This Thesis deals with the using of transformations in model of regression analysis. The first part of the Thesis summarizes the theoretical findings of the regression models, assumption of these models and the possibility of using different types of transformations in the event non-compliance of regression models. The practical part of this Thesis deals with regression analysis of real dataset on school readiness of children from the district of Kolín in 2013 and using transformations in the selected regression model.

This thesis is mainly focused on pricing securities of selected capital protected funds. In its theoretical part, there are summarized approaches and principals that are generally used for derivatives pricing because capital protected funds' securities contain embedded options. Emphasis is put on risk-neutral pricing using Monte Carlo simulation at that point because complicated pay-off functions of these funds are hard to be evaluated analytically. There are also presented main approaches to constructions and portfolio management of these funds from their portfolio manager's viewpoint. Finally, there is made an overview of basic types of capital protected funds issued both in The Czech republic and Europe. Analytical part is focused on evaluation of selected capital protected funds. There is applied a standard approach that is based on a simulation of Geometric Brownian Motion with constant conditional variance and correlation in contrast with an advanced approach where the conditional variance and conditional correlation matrix are simulated as well. That is accomplished with GARCH-in-mean and DCC-GARCH models. Estimated prices are compared with real market prices and there is also performance of the standard models compared with performance of advanced ones.

The stock market is a non-linear field, but many of the best-known portfolio optimization algorithms are based on linear models. In recent years, the rapid development of machine learning has produced flexible models capable of complex pattern recognition. In this paper, we propose two different methods of portfolio optimization; one based on the development of a multivariate time-dependent neural network,thelongshort-termmemory(LSTM),capable of finding lon gshort-term price trends. The other is the linear Markowitz model, where we add an exponential moving average to the input price data to capture underlying trends. The input data to our neural network are daily prices, volumes and market indicators such as the volatility index (VIX).The output variables are the prices predicted for each asset the following day, which are then further processed to produce metrics such as expected returns, volatilities and prediction error to design a portfolio allocation that optimizes a custom utility function like the Sharpe Ratio. The LSTM model produced a portfolio with a return and risk that was close to the actual market conditions for the date in question, but with a high error value, indicating that our LSTM model is insufficient as a sole forecasting tool. However,the ability to predict upward and downward trends was somewhat better than expected and therefore we conclude that multiple neural network can be used as indicators, each responsible for some specific aspect of what is to be analysed, to draw a conclusion from the result. The findings also suggest that the input data should be more thoroughly considered, as the prediction accuracy is enhanced by the choice of variables and the external information used for training. / Aktiemarknaden är en icke-linjär marknad, men många av de mest kända portföljoptimerings algoritmerna är baserad på linjära modeller. Under de senaste åren har den snabba utvecklingen inom maskininlärning skapat flexibla modeller som kan extrahera information ur komplexa mönster. I det här examensarbetet föreslår vi två sätt att optimera en portfölj, ett där ett neuralt nätverk utvecklas med avseende på multivariata tidsserier och ett annat där vi använder den linjära Markowitz modellen, där vi även lägger ett exponentiellt rörligt medelvärde på prisdatan. Ingångsdatan till vårt neurala nätverk är de dagliga slutpriserna, volymerna och marknadsindikatorer som t.ex. volatilitetsindexet VIX. Utgångsvariablerna kommer vara de predikterade priserna för nästa dag, som sedan bearbetas ytterligare för att producera mätvärden såsom förväntad avkastning, volatilitet och Sharpe ratio. LSTM-modellen producerar en portfölj med avkastning och risk som ligger närmre de verkliga marknadsförhållandena, men däremot gav resultatet ett högt felvärde och det visar att vår LSTM-modell är otillräckligt för att använda som ensamt predikteringssverktyg. Med det sagt så gav det ändå en bättre prediktion när det gäller trender än vad vi antog den skulle göra. Vår slutsats är därför att man bör använda flera neurala nätverk som indikatorer, där var och en är ansvarig för någon specifikt aspekt man vill analysera, och baserat på dessa dra en slutsats. Vårt resultat tyder också på att inmatningsdatan bör övervägas mera noggrant, eftersom predikteringsnoggrannheten.

The United States is the world's largest oil consumer demanding about twenty five percent of the total world oil production. Whenever there are difficulties to supply the increasing quantities of oil demanded by the market, the price of oil escalates leading to what is known as oil price spikes or oil price shocks. The last oil price shock which was the longest sustained oil price run up in history, began its course in year 2004, and ended in 2008. This last oil price shock initiated recognizable changes in transportation dynamics: transit operators realized that commuters switched to transit as a way to save gasoline costs, consumers began to search the market for more efficient vehicles leading car manufactures to close 'gas guzzlers' plants, and the government enacted a new law entitled the Energy Independence Act of 2007, which called for the progressive improvement of the fuel efficiency indicator of the light vehicle fleet up to 35 miles per gallon in year 2020. The past trend of gasoline consumption will probably change; so in the context of the problem a gasoline consumption model was developed in this thesis to ascertain how some of the changes will impact future gasoline demand. Gasoline demand was expressed in oil equivalent million barrels per day, in a two steps Ordinary Least Square (OLS) explanatory variable model. In the first step, vehicle miles traveled expressed in trillion vehicle miles was regressed on the independent variables: vehicles expressed in million vehicles, and price of oil expressed in dollars per barrel. In the second step, the fuel consumption in million barrels per day was regressed on vehicle miles traveled, and on the fuel efficiency indicator expressed in miles per gallon. The explanatory model was run in EVIEWS that allows checking for normality, heteroskedasticty, and serial correlation. Serial correlation was addressed by inclusion of autoregressive or moving average error correction terms. Multicollinearity was solved by first differencing. The 36 year sample series set (1970-2006) was divided into a 30 years sub-period for calibration and a 6 year "hold-out" sub-period for validation. The Root Mean Square Error or RMSE criterion was adopted to select the "best model" among other possible choices, although other criteria were also recorded. Three scenarios for the size of the light vehicle fleet in a forecasting period up to 2020 were created. These scenarios were equivalent to growth rates of 2.1, 1.28, and about 1 per cent per year. The last or more optimistic vehicle growth scenario, from the gasoline consumption perspective, appeared consistent with the theory of vehicle saturation. One scenario for the average miles per gallon indicator was created for each one of the size of fleet indicators by distributing the fleet every year assuming a 7 percent replacement rate. Three scenarios for the price of oil were also created: the first one used the average price of oil in the sample since 1970, the second was obtained by extending the price trend by exponential smoothing, and the third one used a longtime forecast supplied by the Energy Information Administration. The three scenarios created for the price of oil covered a range between a low of about 42 dollars per barrel to highs in the low 100's. The 1970-2006 gasoline consumption trend was extended to year 2020 by ARIMA Box-Jenkins time series analysis, leading to a gasoline consumption value of about 10 millions barrels per day in year 2020. This trend line was taken as the reference or baseline of gasoline consumption. The savings that resulted by application of the explanatory variable OLS model were measured against such a baseline of gasoline consumption. Even on the most pessimistic scenario the savings obtained by the progressive improvement of the fuel efficiency indicator seem enough to offset the increase in consumption that otherwise would have occurred by extension of the trend, leaving consumption at the 2006 levels or about 9 million barrels per day. The most optimistic scenario led to savings up to about 2 million barrels per day below the 2006 level or about 3 millions barrels per day below the baseline in 2020. The "expected" or average consumption in 2020 is about 8 million barrels per day, 2 million barrels below the baseline or 1 million below the 2006 consumption level. More savings are possible if technologies such as plug-in hybrids that have been already implemented in other countries take over soon, are efficiently promoted, or are given incentives or subsidies such as tax credits. The savings in gasoline consumption may in the future contribute to stabilize the price of oil as worldwide demand is tamed by oil saving policy changes implemented in the United States.

<p>We investigate some simulation-based approaches for the valuing of the employee stock options. The mathematical models that deal with valuation of such options include the work of Jennergren and Naeslund [L.P Jennergren and B. Naeslund, A comment on valuation of executive stock options and the FASB proposal, Accounting Review 68 (1993) 179-183]. They used the Black and Scholes [F. Black and M. Scholes, The pricing of options and corporate liabilities, Journal of Political Economy 81(1973) 637-659] and extended partial differential equation for an option that includes the early exercise. Some other major relevant works to this mini thesis are Hemmer et al. [T Hemmer, S. Matsunaga and T Shevlin, The influence of risk diversification on the early exercise of employee stock options by executive officers, Journal of Accounting and Economics 21(1) (1996) 45-68] and Baril et al. [C. Baril, L. Betancourt, J. Briggs, Valuing employee stock options under SFAS 123 R using the Black-Scholes-Merton and lattice model approaches, Journal of Accounting Education 25 (1-2) (2007) 88-101]. The underlying assets are studied under the GARCH (generalized autoregressive conditional heteroskedasticity) effects. Particular emphasis is made on the American style employee stock options.</p>

<p>We investigate some simulation-based approaches for the valuing of the employee stock options. The mathematical models that deal with valuation of such options include the work of Jennergren and Naeslund [L.P Jennergren and B. Naeslund, A comment on valuation of executive stock options and the FASB proposal, Accounting Review 68 (1993) 179-183]. They used the Black and Scholes [F. Black and M. Scholes, The pricing of options and corporate liabilities, Journal of Political Economy 81(1973) 637-659] and extended partial differential equation for an option that includes the early exercise. Some other major relevant works to this mini thesis are Hemmer et al. [T Hemmer, S. Matsunaga and T Shevlin, The influence of risk diversification on the early exercise of employee stock options by executive officers, Journal of Accounting and Economics 21(1) (1996) 45-68] and Baril et al. [C. Baril, L. Betancourt, J. Briggs, Valuing employee stock options under SFAS 123 R using the Black-Scholes-Merton and lattice model approaches, Journal of Accounting Education 25 (1-2) (2007) 88-101]. The underlying assets are studied under the GARCH (generalized autoregressive conditional heteroskedasticity) effects. Particular emphasis is made on the American style employee stock options.</p>

Magister Scientiae - MSc / We investigate some simulation-based approaches for the valuing of the employee stock options. The mathematical models that deal with valuation of such options include the work of Jennergren and Naeslund [L.P Jennergren and B. Naeslund, A comment on valuation of executive stock options and the FASB proposal, Accounting Review 68 (1993) 179-183]. They used the Black and Scholes [F. Black and M. Scholes, The pricing of options and corporate liabilities, Journal of Political Economy 81(1973) 637-659] and extended partial differential equation for an option that includes the early exercise. Some other major relevant works to this mini thesis are Hemmer et al. [T Hemmer, S. Matsunaga and T Shevlin, The influence of risk diversification on the early exercise of employee stock options by executive officers, Journal of Accounting and Economics 21(1) (1996) 45-68] and Baril et al. [C. Baril, L. Betancourt, J. Briggs, Valuing employee stock options under SFAS 123 R using the Black-Scholes-Merton and lattice model approaches, Journal of Accounting Education 25 (1-2) (2007) 88-101]. The underlying assets are studied under the GARCH (generalized autoregressive conditional heteroskedasticity) effects. Particular emphasis is made on the American style employee stock options. / South Africa

This dissertation contains three independent essays relating energy economics. The first essay investigates price asymmetry of diesel in South Korea by using the error correction model. Analyzing weekly market prices in the pass-through of crude oil, this model shows asymmetric price response does not exist at the upstream market but at the downstream market. Since time-variant residuals are found by the specified models for both weekly and daily retail prices at the downstream level, these models are implemented by a Generalized Autoregressive Conditional Heteroskedasticity (GARCH) process. The estimated results reveal that retail prices increase fast in the rise of crude oil prices but decrease slowly in the fall of those. Surprisingly, retail prices rarely respond to changes of crude oil prices for the first five days. Based on collusive behaviors of retailers, this price asymmetry in Korea diesel market is explained. The second essay aims to evaluate the new incentive system for biodiesel in South Korea, which keeps the blend mandate but abolishes tax credits for government revenues. To estimate changed welfare from the new policy, a multivariate stochastic simulation method is applied into time-series data for the last five years. From the simulation results, the new biodiesel policy will lead government revenues to increases with the abolishment of tax credit. However, increased prices of blended diesel will cause to decrease demands of both biodiesel and blended diesel, so consumer and producer surplus in the transport fuel market will decrease. In the third essay, the Regression - Seasonal Autoregressive Integrated Moving Average (REGSARIMA) model is employed to predict the impact of air temperature on daily peak load demand in Houston. Compared with ARIMA and Seasonal Model, a REGARIMA model provides the more accurate prediction for daily peak load demand for the short term. The estimated results reveal air temperature in the Houston areas causes an increase in electricity consumption for cooling but to save that for heating. Since the daily peak electricity consumption is significantly affected by hot air temperature, this study makes a conclusion that it is necessary to establish policies to reduce urban heat island phenomena in Houston.

In South Africa various financial institutions and independent vendors have developed residential property valuation models to estimate the current value of historically traded properties. A natural extension to these models has been to develop historical property price indices. In this dissertation, three of the four approaches to developing property price indices will be examined. Through back–testing and other statistical methods, the most accurate and robust approach will be determined. The four major approaches available are the mean valuation per suburb, the median valuation per suburb, the repeat sales approach and hedonic regression. The mean valuation per suburb approach can be biased because of outliers in property prices. However, outliers in property prices will not influence the median valuation per suburb approach, but in cases where property values in a suburb have a skewed distribution, the valuation amount could be distorted. Neither of the above mentioned shortcomings influences the repeat sales or the hedonic regression approach. To follow the hedonic regression approach, the characteristics of the property need to be known. In South Africa, however, the available property data lacks detailed characteristics of traded properties. This dissertation will therefore focus on the first three methods. The repeat sales approach measures the growth in property prices by applying a generalized linear model to properties that have traded more than once. This approach is only possible if there is a representative amount of repeat sales able to fit a model. The focus of this project will be on the repeat sales approach, but all three the approaches discussed will be analysed to prove that the repeat sales approach is the most accurate in developing a property price index for properties in South Africa. / Thesis (M.Sc. (Risk Analysis))--North-West University, Potchefstroom Campus, 2011.

In South Africa various financial institutions and independent vendors have developed residential property valuation models to estimate the current value of historically traded properties. A natural extension to these models has been to develop historical property price indices. In this dissertation, three of the four approaches to developing property price indices will be examined. Through back–testing and other statistical methods, the most accurate and robust approach will be determined. The four major approaches available are the mean valuation per suburb, the median valuation per suburb, the repeat sales approach and hedonic regression. The mean valuation per suburb approach can be biased because of outliers in property prices. However, outliers in property prices will not influence the median valuation per suburb approach, but in cases where property values in a suburb have a skewed distribution, the valuation amount could be distorted. Neither of the above mentioned shortcomings influences the repeat sales or the hedonic regression approach. To follow the hedonic regression approach, the characteristics of the property need to be known. In South Africa, however, the available property data lacks detailed characteristics of traded properties. This dissertation will therefore focus on the first three methods. The repeat sales approach measures the growth in property prices by applying a generalized linear model to properties that have traded more than once. This approach is only possible if there is a representative amount of repeat sales able to fit a model. The focus of this project will be on the repeat sales approach, but all three the approaches discussed will be analysed to prove that the repeat sales approach is the most accurate in developing a property price index for properties in South Africa. / Thesis (M.Sc. (Risk Analysis))--North-West University, Potchefstroom Campus, 2011.