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.

Numerical solutions of certain nonlinear models in European options on a distributed computing environment

Financial modelling in the area of option pricing involves the understanding of the correlations between asset and movements of buy/sell in order to reduce risk in investment. Such activities depend on financial analysis tools being available to the trader with which he can make rapid and systematic evaluation of buy/sell contracts. In turn, analysis tools rely on fast numerical algorithms for the solution of financial mathematical models. There are many different financial activities apart from shares buy/sell activities. The main aim of this chapter is to discuss a distributed algorithm for the numerical solution of a European option. Both linear and non-linear cases are considered. The algorithm is based on the concept of the Laplace transform and its numerical inverse. The scalability of the algorithm is examined. Numerical tests are used to demonstrate the effectiveness of the algorithm for financial analysis. Time dependent functions for volatility and interest rates are also discussed. Applications of the algorithm to non-linear Black-Scholes equation where the volatility and the interest rate are functions of the option value are included. Some qualitative results of the convergence behaviour of the algorithm is examined. This chapter also examines the various computational issues of the Laplace transformation method in terms of distributed computing. The idea of using a two-level temporal mesh in order to achieve distributed computation along the temporal axis is introduced. Finally, the chapter ends with some conclusions.

Finite element modelling of crack detection tests

Four non-destructive tests for determining the length of fatigue cracks within the solder joints of a 2512 surface mount resistor are investigated. The sensitivity of the tests is obtained using finite element analysis with some experimental validation. Three of the tests are mechanically based and one is thermally based. The mechanical tests all operate by applying different loads to the PCB and monitoring the strain response at the top of the resistor. The thermal test operates by applying a heat source underneath the PCB, and monitoring the temperature response at the top of the resistor. From the modelling work done, two of these tests have shown to be sensitive to cracks. Some experimental results are presented but further work is required to fully validate the simulation results.

Assessing the performance of crack detection tests for solder joints

This paper presents both modelling and experimental test data to characterise the performance of four non-destructive tests. The focus is on determining the presence and rough magnitude of thermal fatigue cracks within the solder joints for a surface mount resistor on a strip of FR4 PCB. The tests all operate by applying mechanical loads to the PCB and monitoring the strain response at the top of the resistor. The modelling results show that of the four tests investigated, three are sensitive to the presence of a crack in the joint and its magnitude. Hence these tests show promise in being able to detect cracking caused by accelerated testing. The experimental data supports these results although more validation is required.

Financing of SME's: an asset side story

The main sources of financing for small and medium sized enterprises (SMEs) are equity (internally generated cash), trade credit paid on time, long and short term bank credits, delayed payment on trade credit and other debt. The marginal costs of each financing instrument are driven by asymmetric information (cost of gathering and analysing information) and transactions costs associated with non-payment (costs of collecting and selling collateral). According to the Pecking Order Theory, firms will choose the cheapest source in terms of cost. In the case of the static trade-off theory, firms choose finance so that the marginal costs across financing sources are all equal, thus an additional Euro of financing is obtained from all the sources whereas under the Pecking Order Theory the source is determined by how far down the Pecking Order the firm is presently located. In this paper, we argue that both of these theories miss the point that the marginal costs are dependent of the use of the funds, and the asset side of the balance sheet primarily determines the financing source for an additional Euro. An empirical analysis on a unique dataset of Portuguese SME's confirms that the composition of the asset side of the balance sheet has an impact of the type of financing used and the Pecking Order Theory and the traditional Static Trade-off theory are rejected.

Policy packages as potential routes to urban road pricing in the UK

This paper focuses on urban road pricing as a demand management policy that is often regarded as radical and generally unacceptable. Road pricing often gets delayed or abandoned due to low acceptability. This may be due to the fact that complex interactions and drivers of change affect road transport management and require cooperation within implementation networks. The implementation network is a group of people (referred to as partners and actors) who co-ordinate the introduction of policy tools. The drivers of change include any internal or external influences that have an effect on the time, place, or ‘shape’ of the policy measures being introduced. Demand management measures that focus on 'sustainable transport' usually address a limited set of objectives and are often implemented alone i.e. are not necessarily combined with other policy measures. When combined with other measures, it is not always clear whether the multiple interactions between policy tools and implementation networks have been sufficiently considered. Examples of ongoing implementation of policy package in the UK are the support of road pricing initiatives combined with public transport improvements by the Transport Innovation Fund. The objectives of the paper are twofold. First, we present a review of the UK urban road pricing situation. Second, we contrast the emerging issues against six key implementation factors. The analysis of three existing UK road pricing examples - London, Edinburgh and Durham – shows the importance of combining policy tools. Furthermore, through the above examples and theoretical arguments, we emphasise the additional need of creating and maintaining strong networks when implementing policy packages.