Welcome to the second issue of The Journal of Computational Finance for 2018, which, once again, contains four very interesting papers. Each focuses on a specific type of asset dynamics, with two papers examining a local volatility enhancement of, respectively, interest rate and commodity dynamics; one investigating a hybrid stochastic volatility/stochastic interest rate three-factor model; and one employing a model with factor-based subordinated Lévy processes for multivariate financial derivatives. Different valuation techniques are advocated under these dynamics.
In the issue’s first paper, “Hybrid finite-difference/pseudospectral methods for the Heston and Heston–Hull–White partial differential equations” by Christian Hendricks, Matthias Ehrhardt and Michael Günther, an advanced numerical approach
– based partly on finite differences, partly on pseudospectral discretization – is explained. In the asset direction, finite differences are applied, whereas in the other spatial dimensions (volatility, interest rate, etc) a collocation method is applied. The proposed scheme is highly accurate in the collocated directions, second order in both asset dimension and time, and unconditionally stable.
Dariusz Gatarek and Juliusz Jabłecki provide the second paper in this issue: “A nonparametric local volatility model for swaptions smile”. In it, they price interest rate swaptions based on a nonparametric local volatility Cheyette model. Given market prices of swaptions, a unique diffusion process is constructed that is consistent with these prices. The local volatility component is linked to the entire yield curve. As the authors state, the model is relatively straightforward to calibrate and less involved than other stochastic volatility approaches.
Our third paper is “Local volatility models in commodity markets and online calibration” by Vinicius Albani, Uri M. Ascher and Jorge P. Zubelli. Here, the authors consider a special class of local volatility surfaces in order to price European options on commodity futures. The ill-posedness of the calibration problem is dealt with by means of a Tikhonov-type regularization technique. Empirical tests with market and synthetic data demonstrate the effectiveness of the methodology and the algorithms.
The fourth and final paper in this issue is “Pricing multivariate barrier reverse convertibles with factor-based subordinators” by Marina Marena, Andrea Romeo and Patrizia Semeraro. Factor-based subordinated Lévy processes of variance gamma and normal inverse Gaussian type are studied and used to price multivariate barrier reverse convertibles. The ability to capture smile patterns and empirical correlations is demonstrated. Based on a sensitivity analysis, the impacts of both product characteristics and model features are analyzed. A trade-off between marginal and correlation fit is reported.
I wish you very pleasant reading of this April 2018 issue of The Journal of Computational Finance.
Cornelis W. Oosterlee
CWI – Dutch Center for Mathematics and Computer Science, Amsterdam
Hybrid finite-difference/pseudospectral methods for the Heston and Heston–Hull–White partial differential equations
In this paper, the authors propose a hybrid spatial finite-difference/pseudospectral discretization for European option-pricing problems under the Heston and Heston–Hull–White models.
This paper proposes a nonparametric local volatility Cheyette model and applies it to pricing interest rate swaptions.
This paper introduces a local volatility model for the valuation of options on commodity futures by using European vanilla option prices.
In this paper, the authors study factor-based subordinated Lévy processes in their variance gamma (VG) and normal inverse Gaussian (NIG) specifications, and focus on their ability to price multivariate exotic derivatives.