Mathematical Models and Numerical Methods for Pricing Options on Investment Projects under Uncertainties

In this work, we focus on establishing partial differential equation (PDE) models for pricing flexibility options on investment projects under uncertainties and numerical methods for solving these models. we develop a finite difference method and an advanced fitted finite volume scheme and combine with an interior penalty method, as well as their convergence analyses, to solve the PDE and LCP models developed. The MATLAB program is for implementing testing the models of numerical algorithms developed

Multi-scale Volatility in Option Pricing

This PhD thesis investigated the influence of kaolin and bentonite clays in the ore on flotation, filtration and centrifugal concentration. The results showed that the presence of particularly bentonite in the ore had a detrimental effect on flotation and filtration. The information generated from this work will advance our knowledge as well as provide important information for plant metallurgists. The project, therefore, is essential for the mineral industry that process clay-containing ores

The Effect of Malaysia General Election on Financial Network: An Evidence from Shariah-Compliant Stocks on Bursa Malaysia

Instead of focusing the volatility of the market, the market participants should consider on how the general election affects the correlation between the stocks during 14th general election Malaysia. The 14th general election of Malaysia was held on 9th May 2018. This event has a great impact towards the stocks listed on Bursa Malaysia. Thus, this study investigates the effect of 14th general election Malaysia towards the correlation between stock in Bursa Malaysia specifically the shariah-compliant stock. In addition, this paper examines the changes in terms of network topology for the duration, sixth months before and after the general election. The minimum spanning tree was used to visualize the correlation between the stocks. Also, the centrality measure, namely degree, closeness and betweenness were computed to identify if any changes of stocks that plays a crucial role in the network for the duration of before and after 14th general election Malaysia

Valuation, Empirical Analysis, and Optimal Exercise of Open-End Turbo Certificates

This dissertation analyzes Open-End Turbo Certificates (OETCs), a popular class of retail derivatives. OETCs can be exercised at any time at the investor’s discretion. In order to explain the existence of the certificates jump risk must be considered. We propose and implement an optimal stopping approach to price these securities, which further allows for determining optimal exercise thresholds. They result from the trade-off between benefits from downward jump protection and financing costs. We show that early exercise right has a significant impact on their values. In an empirical analysis pertaining to the years 2007 through 2009 it turns out that certificates which could be rationally held are very rare, although the degree by which the underlying exceeds the optimal exercise thresholds continually declines over the considered period. We suggest three lines of explanation: general market movement, jump risk perception by the market, and increased competition among issuers.Die vorliegende Dissertation behandelt Open-End Turbo Zertifikate (OETCs), eine populäre Klasse von Privatkundenderivaten, die jederzeit durch den Investor ausgeübt werden können. Um ihre Existenz rechtfertigen zu können, muss Sprungrisiko berücksichtigt werden. Zur Preisstellung des Produktes schlagen wir einen Optimal Stopping Ansatz vor und implementieren diesen. Dies erlaubt zudem die Berechnung optimaler Ausübungsschwellen, die aus dem Gegenspiel von Finanzierungskosten einerseits und Schutz gegen Abwärtssprünge andererseits entstehen. Wir zeigen, dass vorzeitige Ausübungsrechte in der Bewertung eine signifikante Rolle spielen. In einer empirischen Analyse für die Jahre 2007 bis 2009 zeigt sich schließlich, dass rationale Investoren nur sehr wenige OETCs halten sollten. Andererseits geht der Grad, um welchen das Underlying die optimale Ausübungsschwelle überschreitet, kontinuierlich zurück. Für diese Beobachtung lassen sich drei Begründungen anführen: allgemeine Marktbewegung, vom Markt wahrgenommenes Sprungrisiko und erhöhter Wettbewerb unter den Anbietern

Applications of robust optimal control to decision making in the presence of uncertainty

This thesis is concerned with robustness of decision making in financial economics. Feedback control models developed in engineering are applied to three separate though linked problems in order to examine the role and impact of robustness in the creation and application of decision rules. Three problems are examined using robust optimal control techniques to evaluate the impact of robustness and stability in financial economic models. The first problem examines the use of linear models of robust optimal control in the pricing of castastrophe based derivatives and finds its relative performance to be superior to the popular jump diffusion and stochastic volatility models in the pricing of these emerging instruments. The novelty of the approach arises from the examination of the impact of robustness and stability of the pricing solution. The second problem involves robustness and stability of hedging. An alternative method of creating hedging rules is developed. The method is based on robust control Lyapunov functions that are simple, robust and stable in operation, yet in practice are not so conservative that they eliminate all trading gains. The third problem involves the development of robust control policies for managing risk, using non-linear robust optimal control techniques to provide clear evidence of superior performance of robust models when compared with existing VAR and EVT approaches to risk management. The novelty in the approach arises from the development of a simple and powerful risk management metric