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.

A distributed algorithm for European options with nonlinear volatility

A distributed algorithm is developed to solve nonlinear Black-Scholes equations in the hedging of portfolios. The algorithm is based on an approximate inverse Laplace transform and is particularly suitable for problems that do not require detailed knowledge of each intermediate time steps.

The parallel solution of early-exercise Asian options with stochastic volatility

This paper describes an parallel semi-Lagrangian finite difference approach to the pricing of early exercise Asian 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. Asian options are contingent claims with payoffs that depend on the average price of an asset over some time interval. The payoff may depend on this average and a fixed strike price (Fixed Strike Asians) or it may depend on the average and the asset price (Floating Strike Asians). The option may also permit early exercise (American contract) or confine the holder to a fixed exercise date (European contract). The Fixed Strike Asian with early exercise is considered here where continuous arithmetic averaging has been used. Pricing such an option where the asset price has a stochastic volatility leads to the requirement to solve a tri-variate partial differential inequation in the three state variables of asset price, average price and volatility (or equivalently, variance). The similarity transformations [6] used with Floating Strike Asian options to reduce the dimensionality of the problem are not applicable to Fixed Strikes and so the numerical solution of a tri-variate problem is necessary. The computational challenge is to provide accurate solutions sufficiently quickly to support realtime trading activities at a reasonable cost in terms of hardware requirements.

A policy-definition language and prototype implementation library for policy-based autonomic systems

This paper presents work towards generic policy toolkit support for autonomic computing systems in which the policies themselves can be adapted dynamically and automatically. The work is motivated by three needs: the need for longer-term policy-based adaptation where the policy itself is dynamically adapted to continually maintain or improve its effectiveness despite changing environmental conditions; the need to enable non autonomics-expert practitioners to embed self-managing behaviours with low cost and risk; and the need for adaptive policy mechanisms that are easy to deploy into legacy code. A policy definition language is presented; designed to permit powerful expression of self-managing behaviours. The language is very flexible through the use of simple yet expressive syntax and semantics, and facilitates a very diverse policy behaviour space through both hierarchical and recursive uses of language elements. A prototype library implementation of the policy support mechanisms is described. The library reads and writes policies in well-formed XML script. The implementation extends the state of the art in policy-based autonomics through innovations which include support for multiple policy versions of a given policy type, multiple configuration templates, and meta-policies to dynamically select between policy instances and templates. Most significantly, the scheme supports hot-swapping between policy instances. To illustrate the feasibility and generalised applicability of these tools, two dissimilar example deployment scenarios are examined. The first is taken from an exploratory implementation of self-managing parallel processing, and is used to demonstrate the simple and efficient use of the tools. The second example demonstrates more-advanced functionality, in the context of an envisioned multi-policy stock trading scheme which is sensitive to environmental volatility

Generic support for policy-based self-adaptive systems

This paper presents a policy definition language which forms part of a generic policy toolkit for autonomic computing systems in which the policies themselves can be modified dynamically and automatically. Targeted enhancements to the current state of practice include: policy self-adaptation where the policy itself is dynamically modified to match environmental conditions; improved support for non autonomics-expert developers; and facilitating easy deployment of adaptive policies into legacy code. The policy definition language permits powerful expression of self-managing behaviours and facilitates a diverse policy behaviour space. Features include support for multiple versions of a given policy type, multiple configuration templates, and meta policies to dynamically select between policy instances. An example deployment scenario illustrates advanced functionality in the context of a multi policy stock trading system which is sensitive to environmental volatility.

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.

The determinants of business performance of estate agency in England and Wales

Purpose: This paper seeks to investigate the factors influencing the business performance of estate agency in England and Wales. Design/methodology/approach: The paper investigates the effect of housing market, company size and pricing policy on business performance in the estate agency sector in England and Wales. The analysis uses the survey data of Woolwich Cost of Moving Survey (a survey of transactions costs sponsored by the Woolwich/Barclays Bank) from 2003 to 2005 to test the hypothesis that the business performance of estate agency is affected by industry characteristics and firm factors. Findings: The empirical analysis indicates that the business performance of estate agency is subject to market environment volatility such as market uncertainty, housing market liquidity and house price changes. The firm factors such as firm size and the level of agency fee have no explanatory power in explaining business performance. The level of agency fee is positively associated with firm size, market environment and liquidity. Research limitations/implications: The research is limited to the data received and is based on a research project on transaction costs designed prior to this analysis. Originality/value: There is little other research that investigates the factors determining the business performance of estate agency, using consecutive data of three years across England and Wales. The findings are useful for practitioners and/or managers to allocate resources and adjust their business strategy to enhance business performance in the estate agency sector.