In this issue of The Journal of Computational Finance, we encounter different contemporary approximations and techniques for financial problems.We have a paper on drift approximation for the SABR/Libor market model, one giving insight into model risk in the context of portfolio optimization and two papers on Fourier techniques.
In a ten-page paper titled "A simple approximation for the no-arbitrage drifts in Libor market model-SABR-family interest-rate models", Riccardo Rebonato presents an effective approximation that reduces the dimensionality of this nontrivial system by one order of magnitude. The validity of the approximation is also demonstrated for a stressed test case.
Model risk is addressed in "A robust set-valued scenario approach for handling modeling risk in portfolio optimization" by Shushang Zhu, Xiaodong Ji and Duan Li. The modeling risk comes from the uncertainty in determining the distribution of the asset returns and the error due to scenario simulations. Robust portfolio selection is placed within a decision framework that can be translated to linear programming and cone programming formulations. The paper shows that model risk can be evaluated and alleviated.
In the first of the two Fourier pricing papers in this issue, Gareth G. Haslip and Vladimir K. Kaishev discuss "A novel Fourier transform B-spline method for option pricing". By means of B-spline interpolation they provide an accurate closed-form representation of the option price under an inverse Fourier transform. Applications include the inverse problem of cross-sectional calibration. From my own research group, "On the application of spectral filters in a Fourier option pricing technique" by M. J. Ruijter, M. Versteegh and myself appears as the current issue's final paper. When dealing with nonsmooth functions - such as a combination of a nonsmooth density and a payoff - spectral filters can be applied to deal efficiently with the so-called Gibbs phenomenon. The use of these filters will enhance the convergence of the Fourier technique employed, which in this case is the Fourier cosine method (the COS method). The simplicity and effectiveness of classical filtering techniques from signal processing are demonstrated.
We are making good progress with the enhancement of The Journal of Computational Finance's electronic submission and manuscript handling system, which should provide an enhanced submission procedure, efficient manuscript handling and swift throughput times.
I wish you very pleasant reading of the present issue.
Cornelis W. Oosterlee
CWI - Dutch Center for Mathematics and Computer Science, Amsterdam
A simple approximation for the no-arbitrage drifts in Libor market model–SABR-family interest-rate models
This paper presents a simple approximation for the noarbitrage drifts that appear in Libor market model SABR-family term structure models.
By means of B-spline interpolation, this paper provides an accurate closed-form representation of the option price under an inverse Fourier transform.
When dealing with nonsmooth functions – such as a combination of a nonsmooth density and a payoff – spectral filters can be applied to deal efficiently with the so-called Gibbs phenomenon. The simplicity and effectiveness of classical filtering…
By introducing the set-valued scenario, this paper proposes a unified robust portfolio selection approach under downside risk measures.