The electrical properties and structure of halo-borate glasses and glass-ceramics

The effect on the electrical properties of doping simple borate materials with various halides has been investigated. Most of the work concentrates on sodium borate as a base material but an extension is made to also consider alkaline-earth borates. Initially, glassy products are examined but later in the project, because of significant and unexpected trends, attention is focussed on re-crystallised glass-ceramics formed from the original glassy specimens. Results indicate that a wide range of halides can be used to reduce the inherent resistivity of the initial borate material. The effect occurs in both the glassy and glass-ceramic samples but is most dramatic 'in the latter case. The reduction is of such magnitude that, unusually, the glass-ceramic frequently has a lower resistivity than the parent glass, and some sodium borate based samples can almost be classed as fast-ion conductors. Any accompanying structural changes were monitored using a range of techniques including X-ray diffraction, infra-red absorption, nuclear magnetic resonance and electron microscopy. These measurements met with varying success though the prominent finding of each investigation is that the added halide is absorbed into the base compound with remarkably little structural rearrangement. Because the resistivity reduction effect is so much greater for the glass-ceramics than for the glasses, investigations on the two types of specimen are discussed independently and differing theories put forward. These theories are thoroughly discussed and comparisons made with publications on analogous materials. For the glasses work on halide doped lithium borates and silver borates is the most similar yet reported, but it is believed that the study on re-crystallised specimens is the only work carried out on any halide doped borate glass-ceramics

An improved simulation method for pricing high-dimensional American derivatives

In this paper, we propose an estimator for pricing high-dimensional American-style options and show that asymptotically its upper bias converges to zero. An advantage of the proposed estimator is that when combined with low discrepancy sequences, it exhibits a superior rate of convergence. Numerical examples are conducted to demonstrate its efficiency

ABSTRACT RECENT ADVANCES IN SIMULATION FOR SECURITY PRICING

Computational methods play an important role in modern finance. Through the theory of arbitragefree pricing, the price of a derivative security can be expressed as the expected value of its payouts under a particular probability measure. The resulting in-tegral becomes quite complicated if there are several state variables or if payouts are path-dependent. Sim-ulation has proved to be a valuable tool for these calculations. This paper summarizes some of the recent applications and developments of the Monte Carlo method to security pricing problems.