After a celebration of the start of the twentieth volume of The Journal of Computational Finance in our last issue, we are now, with the current issue, back in our regular publication sequence. This issue is a diverse one, containing papers on applications in risk management as well as in financial derivatives pricing. Regarding computational methods, as well as Monte Carlo techniques we look at saddlepoint and Fourier methods.
The first research paper of this issue is by Rubén Garcia-Céspedes and Manuel Moreno: "Extended saddlepoint methods for credit risk measurement". The authors extend the well-known saddlepoint approximation within the credit risk context. To determine the loss distribution of a portfolio, the extended method is based on the Taylor expansion of the inverse Laplace transform and on Hermite polynomials. Based on a portfolio that is representative of the Spanish financial situation, it is shown that the extensions help to characterize the portfolio risk accurately.
"Valuation of options on discretely sampled variance: a general analytic approximation" by Gabriel Drimus, Walter Farkas and Elise Gourier is the second paper in the issue. The values of options on discretely sampled realized variances may be significantly higher than the option values of their continuous counterparts. An analytic correction to the value of an option on continuously sampled variance is proposed here under stochastic volatility dynamics. The quality of the approximation is compared by means of numerical techniques for these options on the discretely sampled variance.
Our third paper is "Transform-based evaluation of prices and Greeks of lookback options driven by Lévy processes" by Naser M. Asghari and Michel Mandjes. An efficient numerical inversion technique, based on probabilistic information from theWiener-Hopf decomposition, is proposed to compute prices and Greeks of lookback options under Lévy dynamics. As only an implicit version of the Wiener- Hopf factor is typically available, the Lévy process is approximated by a cleverly chosen approximate process for which the relevant information can be directly extracted. Excellent computational performance is shown for a broad range of Lévy processes.
The issue's final paper is "Faster comparison of stopping times by nested conditional Monte Carlo" by Fabian Dickmann and Nikolaus Schweizer. The authors come up with the interesting insight that deliberately introducing a nested simulation stage in a Monte Carlo algorithm can lead to variance reductions when analyzing stopping times for Bermudan and American options. The robustness of this technique is shown and enhancements are presented by further variance reduction when combining the method with quasi-Monte Carlo and multilevel Monte Carlo schemes.
I 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
This paper reviews and extends the saddlepoint methods currently available to measure credit risk.
In this paper the authors provide a comprehensive treatment of the discretization effect under general stochastic volatility dynamics.
The authors develop a technique, based on numerical inversion, to compute the prices and Greeks of lookback options driven by Lévy processes.
The authors propose a novel method for efficiently comparing the performance of different stopping times.