I am writing this letter on my way to the 2019 edition of the SIAM Conference on Financial Mathematics and Engineering, which is being held in Toronto. Over the years, the program of this biennial conference has chronicled developments in the field, in both academia and industry. It is therefore unsurprising that a large proportion of this year’s program is taken up by topics in machine learning, meanfield games and systemic risk. In parallel, there have been substantial new developments in the more-established areas of volatility modeling, computational portfolio optimization and derivative pricing. The contributions presented in this issue of The Journal of Computational Finance lie in the second category.
Complexity reduction is at the core of our first two papers. In the first, “Application of the Heath–Platen estimator in the Fong–Vasicek short rate model”, Sema Coskun, Ralf Korn and Sascha Desmettre develop an efficient control variate Monte Carlo estimator for bond pricing under stochastic volatility, adapting a powerful generic recipe originally proposed by Heath and Platen. The authors also demonstrate an impressive reduction in the size of the error bounds.
Olena Burkovska, Kathrin Glau, Mirco Mahlstedt and Barbara Wohlmuth utilize reduced basis approximations and proxy-European option prices to speed up the calibration of American options in our second paper: “Complexity reduction for calibration to American options”. This “de-Americanization” appears to fall into a broad class of tricks used in the industry to reduce errors via a surrogate numerical model with the same implied volatility, which leads to interesting overarching questions as to whether a theoretical basis may be found that supports the validity and identifies the limitations of this approach.
The pricing of path-dependent variants of American options is the topic of the issue’s third paper, “Path-dependent American options” by Etienne Chevalier, Vathana Ly Vath and Mohamed Mnif, who provide a rigorous convergence analysis and numerical tests.
In “Skewed target range strategy for multiperiod portfolio optimization using a two-stage least squares Monte Carlo method”, the last paper in this issue, Rongju Zhang, Nicolas Langrené, Yu Tian, Zili Zhu, Fima Klebaner and Kais Hamza present a novel portfolio optimization strategy with a favorable downside risk–return trade-off compared with standard utility-based approaches. This is achieved by the prescription of a target range for the portfolio value within a least squares Monte Carlo-based multiperiod algorithm.
The Journal of Computational Finance strives to disseminate the most important new developments in the field of computational methodology in finance. I look forward to your exciting submissions that will push the frontiers in both emerging and established areas.
I wish you an inspirational read.
University of Oxford
In this paper, the authors construct a Heath-Platen-type Monte Carlo estimator that performs extraordinarily well compared with the crude Monte Carlo estimation.
In this paper, the authors propose and investigate a new method for the calibration to American option price data.
In this paper, the authors investigate a path-dependent American option problem and provide an efficient and implementable numerical scheme for the solution of its associated path-dependent variational inequality.
Skewed target range strategy for multiperiod portfolio optimization using a two-stage least squares Monte Carlo method
In this paper, the authors propose a novel investment strategy for portfolio optimization problems.