Texas’ Mass Emission Cap and Trade program is a mandatory Nitrous Oxide (NOx) abatement program for medium and large stationary sources located in the Houston-Galveston ozone non-attainment area. Effected companies are required to upgrade equipment to meet the current best achievable NOx control technology (BACT) standards or to purchase emission credits in sufficient quantity to cover the difference in emissions between existing equipment and equipment meeting the BACT standard. With over 260 participating companies, the market for emission credits is ever changing, making it difficult to evaluate whether the lowest cost decision is to upgrade equipment or to purchase NOx emission credits. Because equipment upgrades are capital investments, a well informed, rational decision can have a significant impact on the corporate balance sheet. The objective of this research is to aid the decision maker by predicting credit prices based on a Geometric Brownian Motion model based on historical NOx emission credit transactions. The predicted credit price is useful in evaluating the likelihood of the equipment upgrade option being a favorable or unfavorable decision. For the examined cases, modeled results indicate that equipment upgrade is the more cost effective option. / text

The paper examines the impact of fees on the return of a fund investment using different simulation and fee structure models. The results show that fees have a significant expected impact, particularly for well-performing funds. Two simulation models were used, the Geometric Brownian Motion (GBM) model and Merton Jump Diffusion (MJD) model. Two fee structures were also analysed for each simulation, a High-water mark fee structure and a Hurdle fee structure. Comparing the GBM and MJD models, the two tend to generate very similar fee statistics even though the MJD model's day-to-day returns fit better with empirical data. When comparing the HWM and Hurdle fee models, larger differences are observed. While overall average fee statistics are similar, the performance fee statistics are significantly higher in the Hurdle fee structure for assets achieving higher returns, e.g. at least an 8% annual return. However, the HWM fee structure tends to generate higher performance fees for assets with low returns. Regression models are also developed for each combination of the simulation model and fee structure. The regression models reflect the above conclusions and can for investors serve as simple key indicators to estimate expected fund fee payments. The GBM regression results are likely more useful than the MJD regression results, as the parameters of the former are easier to calculate based on historical return data. / Uppsatsen undersöker effekten av avgifter på avkastningen av en fondinvestering med hjälp av olika simuleringar och avgiftsmodeller. Resultaten visar att avgifter förväntas ha en betydande påverkan, särskilt för fonder som genererar hög avkastning. Två simuleringar användes, Geometric Brownian Motion (GBM) och Merton Jump Diffusion (MJD). Två avgiftsstrukturer analyserades också för varje simulering, en High-water mark avgiftsstruktur och en Hurdle avgiftsstruktur. Jämförelse mellan GBM och MJD-modellerna visar att de två tenderar att generera mycket liknande avgiftsstatistik trots att MJD-modellens dagliga avkastning passar bättre med empiriska data. Vid jämförelse av HWM- och Hurdle avgiftsmodellerna observeras större skillnader. Medan den övergripande genomsnittliga avgiftsstatistiken är liknande för avgiftsmodellerna, är resultatbaserade avgifterna betydligt högre i Hurdle avgiftsstrukturen för tillgångar som uppnår högre avkastning, t.ex. minst 8% årlig avkastning. Däremot tenderar HWM-avgiftsstrukturen att generera högre resultatbaserade avgifter för tillgångar med låg avkastning. Regressionsmodeller utvecklades också för varje kombination av simulering och avgiftsstruktur. Regressionmodellerna återspeglar ovanstående slutsatser och kan för investerare fungera som enkla nyckeltal för att uppskatta förväntad kostnad av fondavgifter. GBM-regressionsresultaten är sannolikt mer användbara än MJD-regressionsresultaten, eftersom parametrarna för den förra är lättare att beräkna baserat på historisk avkastningsdata.

The Black-Scholes formula was the widely-used model for option pricing, this formula can be use to calculate the price of option by using current underlying asset prices, strike price, expiration time, volatility and interest rates. The European call option price from the model is a convex and increasing with respect to the initial underlying asset price. Assume underlying asset prices follow a generalized geometric Brownian motion, it is true that option prices increasing with respect to the constant interest rate and volatility, so that the volatility can be a very important factor in pricing option, if the volatility process £m(t) is constant (with £m(t) =£m for any t ) satisfying £m_1 ≤ £m(t) ≤ £m_2 for some constants £m_1 and £m_2 such that 0 ≤ £m_1 ≤ £m_2. Let C_i(t, S_t) be the price of the call at time t corresponding to the constant volatility £m_i (i = 1,2), we will derive that the price of call option at time 0 in the model with varying volatility belongs to the interval [C_1(0, S_0),C_2(0, S_0)].

Yes / We introduce a continuous time model for stock prices in a general factor representation with the noise driven by a geometric Brownian motion process. We derive the theoretical hitting probability distribution for the long-until-barrier strategies and the conditions for statistical arbitrage. We optimize our statistical arbitrage strategies with respect to the expected discounted returns and the Sharpe ratio. Bootstrapping results show that the theoretical hitting probability distribution is a realistic representation of the empirical hitting probabilities. We test the empirical performance of the long-until-barrier strategies using US equities and demonstrate that our trading rules can generate statistical arbitrage profits. / The full-text of this article will be released for public view at the end of the publisher embargo on 16 Sep 2024.

The financial market is a stochastic and complex system that is challenging to model. It is crucial for investors to be able to model the probability of possible outcomes of financial investments and financing decisions in order to produce fruitful and productive investments. This study investigates how Monte Carlo simulations of random walks can be used to model the probability of future stock returns and how the simulations can be improved in order to provide better accuracy. The implemented method uses a mathematical model called Geometric Brownian Motion (GBM) in order to simulate stock prices. Ten Swedish large-cap stocks were used as a data set for the simulations, which in turn were conducted in time periods of 1 month, 3 months, 6 months, 9 months and 12 months. The two main parameters which determine the outcome of the simulations are the mean return of a stock and the standard deviation of historical returns. When these parameters were calculated without weights the method proved to be of no statistical significance. The method improved and thereby proved to be statistically significant for predictions for a 1 month time period when the parameters instead were weighted. By varying the assumptions regarding price distribution with respect to the size of the current time period and using other weights, the method could possibly prove to be more accurate than what this study suggests. Monte Carlo simulations seem to have the potential to become a powerful tool that can expand our abilities to predict and model stock prices. / Den finansiella marknaden är ett stokastiskt och komplext system som är svårt att modellera. Det är angeläget för investerare att kunna modellera sannolikheten för möjliga utfall av finansiella investeringar och beslut för att kunna producera fruktfulla och produktiva investeringar. Den här studien undersöker hur Monte Carlo-simuleringar av så kallade random walks kan användas för att modellera sannolikheten för framtida aktieavkastningar, och hur simuleringarna kan förbättras för att ge bättre precision. Den implementerade metoden använder den matematiska modellen Geometric Brownian Motion (GBM) för att simulera aktiepriser. Tio svenska large-cap aktier valdes ut som data för simuleringarna, som sedan gjordes för tidsperioderna 1 månad, 3 månader, 6 månader, 9 månader och 12 månader. Huvudparametrarna som bestämmer utfallet av simuleringarna är medelvärdet av avkastningarna för en aktie samt standardavvikelsen av de historiska avkastningarna. När dessa parametrar beräknades utan viktning gav metoden ingen statistisk signifikans. Metoden förbättrades och gav då statistisk signifikans på en 1 månadsperiod när parametrarna istället var viktade. Metoden skulle kunna visa sig ha högre precision än vad den här studien föreslår. Det är möjligt att till exempel variera antagandena angående prisernas fördelning med avseende på storleken av den nuvarande tidsperioden, och genom att använda andra vikter. Monte Carlo-simuleringar har därför potentialen att utvecklas till ett kraftfullt verktyg som kan öka vår förmåga att modellera och förutse aktiekurser.

In the literature, many methods are proposed to value American options. However, due to computational difficulty, there are only approximate solution or numerical method to evaluate American options. It is not easy for general investors either to understand nor to apply. In this thesis, we build up an option pricing and virtual asset model system, which provides a friendly environment for general public to calculate early exercise boundary of an American option. This system modularize the well-handled pricing models to provide the investors an easy way to value American options without learning difficult financial theories. The system consists two parts: the first one is an option pricing system, the other one is an asset model simulation system. The option pricing system provides various option pricing methods to the users; the virtual asset model system generates virtual asset prices for different underlying models.

In this thesis, we expand the option pricing and virtual asset model system by Cheng (2005) and include new simulations and maximum likelihood estimation of the parameter of the stochastic differential equations. For easy manipulation of general users, the interface of original option pricing system is modified. In addition, in order to let the system more completely, some stochastic models and methods of pricing and estimation are added. This system can be divided into three major parts. One is an option pricing system; The second is an asset model simulation system; The last is estimation system of the parameter of the model. Finally, the analysis for the data of network are carried out. The differences of the prices between estimator of this system and real market are compared.

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In the presented thesis we study three methods of pricing European currency barrier options. With help of these methods we value selected barrier options with underlying asset EUR/CZK. In the first chapter we introduce the basic definitions from the world of financial derivatives and we describe our data. In the second chapter we deal with the classical model based on geometric Brownian motion of underlying asset and we prove a theorem of valuating Up-In-barrier option in this model. In the third chapter we introduce a model with stochastic volatility, the Heston model. We calibrate this model to market data and we use it to value our barrier options. In the last chapter we describe a jump diffusion model. Again we calibrate this jump diffusion model to market data and price our barrier options. The aim of this thesis is to decribe and to compare different methods of valuating barrier options. 1

[pt] A escolha de uma carreira é uma das decisões mais importantes na vida de uma pessoa, e é feita em um ambiente repleto de incertezas em relação ao futuro. Este trabalho analisa o aspecto financeiro da escolha entre uma carreira numa empresa privada e uma carreira em um órgão público, com ingresso por meio de um concurso. A análise pelo tradicional fluxo de caixa descontado apresenta uma série de limitações por não captar aspectos como a incerteza e a flexibilidade da tomada de decisão. Assim é aplicada uma abordagem segundo a teoria das Opções Reais, que se mostra mais adequada a este caso, pois permite que a flexibilidade de escolha seja modelada e considerada na escolha de carreira de um indivíduo. Neste estudo, os ganhos em uma empresa privada são modelados por meio de um processo estocástico enquanto a carreira pública tem um valor determinístico. Existe flexibilidade de data em relação ao ingresso na carreira pública, porém esta decisão é irreversível. Os resultados sugerem que a opção de ingressar na carreira pública pode ter valor significativo em relação à carreira privada. / [en] Choosing a career is one of the most important decisions in a person s life, and is done in an environment full of uncertainties about the future. This study analyzes the financial aspect of a career choice between a private company and a career in the government, with admission through a contest. The analysis through the traditional discounted cash flow would bring a lot of limitations, not capturing aspects such as uncertainty and flexibility of decision making. So real options theory approach is applied, which appears more appropriate in this case because it allows the flexibility of choice to be modeled and considered in the choice of an individual s career. In this study earnings in a private company are modeled through a stochastic process while public career has a deterministic value. There is flexibility regarding the date of entry into public career, but this decision is irreversible. The results suggest that the option of joining the public career may have significant value in relation to private career.