An Asian option is an example of exotic options. Its payoff depends on the average of the underlying asset prices. The average may be over the entire time period between initiation and expiration or may be over some period of time that begins later than the initiation of the option and ends with the options expiration. The average may be from continuous sampling or may be from discrete sampling. The primary reason to base an option payoff on an average asset price is to make it more difficult for anyone to significantly affect the payoff by manipulation of the underlying asset price. The price of Asian options is not known in closed form, in general, if the arithmetic average is taken into effect. In this dissertation, we shall investigate the pricing theory for Asian options. After a brief introduction to the Black-Scholes theory, we derive the partial differential equations for the value process of an Asian option to satisfy. We do this in several approaches, including the usual extension to Asian options of the Black-Scholes, and the sophisticated martingale approach. Both fixed and floating strike are considered. In the case of the geometric average, we derive a closed form solution for the Asian option. Moreover, we investigate the Asian option price theory under stochastic volatility which is a recent trend in the study of path-dependent option theory. / Thesis (M.Sc.)-University of KwaZulu-Natal, Westville, 2007.

The purpose of this study was to determine how and why students in grade six, in a suburban school division in Manitoba, make decisions regarding optional arts course choices for their grade seven year and their perceptions on these courses for grade seven. There was a particular focus on choice related to music courses. The researcher conducted interviews with students in grade seven who chose music as an option, students in grade seven who did not choose music as an option, and conducted focus group conversations with elementary music educators and middle years‟ music educators. The data indicated that the choice was difficult, that students felt that they should not have to choose and that, with parental support, students chose the option that expressed their passion.

This dissertation looks at various specific applications of stochastic processes in finance. The motivation for this work has been the work on the valuation of the price of an Asian option by Rogers and Shi (1995). Here, we look at functions of integrals of log - Gaussian processes to obtain approximations to the prices of various financial instruments. We look at pricing of bonds and payments contingent on the interest rate. The interest rate is assumed to be log - Gaussian, thus ensuring that it does not go negative. Obtaining the exact price might not be easy in all cases - hence we use of a combination of a conditioning argument and Jensen's inequality to obtain the lower bound to the prices of the bond as well as payments contingent on interest rates. We look at single driver models as well as multi-driver models. We also look at bonds where default is possible. We try to provide a mathematical justification for the choice of the conditioning factor used throughout the thesis to approximate the price of bonds and options. This is similar to the approach used by Rogers and Shi (1995) to valuing an Asian option; but they had provided no mathematical justification. Another part of this dissertation deals with the problem of pricing European call options on stochastically volatile assets. Further, the price and the volatility processes are in general correlated amongst themselves. Obtaining an exact price is quite involved and computation intensive. Most of the previous work in this field has been based on the solution to a system of partial differential equations. As in the case of pricing bonds, here too, we use a conditioning argument to obtain an approximation to the prices. This method is much faster and less computation intensive. We look at the situations of fixed and stochastic interest rates separately and in each case, we look at the volatility process following a simple Brownian motion and an Ornstein Uhlenbeck process. We also look at the value of stop - loss reinsurance contract for the case of a doubly stochastic Poisson process. Finally, we look at an alternative method of pricing bonds and Asian options. This is done by using a direct expansion and thus avoids the numerical integration that is used in the earlier chapters.

Nearly unpredictable turbulence on an overall economic level, radical changes in the legal framework and a shift in the moral concepts prevailing in the general public emphasize the importance of increased corporate flexibility. Usually, most flexibility measurements suffer from the defect that they are not pecuniary, that interactions between different flexibility dimensions are not considered and that they lack the required relatedness to the respective context. These problems contribute to a large extent to the fact that, when making investment decisions, the value of flexibility is considered but intuitively or insufficiently. Frequently, the results are irrational myopic pseudo decisions. The present work can be regarded as an attempt to design a pecuniary and context-related flexibility measure of three single flexibility dimensions in an extremely simplified framework and under restrictive assumptions. The primary method used is Monte Carlo Simulation. The present study shows that the value of flexibility can be substantive and that taking into account the interactions of various single flexibilities when strategic investments are made can be of great importance. In this paper, we work out the connection between "environmental volatility" and the "value of flexibility". Our work shows a numerically strong positive relation between these two properties. (author's abstract) / Series: Working Papers SFB "Adaptive Information Systems and Modelling in Economics and Management Science"

The purpose of this study was to determine how and why students in grade six, in a suburban school division in Manitoba, make decisions regarding optional arts course choices for their grade seven year and their perceptions on these courses for grade seven. There was a particular focus on choice related to music courses. The researcher conducted interviews with students in grade seven who chose music as an option, students in grade seven who did not choose music as an option, and conducted focus group conversations with elementary music educators and middle years‟ music educators. The data indicated that the choice was difficult, that students felt that they should not have to choose and that, with parental support, students chose the option that expressed their passion.

High satisfaction rates and the lack of response variability are problematic areas in survey research. An important area of methodological concern for self-report survey is the sensitivity and reliability of the instrument. This research examines the effects of a positive (right) centred scale on the distribution and reliability of satisfaction responses in a positive respondent population. A total of 216 participants were randomly assigned to one of the following three experimental Likert scale conditions: 5–point equal interval balanced scale; 5–point positive (right) packed scale; 5–point positive (right) centred scale. The distribution of responses occurred in the direction hypothesized. Comparable discrimination was found across the three conditions. Although, the study findings did not prove to be significant, the equal interval balanced scale produced the lowest mean score, contrary to previous research findings.

High satisfaction rates and the lack of response variability are problematic areas in survey research. An important area of methodological concern for self-report survey is the sensitivity and reliability of the instrument. This research examines the effects of a positive (right) centred scale on the distribution and reliability of satisfaction responses in a positive respondent population. A total of 216 participants were randomly assigned to one of the following three experimental Likert scale conditions: 5–point equal interval balanced scale; 5–point positive (right) packed scale; 5–point positive (right) centred scale. The distribution of responses occurred in the direction hypothesized. Comparable discrimination was found across the three conditions. Although, the study findings did not prove to be significant, the equal interval balanced scale produced the lowest mean score, contrary to previous research findings.

This research was carried out by studying possible renovation of a two-storey detached multifamily building by using passive solar design options in a cold climate in Borlänge, Sweden where the heating Degree Days are 4451 (base 20°C). Borlänge`s housing company, Tunabyggen, plans to renovate the project house located inthe multicultural district, Jakobsgårdarna. The goal of the thesis was to suggest a redesign of the current building, decrease the heating energy use, by applying passive solar design and control strategies, in a most reasonable way. In addition ensure a better thermal comfort for the tenants in the dwellings. Literatures have been studied, from which can be inferred that passive design should be abasic design consideration for all housing constructions, because it has advantages to ensure thermal comfort, and reduce the energy use. In addition further savings can be achieved applying different types of control strategies, from which the house will be more personalized, and better adapted to the user’s needs.The proposed method is based on simulations by using TRNSYS software. First a proper building model was set up, which represents the current state of the project building. Then the thermal insulation and the windows were upgraded, based on today's building regulations. The developments of the passive solar options were accomplished in two steps. First of all the relevant basic passive design elements were considered, then those advantages were compared to the advantages of applying new conventional thermostat, and shading control strategies.The results show that there is significant potential with the different types of passive solar design; their usage depends primarily on the location of the site as well as the orientation of the project building. Applying the control strategies, such as thermostat, and shading control, along the thermal insulation upgrade, may lead to significant energy savings (around 40 %), by comparison to the reference building without any upgrade.

Doctor of Philosophy(PhD) / This thesis builds on the real estate lease model of Grenadier which consists of the Black Scholes PDE and an upper reflecting boundary condition. Extending the method of images of Buchen, a new technique was developed to solve this class of problems. Problems that previously required difficult integration can now be solved with algebra and simple integrals. In addition, the compound option in this framework is solved using this new technique. To the best of our knowledge the solution of the compound problem has not been published. An interesting symmetry between this class of problems and the lookback option was also discovered and described in this thesis. The extension of the method of images to include problems with the reflecting boundary condition in the context of real estate leases was presented at the Financial Integrity Research Network Doctoral Tutorials at the University of Technology, Sydney, in 2006. The presentation was awarded the ``FIRN Best Paper Award''. This paper has been submitted to the Journal of Financial Mathematics for publication. The solution to the compound problem in the context of the upward-only market review option is the subject of the next paper.

Thesis (PhD)--Macquarie University, Division of Economic and Financial Studies, Dept. of Statistics, 2008. / Bibliography: p. 73-77. / Introduction -- Lévy processes used in option pricing -- Option pricing for Lévy processes -- Option pricing based on empirical characteristic functions -- Performance of the five models on historical data -- Conclusions -- References -- Appendix A. Proofs -- Appendix B. Supplements -- Appendix C. Matlab programs. / Pricing problems of financial derivatives are among the most important ones in Quantitative Finance. Since 1973 when a Nobel prize winning model was introduced by Black, Merton and Scholes the Brownian Motion (BM) process gained huge attention of professionals professionals. It is now known, however, that stock market log-returns do not follow the very popular BM process. Derivative pricing models which are based on more general Lévy processes tend to perform better. --Carr & Madan (1999) and Lewis (2001) (CML) developed a method for vanilla options valuation based on a characteristic function of asset log-returns assuming that they follow a Lévy process. Assuming that at least part of the problem is in adequate modeling of the distribution of log-returns of the underlying price process, we use instead a nonparametric approach in the CML formula and replaced the unknown characteristic function with its empirical version, the Empirical Characteristic Functions (ECF). We consider four modifications of this model based on the ECF. The first modification requires only historical log-returns of the underlying price process. The other three modifications of the model need, in addition, a calibration based on historical option prices. We compare their performance based on the historical data of the DAX index and on ODAX options written on the index between the 1st of June 2006 and the 17th of May 2007. The resulting pricing errors show that one of our models performs, at least in the cases considered in the project, better than the Carr & Madan (1999) model based on calibration of a parametric Lévy model, called a VG model. --Our study seems to confirm a necessity of using implied parameters, apart from an adequate modeling of the probability distribution of the asset log-returns. It indicates that to precisely reproduce behaviour of the real option prices yet other factors like stochastic volatility need to be included in the option pricing model. Fortunately the discrepancies between our model and real option prices are reduced by introducing the implied parameters which seem to be easily modeled and forecasted using a mixture of regression and time series models. Such approach is computationaly less expensive than the explicit modeling of the stochastic volatility like in the Heston (1993) model and its modifications. / Mode of access: World Wide Web. / x, 111 p. ill., charts