fourier techniques.
In our final paper, “A review of tree-based approaches to solving forward–backward stochastic differential equations”, Long Teng presents a survey of methods based on regression trees for the solution of backward stochastic differential equations and demonstrates the performance on high-dimensional tests.
I wish you an interesting read and an enjoyable festive period.
In this paper, the authors propose to approach the calibration problem of local volatility with Bayesian statistics to infer a conditional distribution over functions given observed data.
This paper extends the branching diffusion Monte Carlo method of Henry-Labordère et al to the case of parabolic partial differential equations with mixed local–nonlocal analytic nonlinearities.
In this paper the authors show how the techniques introduced by Hurd and Zhou in 2010 can be used to derive a pricing framework for rainbow options by using the joint characteristic function of the logarithm of the underlying assets.
This paper looks at ways of solving (decoupled) forward–backward stochastic differential equations numerically using regression trees.