We utilise several asset pricing models that allow for discontinuities in the returns and volatility time series in order to obtain estimates of Value-at-Risk (VaR). The first class of model that we use mixes a continuous diffusion process with discrete jumps at random points in time (Poisson Jump Diffusion Model). We also apply a purely discontinuous model that does not contain any continuous component at all in the underlying distribution (Variance Gamma Model). These models have been shown to have some success in capturing certain characteristics of return distributions, a few being leptokurtosis and skewness. Calibrating these models onto the returns of an index of Australian stocks (All Ordinaries Index), we then use the resulting parameters to obtain daily estimates of VaR. In order to obtain the VaR estimates for the Poisson Jump Diffusion Model and the Variance Gamma Model, we introduce the use of an innovation from option pricing techniques, which concentrates on the more tractable characteristic functions of the models. Having then obtained a series of VaR estimates, we then apply a variety of criteria to assess how each model performs and also evaluate these models against the traditional approaches to calculating VaR, such as that suggested by J.P. Morgan???s RiskMetrics. Our results show that whilst the Poisson Jump Diffusion model proved the most accurate at the 95% VaR level, neither the Poisson Jump Diffusion or Variance Gamma models were dominant in the other performance criteria examined. Overall, no model was clearly superior according to all the performance criteria analysed, and it seems that the extra computational time required to calibrate the Poisson Jump Diffusion and Variance Gamma models for the purposes of VaR estimation do not provide sufficient reward for the additional effort than that currently employed by Riskmetrics.

In this thesis, we investigate two stock price models, the Black-Scholes (BS) model and the Merton Jump-Diffusion (MJD) model. Comparing the logarithmic return of the BS model and the MJD model with empirical stock price data, we conclude that the Merton Jump-Diffusion Model is substantially more suitable for the stock market. This is concluded visually not only by comparing the density functions but also by analyzing mean, variance, skewness and kurtosis of the log-returns. One technical contribution to the thesis is a suggested decision rule for initial guess of a maximum likelihood estimation of the MJD-modeled parameters.

The thesis focuses on pricing complex options using Monte Carlo simulations. Due to the versatility of the Monte Carlo method, we are able to evaluate option prices with various underlying asset models: jump diffusion models, illiquidity models, stochastic volatility and so on. Both European options and Bermudan options are studied in this thesis.For the jump diffusion model in Merton (1973), we demonstrate European and Bermudan option pricing by the Monte Carlo scheme and extend this to multiple underlying assets; furthermore, we analyse the effect of stochastic volatility.For the illiquidity model in the spirit of Glover (2008), we model the illiquidity impact on option pricing in the simulation study. The four models considered are: the first order feedback model with constant illiquidity and stochastic illiquidity; the full feedback model with constant illiquidity and stochastic illiquidity. We provide detailed explanations for the present of path failures when simulating the underlying asset price movement and suggest some measures to overcome these difficulties.

The recent observed growth in the diffusion of Special Purpose Acquisition Companies phenomena on the U.S stock market may be analyzed from a mathematical standpoint, where different approaches of the Bass Diffusion Model might be utilized. The Bass diffusion model originates from analysis of product diffusion, where only a few applications have been seen by financial scholars. The thesis takes a multi analytical approach to examine the phenomena, where multiple regression analysis and Bayesian statistics are used in the parameter estimation processes. Estimated parameter are applied in three different scenarios of expressing the Bass diffusion model in a discrete time state. By utilizing these different approaches that arise, the study shows that the diffusion of Special Purpose Acquisition Companies Initial Public Offerings in fact can be analyzed from a mathematical standpoint utilizing the Bass diffusion model. Some approaches and scenarios indicate better results in terms of fitting the diffusion, while purposing practical actualities towards the reader and market practitioners. The study further purposes potential modifications that might improve the results of fitting the phenomena

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Yes / CO2 capture from natural gas was experimentally and theoretically studied using a dead-end polymeric permeation cell. A numerical model was proposed for the separation of CO2/CH4 using Polytetrafluoroethylene (PTFE) in a flat sheet membrane module and developed based upon the continuity, momentum and mass transfer equations. The slip velocity condition was considered to show the reflection of gas flow in contact with the membrane surface. The solution method was based on the well-known SIMPLE algorithm and implemented using MATLAB to determine the velocity and concentration profiles. Due to change in velocity direction in the membrane module, the hybrid differencing scheme was used to solve the diffusion-convection equation. The results of the model were compared with the experimental data obtained as part of this work and good agreement was observed. The distribution of CO2 concentration inside the feed and permeate chambers was shown and the velocity profile at the membrane surface was also determined using reflection factor for polymericmembrane. The modelling result revealed that increasing the amount of CO2 in gas feed resulted in an increase in the CO2 in the permeate stream while the gas feed pressure increased. By changing the permeability, the model developed by use of the solution-diffusion concept could be used for all polymeric membranes with flat sheet modules.

A rotating diffusion cell (RDC) has been used to study the kinetics of extraction of the transition metals cobalt (II), nickel (II), copper (II) and zinc (II) from sulphate solutions into either of two extractants held in n-heptane; di-(2-ethylhexyl) phosphoric acid (D2EHPA) or di-(2- ethylhexyl) dithiophosphoric acid (D2EHDTPA). The metal concentration was 10 mM and the aqueous pH was held at 4.5. The extractant concentration was varied between 0.015 to 0.4 M. In the case of cobalt extraction by D2EHPA, the metal concentration and the pH were varied Different diluents and modifiers were also studied.The rate of extraction by D2EHDTPA was found to be faster than D2EHPA. A comprehensive mathematical model, based upon established two film theory, was developed and used to describe the above experimental results. The model was also used to predict values of the important parameters. ... These values compared well with those found by other authors but using quite different experimental techniques. OS4 In the case of cobalt extraction by D2EHPA, the more polar diluents lowered the initial rate. The overall model predicts such behaviour where the rate is also dependent on the partition coefficients of the extractant. Finally, the theory of the RDC allows the prediction of the diffusion layer thicknesses, this information together with the reaction zone thickness is used to explore the influences of diffusion and chemical reaction on the overall transfer process. The diffusion processes are calculated to be the most important of the two. This is especially so for the D2EHDTPA systems. / University of Bradford Scholarship Award

Alan Turing explored how patterns emerged in embryos. The modelsexplained by Turing describe how two morphogens interact with eachother and develop certain patterns though different conditions. Usingthe differential equation expressed by Turing gives a lot of freedom inthe choice of variables depending on how the variables are chosen, whichwill be explored and simulated in this thesis. Later, a systems theoreticformulation will be used to explore the stability and controllability ofthe homogenous diffusion problem and Turing’s Reaction and Diffusionproblem. It will be found that under the assumptions made in this thesisboth models will be stable and controllable.

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