Journal of Computational Finance

With this issue of The Journal of Computational Finance, we have something to
celebrate. This is the first issue of the twentieth volume, and we are proud to have reached this milestone. Over the past nineteen volumes, developing advanced robust numerical techniques, accurate solutions and modern scientific computing in the field of financial engineering and financial risk management has become a very prominent area of research. Whereas risk management is ever present nowadays - with all its "valuation adjustments" - the pricing of financial derivatives by means of different techniques and numerical methods for optimal portfolio selection also remains important.

In this celebratory issue we present some recent, novel papers by researchers who have been frequent contributors to and strong supporters of our journal: we have an associate editor, a former editor-in-chief and the current one, and other authors who have published some of their most influential papers in our journal in recent years. Peter Forsyth, our former editor-in-chief, is a co-author, with Kai Ma, of the first paper in the issue: "Numerical solution of the Hamilton-Jacobi-Bellman formulation for continuous-time mean-variance asset allocation under stochastic volatility". The paper deals with robust and accurate numerical solution methods for the nonlinear Hamilton-Jacobi-Bellman partial differential equation (PDE), which describes the dynamic optimal portfolio selection problem. An example of an advanced numerical PDE technique for a relevant problem is given, along with a proof of the convergence of the discrete scheme.

In the author list of the issue's second paper, "High-performance American option pricing", we find Leif Andersen, one of our associate editors and the author of a muchcited 2006 paper on the quadratic exponential Monte Carlo scheme for the Heston model.With his co-authors Mark Lake and Dimitri Offengenden, he presents a paper on a high-performance spectral collocation method for the computation of American put and call option prices. They achieve an enormous speed-up when pricing a large number of American style options, under Black-Scholes dynamics. The computational throughput of the algorithm is close to 100 000 option prices per second per CPU. The research question in this paper is often encountered in industrial banking practice.

Our third paper is by Peter Carr and Dilip Madan, who have been prominent authors in modeling and computation in financial applications for many years. In 1999 they coauthored the influential Journal of Computational Finance paper "Option valuation using the fast Fourier transform". Their paper here, "Adjusting exponential Lévy models toward the simultaneous calibration of market prices for crash cliquets", is written with Ajay Khanna. Based on the insight that a variety of exponential Lévy models, when calibrated to near at-the-money option prices, typically overprice crash cliquets products, the authors propose so-called tail thinning strategies that may be employed to better connect the calibrated models to the crash cliquets prices.

The next paper in the issue, "An exact and efficient method for computing cross-Gammas of Bermudan swaptions and cancelable swaps under the Libor market model", is by Mark Joshi, who has contributed several exciting papers to our journal's success over the years, and Dan Zhu. A new simulation algorithm for computing the Hessians of Bermudan swaptions and cancelable swaps is presented, for which the resulting pathwise estimates are accurate and unbiased. A measure change, which is selected so that the variance of the likelihood ratio part is minimized at each exercise point, is performed to ensure that the first-order derivatives of the pathwise estimates of the price are continuous, resulting in an accurate and efficient simulation scheme.

The final paper in this special anniversary issue, also on Bermudan swaptions and called "Efficient computation of exposure profiles on real-world and risk-neutral scenarios for Bermudan swaptions", is by myself along with Qian Feng, Shashi Jain, Patrik Karlsson and Drona Kandhai. In the paper, real-world and risk-neutral scenarios are combined for the valuation of the exposure values of Bermudan swaptions on realworld Monte Carlo paths. Highly accurate and efficient risk management quantities like expected exposure and potential future exposure are computed, for which the risk-neutral and real-world scenarios need to be combined. Based on the stochastic grid bundling method, a robust regression-based Monte Carlo technique, it is possible to avoid nested Monte Carlo simulations.

At the time of writing this editorial, the referendum result has brought us drastic shifts in stock prices, currencies, commodities like gold, etc. The need for efficient numerical and computational techniques in risk management and in financial derivatives pricing will be ever higher. The future of computational finance is bright. While we celebrate reaching our twentieth volume, we wish you very enjoyable reading of this issue of The Journal of Computational Finance.

Cornelis W. Oosterlee
CWI - Dutch Center for Mathematics and Computer Science, Amsterdam

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