Multigrid for American option pricing with stochastic volatility

The paper describes an implicit finite difference approach to the pricing of American options on assets with a stochastic volatility. A multigrid procedure is described for the fast iterative solution of the discrete linear complementarity problems that result. The accuracy and performance of this approach is improved considerably by a strike-price related analytic transformation of asset prices and adaptive time-stepping.

Phase-accuracy comparisons and improved far-field estimates for 3-D edge elements on tetrahedral meshes

Edge-element methods have proved very effective for 3-D electromagnetic computations and are widely used on unstructured meshes. However, the accuracy of standard edge elements can be criticised because of their low order. This paper analyses discrete dispersion relations together with numerical propagation accuracy to determine the effect of tetrahedral shape on the phase accuracy of standard 3-D edgeelement approximations in comparison to other methods. Scattering computations for the sphere obtained with edge elements are compared with results obtained with vertex elements, and a new formulation of the far-field integral approximations for use with edge elements is shown to give improved cross sections over conventional formulations.

pKa values of aqua ligands of platinum (II) anticancer complexes: [1H, 15N] and 195Pt NMR Studies of cis- and trans- [PtCl2 (NH3) (Cyclohexylamine)]

Syntheses and NMR studies are reported of two 15N-labelled Pt(II) complexes of anticancer interest: cis-PtCl2(15NH3)(c-C6H1115NH2), a metabolite of the orally-active Pt(IV) complex cis,trans,cis-[PtCl2(acetate)2(c-C6H11NH2)(NH3), and trans-[PtCl2(15NH3)(c-C6H1115NH2), a reduction product of the active Pt(IV) complex trans,trans,trans-[PtCl2(OH)2(c-C6H11NH2). For cis-[PtCl2(15NH3)(c-C6H1115NH2), hydrolysis was faster for the chloride ligand trans to cyclohexylamine, and the pKa values determined by [1H, 15N NMR spectroscopy for the two cis monoaqua isomers were the same (6.73). The trans monoaqua complex was a stronger acid with pKa of 5.4 (determined by 195Pt NMR). For the cis diaqua complex, pKa values of 5.68 and 7.68 were determined.

[1H,15N] N.M.R. Kinetic Studies of Reactions of cis- and trans-[PtCl2(15NH3)(c-C6H1115NH2)] with Guanosine 5'-Monophosphate

cis-[PtCl2(15NH3)(c-C6H11NH2)] is an active metabolite of the oral platinum(IV) anticancer drug cis,trans,cis-[PtCl2(CH3CO2)2(NH2)(c-C6H11NH2)]. Since it is likely that guanine bases on DNA are targets for this drug, we have analysed the kinetics of reaction of this platinum(II) metabolite with guanosine 5′-monophosphate (5′-GMP) at 310 K, pH 7, using [1H, 15N] n.m.r. methods. Reactions of the trans isomer are reported for comparison. The reactions proceed via aquated intermediates, and, for the cis isomer, the rates of aquation and substitution of H2O by 5′-GMP are 2-5 times faster trans to the amine ligand (c-C6H11NH2) compared to trans to NH3 for both the first and second steps. For the trans complex, the first aquation step is c. 3 times faster than for the cis complex, as expected from the higher trans influence of Cl¯, whereas the rate of the second aquation step (trans to N7 of 5′-GMP) is comparable to that trans to NH3. These findings have implications for the courses of reactions with DNA.

Coupled 3-D finite difference time domain and finite volume methods for solving microwave heating in porous media

Computational results for the microwave heating of a porous material are presented in this paper. Combined finite difference time domain and finite volume methods were used to solve equations that describe the electromagnetic field and heat and mass transfer in porous media. The coupling between the two schemes is through a change in dielectric properties which were assumed to be dependent both on temperature and moisture content. The model was able to reflect the evolution of temperature and moisture fields as the moisture in the porous medium evaporates. Moisture movement results from internal pressure gradients produced by the internal heating and phase change.

Parallel performance in multi-physics simulation

A comprehensive simulation of solidification/melting processes requires the simultaneous representation of free surface fluid flow, heat transfer, phase change, non-linear solid mechanics and, possibly, electromagnetics together with their interactions in what is now referred to as "multi-physics" simulation. A 3D computational procedure and software tool, PHYSICA, embedding the above multi-physics models using finite volume methods on unstructured meshes (FV-UM) has been developed. Multi-physics simulations are extremely compute intensive and a strategy to parallelise such codes has, therefore, been developed. This strategy has been applied to PHYSICA and evaluated on a range of challenging multi-physics problems drawn from actual industrial cases.

A framework for historical case-based reasoning

This paper presents a framework for Historical Case-Based Reasoning (HCBR) which allows the expression of both relative and absolute temporal knowledge, representing case histories in the real world. The formalism is founded on a general temporal theory that accommodates both points and intervals as primitive time elements. A case history is formally defined as a collection of (time-independent) elemental cases, together with its corresponding temporal reference. Case history matching is two-fold, i.e., there are two similarity values need to be computed: the non-temporal similarity degree and the temporal similarity degree. On the one hand, based on elemental case matching, the non-temporal similarity degree between case histories is defined by means of computing the unions and intersections of the involved elemental cases. On the other hand, by means of the graphical presentation of temporal references, the temporal similarity degree in case history matching is transformed into conventional graph similarity measurement.

Case base reduction using solution-space metrics

In this paper we propose a case base reduction technique which uses a metric defined on the solution space. The technique utilises the Generalised Shepard Nearest Neighbour (GSNN) algorithm to estimate nominal or real valued solutions in case bases with solution space metrics. An overview of GSNN and a generalised reduction technique, which subsumes some existing decremental methods, such as the Shrink algorithm, are presented. The reduction technique is given for case bases in terms of a measure of the importance of each case to the predictive power of the case base. A trial test is performed on two case bases of different kinds, with several metrics proposed in the solution space. The tests show that GSNN can out-perform standard nearest neighbour methods on this set. Further test results show that a caseremoval order proposed based on a GSNN error function can produce a sparse case base with good predictive power.

Requirements and design of an integrated European environmental information communication system, (IEEICS)

The needs for various forms of information systems relating to the European environment and ecosystem are reviewed, and limitations indicated. Existing information systems are reviewed and compared in terms of aims and functionalities. We consider TWO technical challenges involved in attempting to develop an IEEICS. First, there is the challenge of developing an Internet-based communication system which allows fluent access to information stored in a range of distributed databases. Some of the currently available solutions are considered, i.e. Web service federations. The second main challenge arises from the fact that there is general intra-national heterogeneity in the definitions adopted, and the measurement systems used throughout the nations of Europe. Integrated strategies are needed.

Models and tools for an integrated European environmental management and decision support system, (IEEMDSS)

This work proceeds from the assumption that a European environmental information and communication system (EEICS) is already established. In the context of primary users (land-use planners, conservationists, and environmental researchers) we ask what use may be made of the EEICS for building models and tools which is of use in building decision support systems for the land-use planner. The complex task facing the next generation of environmental and forest modellers is described, and a range of relevant modelling approaches are reviewed. These include visualization and GIS; statistical tabulation and database SQL, MDA and OLAP methods. The major problem of noncomparability of the definitions and measures of forest area and timber volume is introduced and the possibility of a model-based solution is considered. The possibility of using an ambitious and challenging biogeochemical modelling approach to understanding and managing European forests sustainably is discussed. It is emphasised that all modern methodological disciplines must be brought to bear, and a heuristic hybrid modelling approach should be used so as to ensure that the benefits of practical empirical modelling approaches are utilised in addition to the scientifically well-founded and holistic ecosystem and environmental modelling. The data and information system required is likely to end up as a grid-based-framework because of the heavy use of computationally intensive model-based facilities.

Assessing the scalability of multiphysics tools for modeling solidification and melting processes on parallel clusters

A comprehensive solution of solidification/melting processes requires the simultaneous representation of free surface fluid flow, heat transfer, phase change, nonlinear solid mechanics and, possibly, electromagnetics together with their interactions, in what is now known as multiphysics simulation. Such simulations are computationally intensive and the implementation of solution strategies for multiphysics calculations must embed their effective parallelization. For some years, together with our collaborators, we have been involved in the development of numerical software tools for multiphysics modeling on parallel cluster systems. This research has involved a combination of algorithmic procedures, parallel strategies and tools, plus the design of a computational modeling software environment and its deployment in a range of real world applications. One output from this research is the three-dimensional parallel multiphysics code, PHYSICA. In this paper we report on an assessment of its parallel scalability on a range of increasingly complex models drawn from actual industrial problems, on three contemporary parallel cluster systems.

Semi-Lagrange time integration for PDE models of asian options

Semi-Lagrange time integration is used with the finite difference method to provide accurate stable prices for Asian options, with or without early exercise. These are combined with coordinate transformations for computational efficiency and compared with published results

Microwave modelling and validation in food thawing applications

Developing temperature fields in frozen cheese sauce undergoing microwave heating were simulated and measured. Two scenarios were investigated: a centric and offset placement on the rotating turntable. Numerical modeling was performed using a dedicated electromagnetic Finite Difference Time Domain (FDTD) module that was two-way coupled to the PHYSICA multiphysics package. Two meshes were used: the food material and container were meshed for the heat transfer and the microwave oven cavity and waveguide were meshed for the microwave field. Power densities obtained on the structured FDTD mesh were mapped onto the unstructured finite volume method mesh for each time-step/turntable position. On heating for each specified time-step the temperature field was mapped back onto the FDTD mesh and the electromagnetic properties were updated accordingly. Changes in thermal/electric properties associated with the phase transition were fully accounted for as well as heat losses from product to cavity. Detailed comparisons were carried out for the centric and offset placements, comparing experimental temperature profiles during microwave thawing with those obtained by numerical simulation.

Variable frequency microwave curing of polymer materials in microelectronics packaging applications

The use of variable frequency microwave technology in curing of polymer materials used in microelectronics applications is discussed. A revolutionary open-ended microwave curing system is outlined and assessed using experimental and numerical approaches. Experimental and numerical results are presented, demonstrating the feasibility of the system