Thesis (doctoral)--Johann Wolfgang Goethe-University, 2004. / Includes bibliographical references.

Originally presented as the author's doctoral thesis to the European Business School, Oestrich-Winkel. / Includes bibliographical reference (p. [345]-353) and index.

Thesis (MSc (Mathematics))--Stellenbosch University, 2008. / The computation of the greeks of an option is an important aspect of financial mathematics. The information gained from knowing the value of a greek of an option can help investors decide whether or not to hold on to or to sell their options to avoid losses or gain a profit. However, there are technical difficulties that arise from having to do this. Among them is the fact that the mathematical formula for the value some options is complex in nature and evaluating their greeks may be cumber- some. On the other hand the greek might have to be numerically estimated if the option does not posses an explicit evaluation formula. This could be a computationally expensive undertaking. Malliavin calculus offers us a solution to these problems. We can find formula that can be used in combination with Monte Carlo simulations to give results quickly and which are not computationally expensive to obtain and hence give us an degree of accuracy higher that non Malliavin calculus techniques. This thesis will develop the Malliavin calculus tools that will enable us to develop the tools which we will then use to compute the greeks of some known options.

When a stock is added into the S&P 500 Index, it is automatically "cross-listed" in the index derivative markets (i.e., S&P 500 Index futures and Index options). I examined the effects of such cross-listing on the trading volume and return volatility of the underlying component stocks. Traditional finance theory asserts that futures and "cash" markets are connected by arbitrage mechanism that brings both markets to equilibrium. When arbitrage opportunities arise, arbitrageurs buy (sell) the index portfolio and take short (long) positions in the corresponding index derivative contracts until prices return to theoretical levels. Such mechanical arbitrage trading tends to create large order flows that could be difficult for the market to absorb, resulting in price changes. Utilizing a list of S&P 500 index composition changes occurring over the period September 1976 to December 2005, I investigated the market-adjusted volume turnover ratios and return variances of the stocks being added to and deleted from the S&P 500, surrounding the effective day of index membership changes. My primary finding is that, after the introduction of the S&P 500 index futures and options contracts, stocks added to the S&P 500 experience significant increase in both trading volume and return volatility. However, deleted stocks experience no significant change in either trading volume or return volatility. Both daily and monthly return variances increase following index inclusion, consistent with the hypothesis that derivative transactions "fundamentally" destabilize the underlying securities. I argue that the increase in trading volume and return volatility may be attributed to index arbitrage transactions as derivative markets provide more routes for index arbitrageurs to trade. Other index trading strategies such as portfolio insurance and program trading may also contribute to the results. On the other hand, a deleted stock is not associated with changes in trading volume and volatility since it represents an extremely small fraction of the market value-weighted index portfolio, and the influence of index trading strategies becomes slight for these shares. Furthermore, evidence is provided that trading volume and return volatility are positively related.

With many genetic traits discovered and many more in progress, it is imperative to the industry that firms (biotechnology companies) decide on the trait valuation and pricing. This includes more than one trait (also referred to as stacked traits) in a single variety of crop; the risk and uncertainty of expected returns associated with the development and release of a variety increases even more in case of stacked traits. The purpose of this thesis is to develop a model that can be used for the valuing and pricing of genetically modified (GM) traits that are random, sporadic, and non-persistent (e.g. drought tolerance, heat/cold stress) using the real option approach. The efficiency gain in case of occurrence of random event and expression of GM traits will be measured and used as a decision factor in determining the value of GM trait(s) at different phases of development. Risk premiums representing the value of GM trait to growers is calculated across risk averse attitudes. The return to labor and management (RTLM) provided by a GM trait is used to calculate the risk premiums when variation in parameters is allowed to be same as that reflected in historical data and gains from GM traits are realized. Monte Carlo simulation and stochastic efficiency with respect to a function (SERF) are used to estimate the certainty equivalents that decision makers would place on a risky alternative relative to a no risk investment. Certainty equivalents are estimated across a range of risk aversion coefficients and used to rank alternatives and determine where preferences among alternatives change while estimating risk premiums for the base case (no trait), drought tolerance, cold tolerance, NUB, and All traits (all traits combined into one as a stacked trait). Premiums provide perspective on the magnitude of differences in relative preferences among choices. The range of ARAC utilized was from 0.00 to 0.15 for all three crops. The risk premiums are treated as a potential source of revenue in the model as a technology fee charged by a biotech company. This thesis uses the Real Option methodology to evaluate GM traits as Option values at various stages of development. This approach helps managers decide the best possible option in making a certain decision today. It is also helpful in comparing different pathways (series of decisions) and thus better exploits the potential cash return in the future from investments made today (Figure D.1, Figure D.2). Three possible options to "continue", "wait", and "abandon" were modeled in this thesis. Such modeling determines the possible option values of GM traits at different stages of development depending on the kind of choices made at different points of time. This thesis shows that various GM traits that are out-of-money (OTM) at initial stages have increased probability of being in-the-money (ITM) at later stages of development. Sensitivities show that a share of potential technology fees and acreage of GM crops play a significant role in option values being ITM. Stacked traits provide a better chance of being ITM, thus the option to continue will be exercised by management. The option to wait causes reduction in option value. Among individual traits, drought tolerance has the greatest maximum option value in most cases. Therefore, if management has to choose the development of only one GM trait, it is most likely to choose to invest in the development of drought tolerance.

This thesis is concerned with the investigation of numerical methods for the solution of the Hamilton-Jacobi-Bellman (HJB) equations arising in European and American option pricing with proportional transaction costs. We first consider the problem of computing reservation purchase and write prices of a European option in the model proposed by Davis, Panas and Zariphopoulou [19]. It has been shown [19] that computing the reservation purchase and write prices of a European option involves solving three different fully nonlinear HJB equations. In this thesis, we propose a penalty approach combined with a finite difference scheme to solve the HJB equations. We first approximate each of the HJB equations by a quasi-linear second order partial differential equation containing two linear penalty terms with penalty parameters. We then develop a numerical scheme based on the finite differencing in both space and time for solving the penalized equation. We prove that there exists a unique viscosity solution to the penalized equation and the viscosity solution to the penalized equation converges to that of the original HJB equation as the penalty parameters tend to infinity. We also prove that the solution of the finite difference scheme converges to the viscosity solution of the penalized equation. Numerical results are given to demonstrate the effectiveness of the proposed method. We extend the penalty approach combined with a finite difference scheme to the HJB equations in the American option pricing model proposed by Davis and Zarphopoulou [20]. Numerical experiments are presented to illustrate the theoretical findings.

Thesis (MComm (Business Management))--University of Stellenbosch, 2006. / For the last 40 years, academics advocated the use of the traditional Discounted Cash Flow (DCF) techniques but these suggestions were ignored by practitioners for a long time. The Net Present Value (NPV), Internal Rate of Return (IRR) and Present Value Payback Period (PVPP) are now some of the more widely used traditional DCF-based techniques, especially among large firms. However, academics are now criticising these techniques as they are based on rigid assumptions that ignore the management of flexibility in projects. The Real Option Valuation (ROV) is suggested as an alternative technique because it implicitly incorporates this flexibility in project valuation. With ROV, opportunities in projects are treated as real options and are therefore valued using financial option principles. Real options give the firm the opportunity to act on an investment project (invest, abandon, rescale) at a later date, when more information is available. As with the traditional DCF-based techniques in the past, few firms seem to have adopted ROV despite academics’ recommendations. This study is thus aimed at determining through a survey, whether the largest firms in South Africa, specifically those included in the JSE/FTSE Top 40 index, are using ROV. Based on the results of the survey, it is concluded that firms generally do not use ROV as only nine percent of the respondents were found to be using it. This is largely attributed to managers being unaware of the technique, and to some extent, to the technique’s complexity. On the other hand, managers were generally found to recognise the flexibility despite not using ROV, although it was not confirmed whether they quantify this flexibility.

Nicotinic acid adenine dinucleotide phosphate (NAADP) is a potent Ca²⁺ mobilising messenger in mammalian and non-mammalian cells. Studies on a variety of cell types suggest that NAADP evokes Ca²⁺ release from a lysosome-related store and via activation of a receptor distinct from either ryanodine receptors (RyR) or inositol 1,4,5-trisphosphate (IP₃) receptors (IP₃R). However, the identity of the NAADP receptor has, until now, remained elusive. In this thesis I have shown that NAADP-evoked Ca²⁺ release from lysosomes is underpinned by two-pore channels (TPCs), of which there are 3 subtypes, TPC1, TPC2 and TPC3. When stably over-expressed in HEK293 cells, TPC2 was found to be specifically targeted to lysosomes, while TPC1 and TPC3 were targeted to endosomes. Initial Ca²⁺ signals via TPC2, but not those via TPC1, were amplified into global Ca²⁺ waves by Ca²⁺-induced Ca²⁺ release (CICR) from the endoplasmic reticulum (ER) via IP₃Rs. I have shown that, consistent with a role for TPCs in NAADP-mediated Ca²⁺ release, TPC2 is expressed in pulmonary arterial smooth muscle cells (PASMCs), is likely targeted to lysosomal membranes, and that TPCs also underpin NAADP-evoked Ca²⁺ signalling in this cell type. However, and in contrast to HEK293 cells, in PASMCs NAADP evokes spatially restricted Ca²⁺ bursts that are amplified into global Ca²⁺ waves by CICR from the sarcoplasmic reticulum (SR) via a subpopulation of RyRs, but not via IP₃Rs. I have demonstrated that lysosomes preferentially co-localise with RyR subtype 3 (RyR3) in the perinuclear region of PASMCs to comprise a “trigger zone” for Ca²⁺ signalling by NAADP, away from which a propagating Ca²⁺ wave may be carried by subsequent recruitment of RyR2. The identification of TPCs as a family of NAADP receptors may further our understanding of the mechanisms that confer the versatility of Ca²⁺ signalling which is required to regulate such diverse cellular functions as gene expression, fertilization, cell growth, and ultimately cell death.

published_or_final_version / Business Administration / Master / Master of Business Administration

This thesis presents several problems based on papers written jointly by the author and Dr. Christian-Oliver Ewald. Firstly, the author extends the model presented by Fershtman and Nitzan (1991), which studies a deterministic differential public good game. Two types of volatility are considered. In the first case the volatility of the diffusion term is dependent on the current level of public good, while in the second case the volatility is dependent on the current rate of public good provision by the agents. The result in the latter case is qualitatively different from the first one. These results are discussed in detail, along with numerical examples. Secondly, two existing lines of research in game theoretic studies of fisheries are combined and extended. The first line of research is the inclusion of the aspect of predation and the consideration of multi-species fisheries within classical game theoretic fishery models. The second line of research includes continuous time and uncertainty. This thesis considers a two species fishery game and compares the results of this with several cases. Thirdly, a model of a fishery is developed in which the dynamic of the unharvested fish population is given by the stochastic logistic growth equation and it is assumed that the fishery harvests the fish population following a constant effort strategy. Explicit formulas for optimal fishing effort are derived in problems considered and the effects of uncertainty, risk aversion and mean reversion speed on fishing efforts are investigated. Fourthly, a Dixit and Pindyck type irreversible investment problem in continuous time is solved, using the assumption that the project value follows a Cox-Ingersoll- Ross process. This solution differs from the two classical cases of geometric Brownian motion and geometric mean reversion and these differences are examined. The aim is to find the optimal stopping time, which can be applied to the problem of extracting resources.