On April 18-21, 2011 a Lorentz workshop on "Quantitative Methods in Financial and Insurance Mathematics" took place in Leiden in the Netherlands, with almost seventy participants from many different countries. The main purposes of the workshop were:
(1) to bring together researchers from financial and actuarial mathematics to discuss the different stochastic models involved in their (financial, insurance and pension) products, and the different concepts used to reduce the risk of losses due to unexpected market conditions, and
(2) to bring together experts using different numerical techniques (Monte Carlo, partial differential equations, quadrature) in order to inform each other about the latest advances and, in particular, to exchange information about cross fertilisation of these methods.
These topics were discussed in twenty-six scientific presentations by international experts from quantitative finance and insurance mathematics. This special issue of The Journal of Computational Finance gives some highlights from the very interesting work presented during the week in Leiden. We have enough material for two special issues related to the workshop and five further papers will appear in the next issue of the journal. In this issue, the focus is on advances in modeling and numerical techniques.
The first paper, "Efficient and accurate log-Lévy approximations of Lévy-driven LIBOR models" by Antonis Papapantoleon, John Schoenmakers and David Skovmand, considers a Lévy-driven LIBOR model and introduces effective higher-order approximation schemes for the interest rate dynamics.
In the second paper, "An equity interest rate hybrid model with stochastic volatility and the interest rate smile", Lech A. Grzelak and Cornelis W. Oosterlee develop an equity-interest rate hybrid model based on the Heston stochastic volatility and LIBOR market models and demonstrate its highly efficient calibration using Fourier-based techniques.
In the third paper, "Calibration and Monte Carlo pricing of the SABR-Hull-White model for long-maturity equity derivatives", Bin Chen, Lech A. Grzelak and Cornelis W.Oosterlee consider a hybrid SABR-Hull-White model and propose a projection formula and Monte Carlo techniques that allow for a fast calibration and pricing of exotic derivatives.
The fourth paper in the issue, "Numerical valuation of basket credit derivatives in structural jump-diffusion models" by Karolina Bujok and Christoph Reisinger, discusses the effective pricing of basket credit derivatives in a multivariate structural jump-diffusion model using Monte Carlo finite difference discretization of the resulting stochastic partial differential equation.
In the fifth paper, "Sato two-factor models for multivariate option pricing", Florence Guillaume defines a Sato model for multiasset option prices and shows, through numerical examples, that this model both provides a good fit to univariate option surfaces and can adequately reproduce market-implied correlations. We hope you enjoy reading these papers.
Quantitative Methods in Financial and Insurance Mathematics: Part 1
LETTER FROM THE GUEST EDITORS
Karel J. In 't Hout - University of Antwerp
CornelisW. Oosterlee - CWI/Delft University of Technology
Calibration and Monte Carlo pricing of the SABR–Hull–White model for long-maturity equity derivatives