This issue of The Journal of Computational Finance is, once again, diverse and interesting in terms of the numerical techniques employed in its contributions. We have one paper that deals with lattice trees, another that deals with numerics for partial differential equations (PDEs), and another that deals with a special Monte Carlo method for pricing financial derivatives. Each of the applications of these known numerical methods is quite remarkable. In addition to these three papers, we have a paper on statistics that aims to prevent overfitting in backtesting applications. Each of the issue’s papers presents analysis and gives insight into the performance of the various techniques.
The first of the numerical papers is “An efficient convergent lattice method for Asian option pricing with superlinear complexity” by Ling Lu,Wei Xu and Zhehui Qian. In this paper Curran’s willow tree model forms the basis of an efficient lattice method for pricing path-dependent Asian options. The error bounds and convergence rate of the proposed lattice method are analyzed, and the method is numerically compared with competitor methods. The authors find that their method exhibits favorable results.
“The probability of backtest overfitting” by David H. Bailey, Jonathan M. Borwein, Marcos López de Prado and Qiji Jim Zhu is the second paper in this issue. It deals with statistics and presents formulas and approximation techniques to determine the probability of backtest overfitting.A framework is presented for modeling in-sample and out-of-sample performances. The probability of backtested overfitting is defined as the probability that an optimal in-sample strategy underperforms in mean out-of sample testing. The insights in this paper are highly valuable for investment firms and portfolio managers relying on simulations based on historical market data.
Antonia Mayerhofer and Karsten Urban present our third paper, “A reduced basis method for parabolic PDEs with parameter functions and application to option pricing”, which deals with the issue’s second numerical technique. Solving an option pricing PDE multiple times, eg, for calibration, is the topic of discussion here. For these so-called multi-query problems, reduced basis methods are presented on the basis of rigorous mathematical theory. It is the space-time variational formulation of the PDE that forms the basis for the techniques proposed. By combining an offline computational phase with an online one, the CPU time required for the important online phase can be drastically reduced.
The issue’s fourth paper, “Valuation of barrier options using sequential Monte Carlo” by PavelV. Shevchenko and Pierre Del Moral, contributes the third numerical technique. The authors apply the sequential Monte Carlo method, which is well known in classical engineering, to pricing an exotic option within the context of financial engineering. Special enhancements of the technique, which are tailored to discretely and continuously monitored barrier options, give rise to smaller variances and higher efficiency than the classical Monte Carlo techniques for barrier options. Significant
improvements in performance are found when the probability of not hitting the barrier is small.
This issue heralds the start of a new era for The Journal of Computational Finance. Until now, we have always had four issues per year, but due to the increasing popularity of the journal and the high quality of recent submissions, we have decided to publish five issues per year starting from Volume 21. Our next issue will be published in June; in the meantime, enjoy reading The Journal of Computational Finance.
CWI – Dutch Center for Mathematics and Computer Science, Amsterdam
In this paper the authors present an efficient convergent lattice method for Asian option pricing with superlinear complexity.
The authors propose a general framework to assess the probability of backtest overfitting (PBO).
A reduced basis method for parabolic partial differential equations with parameter functions and application to option pricing
The authors introduce an RB space–time variational approach for parametric PPDEs with coefficient parameters and a variable initial condition.
The authors present Sequential Monte Carlo (SMC) method for pricing barrier options.