Lars Josef Höök

BENCHOP – The BENCHmarking project in option pricing

The aim of the BENCHOP project is to provide the finance community with a common suite of benchmark problems for option pricing. We provide a detailed description of the six benchmark problems together with methods to compute reference solutions. We have implemented fifteen different numerical methods for these problems, and compare their relative performance. All implementations are available on line and can be used for future development and comparisons.

A model for self-consistent simulation of ICRH suitable for integrating modelling

A self-consistent modelling of ion cyclotron resonance heating (ICRH) is reviewed with the aim of obtaining a fast robust scheme suitable for routine simulation for transport codes and data analysis. Due to the complexity of calculating the wave field and the distribution function self-consistently simplifications are necessary. To improve modelling of the wave field, methods are developed to include higher order finite Larmor radius terms, up-and downshifts of the parallel wave number and to improve calculations of damping due to the transit time magnetic pumping in finite element wave codes without decomposing the wave locally into planar waves. A new code, SELFO-light, for self-consistent modelling of ion cyclotron heating suitable for routine calculations is developed. The code is based on coupling the global wave code LION with a simple one-dimensional time-dependent Fokker-Planck code. Both the wave and the Fokker-Planck codes use finite element representations. The importance of self-consistent modelling of ion cyclotron heating is illustrated by studying the effect on the power partition for a fast wave current drive scenario at lower harmonic resonances in a deuterium plasma. It is found that the fraction of the power absorbed on the deuterium and the time to reach the steady state vary strongly depending on the position of the resonances. It is found that the deuterium absorption becomes strongly localized to regions where the resonances are tangential to the magnetic flux surfaces.

Embryonic expression patterns and phylogenetic analysis of panarthropod sox genes: insight into nervous system development, segmentation and gonadogenesis

BackgroundSox (Sry-related high-mobility-group box) genes represent important factors in animal development. Relatively little, however, is known about the embryonic expression patterns and thus possible function(s) of Sox genes during ontogenesis in panarthropods (Arthropoda+Tardigrada+Onychophora). To date, studies have been restricted exclusively to higher insects, including the model system Drosophila melanogaster, with no comprehensive data available for any other arthropod group, or any tardigrade or onychophoran.ResultsThis study provides a phylogenetic analysis of panarthropod Sox genes and presents the first comprehensive analysis of embryonic expression patterns in the flour beetle Tribolium castaneum (Hexapoda), the pill millipede Glomeris marginata (Myriapoda), and the velvet worm, Euperipatoides kanangrensis (Onychophora). 24 Sox genes were identified and investigated: 7 in Euperipatoides, 8 in Glomeris, and 9 in Tribolium. Each species possesses at least one ortholog of each of the five expected Sox gene families, B, C, D, E, and F, many of which are differentially expressed during ontogenesis.ConclusionSox gene expression (and potentially function) is highly conserved in arthropods and their closest relatives, the onychophorans. Sox B, C and D class genes appear to be crucial for nervous system development, while the Sox B genes Dichaete (D) and Sox21b likely play an additional conserved role in panarthropod segmentation. The Sox B gene Sox21a likely has a conserved function in foregut and Malpighian tubule development, at least in Hexapoda. The data further suggest that Sox D and E genes are involved in mesoderm differentiation, and that Sox E genes are involved in gonadal development.The new data expand our knowledge about the expression and implied function of Sox genes to Mandibulata (Myriapoda+Pancrustacea) and Panarthropoda (Arthropoda+Onychophora).

Randomized quasi-Monte Carlo simulation of fast-ion thermalization

This work investigates the applicability of the randomized quasi-Monte Carlo method for simulation of fast-ion thermalization processes in fusion plasmas, e.g. for simulation of neutral beam injection and radio frequency heating. In contrast to the standard Monte Carlo method, the quasi-Monte Carlo method uses deterministic numbers instead of pseudo-random numbers and has a statistical weak convergence close to , where N is the number of markers. We have compared different quasi-Monte Carlo methods for a neutral beam injection scenario, which is solved by many realizations of the associated stochastic differential equation, discretized with the Euler–Maruyama scheme. The statistical convergence of the methods is measured for time steps up to 214.

Library for RF Interactions in Orbit Following Codes

A new code-library has been developed to handle quasi-linear wave particle interactions in orbit following Monte Carlo codes, RFOF (RF interactions in Orbit Following codes). This library will enab ...

The Kolmogorov forward fractional partial differential equation for the CGMY-process with applications in option pricing

Abstract In this paper we derive the Kolmogorov forward fractional partial differential equation (FPDE) for the CGMY-process. The resulting FPDE is solved numerically with a second order method in space and Backward Differentiation Formula of order two in time. We price options by integrating the resulting probability density function multiplied by the pay-off function of the option. Hence, we only have to solve one FPDE to price several options. This is useful in practical applications where it is common to price many options simultaneously for the same underlying diffusion model. The traditional way to price options requires the solution of one FPDE per option. Since the FPDEs are of similar type and complexity, the advantage of our suggested method is obvious in the case of pricing multiple European type options on the same underlying asset when only the pay-off function differs. The numerical experiments verify that the extra cost of pricing several options compared to only one option is very small with our suggested method.

Efficient computation of the quasi likelihood function for discretely observed diffusion processes

An efficient numerical method for nearly simultaneous computation of all conditional moments needed for quasi maximum likelihood estimation of parameters in discretely observed stochastic differential equations is presented. The method is not restricted to any particular dynamics of the stochastic differential equation and is virtually insensitive to the sampling interval. The key contribution is that computational complexity is sublinear in terms of expensive operations in the number of observations as all moments can be computed offline in a single operation. Simulations show that the bias of the method is small compared to the random error in the estimates, and to the bias of comparable methods. Furthermore the computational cost is comparable (actually faster for moderate and large data sets) to the simple, but in some applications badly biased, the Euler-Maruyama approximation.

Composition schemes for the stochastic differential equation describing collisional pitch-angle diffusion

Composition schemes for the stochastic differential equation describing collisional pitch-angle diffusion

A dielectric response model for FEM solutions of ICRF wave fields

Modelling of fast wave ICRF heating in large machines with high density such as DEMO is challenging because of the short wave lengths. Therefore, fast, efficient global wave solvers are necessary. A major difficulty with calculating the wave field in a spatial dispersive medium is that the dielectric tensor becomes a function of the local wave vector, which in its turn depends on the solution. Furthermore, the solution may consist of several waves co-existing at the same location subjected to separate response functions. In order to model upshift of the parallel wave vector, higher order FLR-effects on the cyclotron absorption and TTMP damping for the electron absorption methods based on iteration, suitable for FEM codes, are proposed.