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 crossfertilisation 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 gained enough material for two special issues related to the workshop: this is the second of those two special issues. The focus here is on advances in numerical techniques for computing prices of financial derivatives.
The first paper, "Applications of periodic and quasiperiodic decompositions to options pricing" by Dominique Bang, introduces periodic and quasiperiodic decompositions as highly efficient alternatives to Fourier-based option pricing.
In the second paper, "Proper orthogonal decomposition for pricing options", Olivier Pironneau presents a highly efficient option pricing technique based on proper orthogonal decompositions from model order reduction. In the third paper, "Transform analysis and asset pricing for diffusion processes: a recursive approach", Marc J. Goovaerts, Roger J. A. Laeven and Zhaoning Shang propose a Laplace transform method based on recursions for specific diffusion processes.
The fourth paper, "Alternating direction implicit finite difference schemes for the Heston-Hull-White partial differential equation" by Tinne Haentjens and Karel J. In 't Hout, discusses the highly efficient pricing of the Heston-Hull-White partial differential equation using alternating direction implicit finite difference schemes.
In the fifth paper, "Pricing pension plans based on average salary without early retirement: partial differential equation modeling and numerical solution", Maria del Carmen Calvo-Garrido and Carlos Vázquez define a partial differential equation for the valuation of pension plans and consider its accurate numerical solution.
We hope you enjoy reading these papers.
Quantitative Methods in Financial and Insurance Mathematics: Part 2
LETTER FROM THE GUEST EDITORS
Karel J. In 't Hout - University of Antwerp
CornelisW. Oosterlee - CWI/Delft University of Technology
Alternating direction implicit finite difference schemes for the Heston-Hull-White partial differential equation
Pricing pension plans based on average salary without early retirement: partial differential equation modeling and numerical solution