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1
Carvalho, João Pereira. "Portfolio insurance strategies : an analysis of path dependencies." Master's thesis, Instituto Superior de Economia e Gestão, 2013. http://hdl.handle.net/10400.5/5893.
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Mestrado em Ciências Empresariais<br>This thesis makes an evaluation of the path-dependency/independency of the most
widespread Portfolio Insurance strategies, i.e. CPPI, OBPI and SLPI, using Monte
Carlo simulations. Also, it is known that for the CPPI with multiplier higher than 1,
an undesirable path-dependent behavior called ‘cash-lock’, can occur in some market
scenarios. But in what scenarios and how often? In this thesis we show on an empirical level, that for most of the chosen market scenarios, CPPI 3 and CPPI 5 strategies can in fact get cash-locked easily. This is a rather undesirable feature to investors, particularly if it occurs on investments whose return has to be paid at a long maturity, which is the case for many of the CPPIs offered by financing institutions. To clearly show the path dependency we assume we know the value of the underlying risky asset not only at inception but also at maturity, and study the payoff distributions for the different PI under different market conditions and product specifications. To do so, we proceed with Monte Carlo simulations of the underlying risky asset paths, all conditioned to the same final value using Gaussian Processes for Machine Learning Regression. We model the risky asset as geometric Brownian motion.
We expect that this study will contribute to reinforce the idea that CPPI products need affordable solutions to prevent cash-locked investments, which is a major drawback to investors.<br>Esta tese faz uma avaliação das (in)dependências do caminho das estratégias mais difundidas de Portfolio Insurance (PI), ou seja, CPPI, OBPI e SLPI, utilizando simulações de Monte Carlo. Além disso, sabe-se que para a estratégia CPPI com multiplicador superior a 1, um comportamento dependente do caminho e indesejável chamado ‘cashlock’, i.e bloqueio no activo sem risco, pode ocorrer em alguns cenários de mercado.
Mas em que situações e com que frequência? Neste trabalho mostramos por via de simulações, que para a maioria dos cenários de mercado escolhidos, as estratégias CPPI 3 e CPPI 5 podem facilmente ficar . Esta é uma característica muito indesejável para os investidores, especialmente se ocorrer em investimentos que não estão totalmente cobertos e cujo retorno tem que
ser pago num longo prazo de vencimento, que é o caso de muitos dos CPPIs oferecidos pelas instituições financeiras. Para destacar a dependência do caminho, assumimos que se sabe o valor do activo de risco na maturidade. Estudamos, assim, as distribuições do valor na maturidade das diferentes estratégias PI sob diferentes condições de mercado e de produto. Para isso, procedemos com simulações de Monte Carlo dos caminhos do activo de risco subjacente, todos condicionados com o mesmo valor final, usando a regressão de Processos Gaussianos para Aprendizagem Automática. Neste estudo, modelou-se o activo de risco de acordo com o movimento Browniano geométrico. Esperamos que este estudo contribua para reforçar a ideia de que os produtos
CPPI com m > 1 precisam de soluções acessíveis para evitar que os investimentos terminem em cash-lock, o que é uma grande desvantagem para os investidores.
2
Lidén, Joel. "Stock Price Predictions using a Geometric Brownian Motion." Thesis, Uppsala universitet, Tillämpad matematik och statistik, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-353586.
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Erven, Matthias [Verfasser]. "On the Lifetime of a Conditioned Brownian Motion / Matthias Erven." München : Verlag Dr. Hut, 2012. http://d-nb.info/1020298936/34.
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Tanner, Stephen. "Non-tangential and conditioned Brownian convergence of pluriharmonic functions /." Thesis, Connect to this title online; UW restricted, 1999. http://hdl.handle.net/1773/5729.
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Karangwa, Innocent. "Comparing South African financial markets behaviour to the geometric Brownian Motion Process." Thesis, University of the Western Cape, 2008. http://etd.uwc.ac.za/index.php?module=etd&action=viewtitle&id=gen8Srv25Nme4_4787_1363778247.
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<p>This study examines the behaviour of the South African financial markets with regards to the Geometric Brownian motion process. It uses the daily, weekly, and monthly stock returns time series of some major securities trading in the South African financial market, more specifically the US dollar/Euro, JSE ALSI Total Returns Index, South African All Bond Index, Anglo American Corporation, Standard Bank, Sasol, US dollar Gold Price , Brent spot oil price, and South African white maize near future. The assumptions underlying the <br>Geometric Brownian motion in finance, namely the stationarity, the normality and the independence of stock returns, are tested using both graphical (histograms and normal plots) <br>and statistical test (Kolmogorov-Simirnov test, Box-Ljung statistic and Augmented Dickey-Fuller test) methods to check whether or not the Brownian motion as a model for South <br>African financial markets holds. The Hurst exponent or independence index is also applied to support the results from the previous test. Theoretically, the independent or Geometric <br>Brownian motion time series should be characterised by the Hurst exponent of ½<br>. A value of a Hurst exponent different from that would indicate the presence of long memory or <br>fractional Brownian motion in a time series. The study shows that at least one assumption is violated when the Geometric Brownian motion process is examined assumption by <br>assumption. It also reveals the presence of both long memory and random walk or Geometric Brownian motion in the South African financial markets returns when the Hurst index analysis is used and finds that the Currency market is the most efficient of the South African financial markets. The study concludes that although some assumptions underlying the <br>rocess are violated, the Brownian motion as a model in South African financial markets can not be rejected. It can be accepted in some instances if some parameters such as the Hurst exponent are added.</p>
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Erven, Matthias [Verfasser], G. [Akademischer Betreuer] Sweers, and B. [Akademischer Betreuer] Kawohl. "On the Lifetime of a Conditioned Brownian Motion / Matthias Erven. Gutachter: G. Sweers ; B. Kawohl." Köln : Universitäts- und Stadtbibliothek Köln, 2011. http://d-nb.info/1038170036/34.
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Geiss, Stefan. "On quantitative approximation of stochastic integrals with respect to the geometric Brownian motion." SFB Adaptive Information Systems and Modelling in Economics and Management Science, WU Vienna University of Economics and Business, 1999. http://epub.wu.ac.at/1774/1/document.pdf.
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We approximate stochastic integrals with respect to the geometric Brownian motion by stochastic integrals over discretized integrands, where deterministic, but not necessarily equidistant, time nets are used. This corresponds to the approximation of a continuously adjusted portfolio by a discretely adjusted one. We compute the approximation orders of European Options in the Black Scholes model with respect to L_2 and the approximation order of the standard European-Call and Put Option with respect to an appropriate BMO space, which gives information about the cost process of the discretely adjusted portfolio. (author's abstract)<br>Series: Report Series SFB "Adaptive Information Systems and Modelling in Economics and Management Science"
8
Feng, Zijie. "Stock-Price Modeling by the Geometric Fractional Brownian Motion: A View towards the Chinese Financial Market." Thesis, Linnéuniversitetet, Institutionen för matematik (MA), 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-78375.
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As an extension of the geometric Brownian motion, a geometric fractional Brownian motion (GFBM) is considered as a stock-price model. The modeled GFBM is compared with empirical Chinese stock prices. Comparisons are performed by considering logarithmic-return densities, autocovariance functions, spectral densities and trajectories. Since logarithmic-return densities of GFBM stock prices are Gaussian and empirical stock logarithmic-returns typically are far from Gaussian, a GFBM model may not be the most suitable stock price model.
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Vardar, Ceren. "On the Correlation of Maximum Loss and Maximum Gain of Stock Price Processes." Bowling Green State University / OhioLINK, 2008. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1224274306.
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MOSZKOWICZ, VIKTOR NIGRI. "VALIDATION OF THE PROJECT VALUATION CRITERION USING THE REAL OPTIONS THEORY: BRAZILIAN OIL FIELDS E AND P, CONSIDERING PRICES AS GEOMETRIC BROWNIAN MOTION." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2003. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=3592@1.
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COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR<br>As vantagens de incluir a flexibilidade gerencial e a
analogia às opções financeiras nos critérios de avaliação
de projetos têm sido alvo de discussões teóricas no
ramo das finanças. Diversos autores criticam os métodos de
análise de investimentos utilizados correntemente, que têm
como principal representante o fluxo de caixa descontado
(FCD), apoiando-se na noção de que os gerentes ao tomarem
decisões devem utilizar técnicas que reflitam as
flexibilidades disponíveis. Nesse sentido, a presente
dissertação tem por finalidade validar as vantagens
sugeridas na utilização da teoria de Opções Reais através
de um back-testing, que tem como objeto campos de
petróleo com características representativas da indústria
petrolífera brasileira. Estes testes serão realizados para
o período de 1970 a 1990, sendo contemplada a incerteza
econômica e excluindo-se as incertezas técnicas. O modelo
desenvolvido em Excel e VBA (Visual Basic for Applications)
para decisões de investimento considera as opções de espera
de até dois anos e de escolha entre três intensidades de
produção. O Movimento Geométrico Browniano foi assumido
como o processo estocástico para representar a evolução dos
preços reais do petróleo em dólares americanos ao longo do
tempo, e sua volatilidade foi variada a título de análise
de sensibilidade. Por fim, cabe ressaltar que os resultados
obtidos não devem ser aceitos como definitivos, e sim como
base de futuros trabalhos na linha de estudos empíricos
para verificar e validar as vantagens teóricas das Opções
Reais em relação aos demais critérios utilizados na
prática.<br>Financial researchers have discussed a lot about the
theoretical advantages of including the managerial
flexibility and the financial options analogy in projects
valuation criteria. Plenty of authors criticize the
currently used investment analysis methods, mainly
represented by the discounted cash flow, supported by the
notion that the managers should use techniques that better
reflect the available flexibility to take their decisions.
In this sense, the present dissertation has the objective
of validating the suggested advantages of using the Real
Options theory through a back-testing focused on oil fields
with Brazilian oil industry representative characteristics.
Those tests will be carried out for the 1970-1990 period,
considering the economic uncertainty and excluding the
technical uncertainties. The investment decisions model
developed in Excel and VBA (Visual Basic for Applications)
contemplates the options of waiting till two years and of
choosing among three exploitation intensities. The Geometric
Brownian Motion was assumed as the stochastic process to
represent the real oil prices time evolution, and its
volatility was varied to generate a sensibility analysis.
Finally it is worthy to state that the results shall not be
accepted as definitive, and just as a foundation to future
studies on the empirical research line of verifying and
validating the theoretical advantages of the Real Options
with regard to others currently used criteria.
11
Brodd, Tobias, and Adrian Djerf. "Monte Carlo Simulations of Stock Prices : Modelling the probability of future stock returns." Thesis, KTH, Skolan för elektroteknik och datavetenskap (EECS), 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-229752.
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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.<br>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.
12
Londani, Mukhethwa. "Numerical Methods for Mathematical Models on Warrant Pricing." University of the Western Cape, 2010. http://hdl.handle.net/11394/8210.
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>Magister Scientiae - MSc<br>Warrant pricing has become very crucial in the present market scenario. See, for example, M. Hanke and K. Potzelberger, Consistent pricing of warrants and traded options, Review Financial Economics 11(1) (2002) 63-77 where the authors indicate that warrants issuance affects the stock price process of the issuing company. This change in the stock price process leads to subsequent changes in the prices of options written on the issuing company's stocks. Another notable work is W.G. Zhang, W.L. Xiao and C.X. He, Equity warrant pricing model under Fractional Brownian motion and an empirical study, Expert System with Applications 36(2) (2009) 3056-3065 where the authors
construct equity warrants pricing model under Fractional Brownian motion and deduce the European options pricing formula with a simple method. We study this paper in details in this mini-thesis. We also study some of the mathematical models on warrant pricing using the Black-Scholes framework. The relationship between the price of the warrants and the price of the call accounts for the dilution effect is also studied mathematically. Finally we do some numerical simulations to derive the value of warrants.
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Siu, Daniel. "Stochastic Hybrid Dynamic Systems: Modeling, Estimation and Simulation." Scholar Commons, 2012. http://scholarcommons.usf.edu/etd/4405.
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Stochastic hybrid dynamic systems that incorporate both continuous and discrete dynamics have been an area of great interest over the recent years. In view of applications, stochastic hybrid dynamic systems have been employed to diverse fields of studies, such as communication networks, air traffic management, and insurance risk models. The aim of the present study is to investigate properties of some classes of stochastic hybrid dynamic systems.
The class of stochastic hybrid dynamic systems investigated has random jumps driven by a non-homogeneous Poisson process and deterministic jumps triggered by hitting the boundary. Its real-valued continuous dynamic between jumps is described by stochastic differential equations of the It\^o-Doob type. Existing results of piecewise deterministic models are extended to obtain the infinitesimal generator of the stochastic hybrid dynamic systems through a martingale approach. Based on results of the infinitesimal generator, some stochastic stability results are derived. The infinitesimal generator and stochastic stability results can be used to compute the higher moments of the solution process and find a bound of the solution.
Next, the study focuses on a class of multidimensional stochastic hybrid dynamic systems. The continuous dynamic of the systems under investigation is described by a linear non-homogeneous systems of It\^o-Doob type of stochastic differential equations with switching coefficients. The switching takes place at random jump times which are governed by a non-homogeneous Poisson process. Closed form solutions of the stochastic hybrid dynamic systems are obtained. Two important special cases for the above systems are the geometric Brownian motion process with jumps and the Ornstein-Uhlenbeck process with jumps. Based on the closed form solutions, the probability distributions of the solution processes for these two special cases are derived. The derivation employs the use of the modal matrix and transformations.
In addition, the parameter estimation problem for the one-dimensional cases of the geometric Brownian motion and Ornstein-Uhlenbeck processes with jumps are investigated. Through some existing and modified methods, the estimation procedure is presented by first estimating the parameters of the discrete dynamic and subsequently examining the continuous dynamic piecewisely.
Finally, some simulated stochastic hybrid dynamic processes are presented to illustrate the aforementioned parameter-estimation methods. One simulated insurance example is given to demonstrate the use of the estimation and simulation techniques to obtain some desired quantities.
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Wu, Cheng-Hsun, and 吳政訓. "A generalization of geometric Brownian motion with applications." Thesis, 2009. http://ndltd.ncl.edu.tw/handle/52678500671397304971.
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博士<br>國立中央大學<br>數學研究所<br>97<br>Brownian motion is a rigorous mathematical model (Wiener (1923), Levy (1948),
Ciesielski (1961)) with fruitful applications ranging from biology (Brown (1827)),
physics (Einstein (1905), Mazo (2002)), economy and financial engineering
(Bachelier (1900), Black and Scholes (1973)), to stochastic calculus (Ito (1944)),
among others.
Functional of Brownian motion is also useful in stochastic modeling. This is
particularly true for geometric Brownian motion. For instance, it has been applied to
model prices of stock (page 365 in Karlin and Taylor (1975), Black and
Scholes(1973)), rice (Yoshimoto el al. (1996)), labor (page 363 in Karlin and Taylor
(1975)) and others (Shoji (1995)). See Yor (2001) for more details.
Although geometric Brownian motion has a great variety of applications, it can not
cover all the random phenomena. It is then desirable to find a general model with
geometric Brownian motion as a special model. The purpose of this paper is to
investigate the generalizations of geometric Brownian motion
and its variants.
For the processes mentioned above, we will first study their mathematical properties. Next, we will discuss their applications in financial engineering. In practice, the parameters are unknown and have to be inferred from
realizations of processes. We will present estimation and test procedures.
15
Ya-HungLu and 盧亞鴻. "Estimation of a Bivariate Geometric Brownian Motion with Change-points." Thesis, 2010. http://ndltd.ncl.edu.tw/handle/52888091028452490683.
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碩士<br>國立成功大學<br>統計學系碩博士班<br>98<br>Bivariate geometric Brownian motion is widely used in modeling bavariate correlated economical data. Based on this model, the task of detecting change-points is considered. A likelihood-based approach for estimating the positions of change-points and a testing procedure for testing which parameter in the process is changed after the estimated change-point are proposed. In addition, both known and unknown the number of change-points are considered. Finally, gold and crede-oil (Brent crude) data are analyzed to illustrate the proposed method. Numerical results show that the proposed procedure is
useful.
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Lai, Chin-chen, and 賴沁蓁. "Dollar Cost Averaging and Value Averaging under Geometric Brownian Motion Model." Thesis, 2009. http://ndltd.ncl.edu.tw/handle/97077430337382135320.
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碩士<br>國立成功大學<br>統計學系碩博士班<br>97<br>This thesis studies the dollar-cost averaging and the value averaging. We use the internal rate of return to compare these two investment strategies. Assuming a geometric Brownian motion for stock prices, we use Monte Carlo technique to study the dollar-cost averaging and the value averaging under various settings of market price volatilities, investment time horizons, amount change , and market trend. A comparison of the results on Monte Carlo simulation and empirical Taiwan stock index was made. Simulation dictates that with larger price volatility, the value averaging will be better than the dollar-cost averaging under longer investment time horizon. . Both simulation and empirical study show that , by decreasing investment amount of each period, the internal rate of return and risk of the value averaging are higher than those of the dollar-cost averaging. But the risk borne by the unit expected return of the value averaging is less than that of the dollar-cost averaging.
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Tsai, Ming-Jhih, and 蔡明志. "Geometric Brownian Motion with multiplicative Jumps and its application to Derivatives Evaluation." Thesis, 2005. http://ndltd.ncl.edu.tw/handle/10208774416012141486.
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碩士<br>國立成功大學<br>統計學系碩博士班<br>93<br>The purpose of this study was to examine the model of geometric Brownian motion with multiplicative jumps. An iterative procedure was proposed to detect the jumps which follow a Poisson process with rate of intensityλ. The maximum likelihood method was used to estimate the parameterλ and the jump size. The algorithm of this iterative procedure was implemented in Matlab. The theoretical Black-Scholes, the market, and the simulated option prices were obtained through the investigation of a Taiwanese empirical study. The inclusion of the jump in the GBM resulted in option prices different from the Black-Scholes prices.
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Osborne, Bryan A. 1980. "Geometric brownian motion modeling of the Houston-Galveston nitrous oxide cap and trade market." Thesis, 2009. http://hdl.handle.net/2152/ETD-UT-2009-12-560.
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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.<br>text
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Hsue, Pei-Shan, and 徐珮珊. "Value-at-Risk Evaluation in Stock Price-A Comparison between Extended Ohlson Model and Geometric Brownian Motion Model." Thesis, 2008. http://ndltd.ncl.edu.tw/handle/42730979032342347888.
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碩士<br>中原大學<br>國際貿易研究所<br>96<br>In his equity valuation model, Ohlson (1995) shows that stock price can be expressed as the summation of abnormal earnings, book value, and non-accounting information. However, numbers shown in financial statement (such as abnormal earnings and book value) can only provide a limited measure of stock price, because they do not reflect other important information about firms’ fundamentals. Especially, Ohlson did not define the non-accounting information very clearly, so this thesis first revises Ohlson equity valuation model by replacing his “non-accounting information” with several important factors, including “macroeconomic variables” and “company factors” and re-evalute the stock price. Secondly, based on the revised Ohlson equity evaluation model, I use Monte Carlo simulation to calculate Value-at-Risk (VaR) for corporate. Finally, to measure and compare the VaRs of the revised Ohlson model and Brownian Motion, then choose the model that can forecast stock price and VaR more officiently.
In empirical study, I use Random effect model with fixed slope to evaluate the stock price in Taiwan 50 index constituents. To differentiate between empirical studies and forecast perform evaluation, sample periods spans from 1999 Q4 to 2006 Q3 and 2006 Q4 to 2007 Q3 separately.
The empirical results show as follows:
1.Financial indices, including book value and abnormal profit in original Ohlson equity valuation model all have positive effect on stock price.
2.By adding macroeconomic variables and company factors to represent non-accounting information in original Ohlson equity valuation model, the fitness of the revised model is improved.
3.In most sample companies, the VaR calculated from revised Ohlson equity evaluation model is lower than that from Geometric Brownian movement. In addition, for out-of-sample forecast performance, the revised Ohlson equity evaluation model has better VaR forecast performance than Geometric Brownian movement. However, in stock price forecasting, the result is complete opposite.
Keywords:
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Svoboda, Miroslav. "Asijské perpetuity." Master's thesis, 2020. http://www.nusl.cz/ntk/nusl-415941.
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This Master thesis studies Asian perpetuities, which is a term standing for European type of options with an average asset as the underlying asset and the execution time of the option in infinity. Assuming Geometric Brownian motion model of price of an asset, the goal of this thesis is to study behavior of the average of the asset price. Three different types of averaging are considered: arithmetic, geometric and harmonic average. The average values of the log-normals maintain the known distribution only for the geometric average. As it is shown in the thesis; however, when the average is examined on infinite time horizon, the arithmetic and harmonic averages maintain the inverse gamma distribution or gamma distribution, respectively. This result enables the computation of the price of Asian perpetuity which is also examined in the thesis. 1
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Ribeiro, Maria Madalena Rodrigues. "Avaliação de opções americanas via simulação de Monte Carlo." Master's thesis, 2010. http://hdl.handle.net/10451/8598.
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Tese de mestrado em Matemática Financeira, apresentada à Universidade de Lisboa, através da Faculdade de Ciências, 2010<br>Esta tese foca-se no estudo da avaliação de opções americanas via método dos mínimos quadrados de Monte Carlo [Least Square Monte Carlo (LSM)] de Longstaff-Schwartz (2001), que consiste na avaliação de opções americanas através de simulações e de regressões simples. Para efectuar o estudo implementou-se o algoritmo do referido método, em MatLab. Para um estudo mais aprofundado e comparativo, implementou-se o método utilizando diversos modelos, nomeadamente o modelo CEV, o modelo JDCEV e também o Geometric Brownian Motion (GBM).
Comparou-se os diversos resultados estudando assim a adequabilidade dos diferentes modelos na avaliação deste tipo de opções. Foi efectuada uma outra comparação para o Geometric Brownian Motion: foram consideradas, neste processo, funções básicas diferentes, que foram utilizadas na regressão do método LSM, pretendendo assim analisar qual a melhor forma de avaliar as referidas opções.<br>The present thesis focuses on the study of American options using the Longstaff-Schwartz (2001) Least Square Monte Carlo (LSM) method, which involves simulations and simple regressions. To elaborate the study the algorithm of the above mentioned method was implemented in Matlab. The valuation method was implemented under different models namely the Constant Elasticity of Variance (CEV), the Jump-to-Default extended CEV (JDCEV) model, and the Geometric Brownian Motion (GBM). A different kind of comparison was performed for the Geometric Brownian Motion: different basic functions were considered for the LSM method regression, with the purpose of finding the best method to evaluate the mentioned options.
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Klůjová, Jana. "Stínové ceny a řízení portfolia s proporcionálními transakčními náklady." Master's thesis, 2013. http://www.nusl.cz/ntk/nusl-321391.
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The diploma thesis describes portfolio management with proportional transaction costs. The main aim is to describe using of shadow prices to find the optimal Markov policies keeping the proportion of the investor's wealth invested in the risky asset within the corresponding interval in order to maximize the long run geometric growth rate. On the real market, the investor must pay transaction costs when he buys/sells shares. In the diploma thesis we transform these prices into the shadow price; when trading in the shadow price there are no transaction costs. The solution itself is based on Itô formula and the martingal theory. The prices of shares are modeled as geometric Brownian motion. Powered by TCPDF (www.tcpdf.org)
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Ferreira, Paulo Fernando Marques. "Evaluating investment opportunities under different model dynamics: Some managerial insights." Master's thesis, 2012. http://hdl.handle.net/10071/6397.
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The Net Present Value is the most well known measure of project valuation for managers. However it requires an investment decision made in the moment as well as the cash outflow of the investment. However, a manager has different levels of flexibility in the exercise of his functions that the classic Net Present Value valuation does not take in account. An investment can be delayed to a pre-committed date, can have the decision delayed by a certain or an endlessly period of time, and can be reverted. Despite not applicable to all parameters, the numerical analysis made in this thesis has a pretty straight-forward conclusion, the higher the flexibility a manager can dispose, the value of the project for the manager rises.
A project value is not only affected by its parameters and by the flexibility disposed to the manager. The model dynamic in which a project is calculated is also a very important tool for managers to consider. The most used model dynamic to value real options is the Geometric Brownian Motion, which assumes constant volatility. Constant volatility is not a legit assumption to take, since a wide range of assets and markets do not have constant volatility. To overcome this flaw, the Constant Elasticity of Variance diffusion model is considered in this thesis. Numerical analysis made in this thesis proves that a manager is exposed to real options valuation errors by assuming constant volatility.<br>O Valor Atualizado Líquido é a mais conhecida medida de avaliação de projetos para gestores. No entanto, requer uma decisão de investimento imediatamente assim como o cash outflow do investimento. Contudo, um gestor tem diferentes níveis de flexibilidade no exercício das suas funções, flexibilidade essa que a avaliação com o clássico Valor Atualizado Líquido não tem em conta. Um investimento pode ser adiado para uma data pré-acordada, pode ser adiada a decisão até um certo ou um indefinido período de tempo, e pode ser revertido. Apesar de não ser aplicável para todos os parâmetros, a análise numérica feita nesta tese tem uma conclusão clara, quanto maior a flexibilidade que um gestor dispõe, maior o valor do projeto para o gestor.
O valor de um projeto não é só afetado pelos seus parâmetros e pela flexibilidade à disposição do gestor. A dinâmica do modelo no qual o projeto é calculado é também um fator muito importante para o gestor ter em conta. O modelo mais usado para avaliar opções reais é o movimento Browniano geométrico, que assume uma volatilidade constante. Volatilidade constante não é uma assunção legítima de fazer, visto que um largo espectro de ativos e mercados não têm volatilidade constante. Para superar esta falha, o modelo de difusão da Constante Elasticidade da Variância é considerado nesta tese. A análise numérica feita nesta tese prova que um gestor na avaliação de opções está exposto a erros por assumir a volatilidade constante.
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Mudzimbabwe, Walter. "Pricing methods for Asian options." Thesis, 2010. http://hdl.handle.net/11394/3468.
Full textAbstract:
>Magister Scientiae - MSc<br>We present various methods of pricing Asian options. The methods include Monte Carlo simulations designed using control and antithetic variates, numerical solution of partial differential equation and using lower bounds.The price of the Asian option is known to be a certain risk-neutral expectation. Using the Feynman-Kac theorem, we deduce that the problem of determining the expectation implies solving a linear parabolic partial differential equation. This partial differential equation does not admit explicit solutions due to the fact that the distribution of a sum of lognormal variables is not explicit. We then solve the partial differential equation numerically using finite difference and Monte Carlo methods.Our Monte Carlo approach is based on the pseudo random numbers and not deterministic sequence of numbers on which Quasi-Monte Carlo methods are designed. To make the Monte Carlo method more effective, two variance reduction techniques are discussed.Under the finite difference method, we consider explicit and the Crank-Nicholson’s schemes.
We demonstrate that the explicit method gives rise to extraneous solutions because the stability conditions are difficult to satisfy. On the other hand, the Crank-Nicholson method is unconditionally stable and provides correct solutions.
Finally, we apply the pricing methods to a similar problem of determining the price of a European-style arithmetic basket option under the Black-Scholes framework. We find the optimal lower bound, calculate it numerically and compare this with those obtained by the Monte Carlo and Moment Matching methods.Our presentation here includes some of the most recent advances on Asian options, and we contribute in particular by adding detail to the proofs and explanations. We also
contribute some novel numerical methods. Most significantly, we include an original
contribution on the use of very sharp lower bounds towards pricing European basket
options.
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Macháček, Adam. "Oceňování bariérových opcí." Master's thesis, 2013. http://www.nusl.cz/ntk/nusl-321410.
Full textAbstract:
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
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Myšičková, Ivana. "Odhad rizika v měsíčním horizontu na základě dvouleté časové řady." Master's thesis, 2014. http://www.nusl.cz/ntk/nusl-335066.
Full textAbstract:
The thesis describes commonly used measures of risk, such as volatility, Value at Risk (VaR) and Expected Shortfall (ES), and is tasked with creating models for measuring market risk. It is concerned with the risk over daily and over monthly horizons and shows the shortcomings of a square-root-of-time approach for converting VaR and ES between horizons. Parametric models, geometric Brownian motion (GBM) and GARCH process, and non-parametric models, historical simulation (HS) and some its possible improvements, are presented. The application of these mentioned models is demonstrated using real data. The accuracy of VaR models is proved through backtesting and the results are discussed. Part of this thesis is also a simulation study, which reveals the precision of VaR and ES estimates.
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Miranda, Guilherme Donário. "On the application of structural credit risk models to sovereign issuers." Master's thesis, 2018. http://hdl.handle.net/10400.14/25494.
Full textAbstract:
This dissertation uses CDS spreads to extract the probability of default of the Portuguese sovereign using a structural credit risk model. The model considered assumes that the government revenue follows a geometric Brownian motion. In addition, the government is assumed to have fixed costs corresponding to its total expenditure. The sovereign defaults at the first time its revenue falls below a certain level, which is estimated in this thesis as a multiple of the government debt. Under the assumption of a 40% recovery rate, estimates on the 5-year probability of default were extracted. This was done both under the risk neutral and the physical measure. This was possible assuming that the market price of risk implicit in sovereign CDS markets was equal to the one implied in Portuguese listed equities.
The results obtained were in line with expectations. The probability of default of the Portuguese government is close to zero in 2007, 2008, 2016 and 2017 and reaches very high levels in 2011 and 2012. Though the highest probability of default (under both measures) is observed in 2011, the largest difference between the probability of default under the risk neutral and physical measures is observed in 2012. In this year, the difference in the 5-year probability of default under the two measures reaches 13.90 percentage points.<br>Esta tese utiliza spreads dos CDS para extrair a probabilidade de incumprimento do Estado Português utilizando um modelo estrutural de risco de crédito. O modelo considerado assume que a receita do governo segue um movimento Browniano geométrico. Para além disso, assume-se que o governo tem custos fixos correspondentes à sua despesa total. O soberano entra em incumprimento quando a sua receita desce abaixo de um determinado nível que, nesta tese, é estimado como um múltiplo da dívida soberana. Assumindo uma taxa de recuperação de 40%, a probabilidade de incumprimento a 5 anos foi extraída na medida neutra ao risco e a física. Isto foi possível assumindo que o preço de mercado do risco implícito nos CDS dos soberanos era igual ao implícito em empresas Portuguesas cotadas em bolsa.
Os resultados obtidos estão em linha com os esperados. A probabilidade de incumprimento do estado Português a 5 anos foi próxima de zero nos anos de 2007, 2008, 2016 e 2017 e atingiu níveis extremamente elevados em 2011 e 2012. O valor mais elevado para esta variável, em ambas as medidas, foi observado em 2011. A maior diferença entre a medida neutra ao risco e a medida física ocorreu em 2012. Neste ano, a diferença na probabilidade de incumprimento a 5 anos entre as duas medidas atingiu 13.90 pontos percentuais.
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Bukhari, Abdulwahab Abdullatif. "Optimization of production allocation under price uncertainty : relating price model assumptions to decisions." Thesis, 2011. http://hdl.handle.net/2152/ETD-UT-2011-08-3780.
Full textAbstract:
Allocating production volumes across a portfolio of producing assets is a complex optimization problem. Each producing asset possesses different technical attributes (e.g. crude type), facility constraints, and costs. In addition, there are corporate objectives and constraints (e.g. contract delivery requirements). While complex, such a problem can be specified and solved using conventional deterministic optimization methods. However, there is often uncertainty in many of the inputs, and in these cases the appropriate approach is neither obvious nor straightforward. One of the major uncertainties in the oil and gas industry is the commodity price assumption(s). This paper investigates this problem in three major sections: (1) We specify an integrated stochastic optimization model that solves for the optimal production allocation for a portfolio of producing assets when there is uncertainty in commodity prices, (2) We then compare the solutions that result when different price models are used, and (3) We perform a value of information analysis to estimate the value of more accurate price models. The results show that the optimum production allocation is a function of the price model assumptions. However, the differences between models are minor, and thus the value of choosing the “correct” price model, or similarly of estimating a more accurate model, is small. This work falls in the emerging research area of decision-oriented assessments of information value.<br>text
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El-Khatib, Mayar. "Highway Development Decision-Making Under Uncertainty: Analysis, Critique and Advancement." Thesis, 2010. http://hdl.handle.net/10012/5741.
Full textAbstract:
While decision-making under uncertainty is a major universal problem, its implications in the field of transportation systems are especially enormous; where the benefits of right decisions are tremendous, the consequences of wrong ones are potentially disastrous.
In the realm of highway systems, decisions related to the highway configuration (number of lanes, right of way, etc.) need to incorporate both the traffic demand and land price uncertainties. In the literature, these uncertainties have generally been modeled using the Geometric Brownian Motion (GBM) process, which has been used extensively in modeling many other real life phenomena. But few scholars, including those who used the GBM in highway configuration decisions, have offered any rigorous justification for the use of this model.
This thesis attempts to offer a detailed analysis of various aspects of transportation systems in relation to decision-making. It reveals some general insights as well as a new concept that extends the notion of opportunity cost to situations where wrong decisions could be made. Claiming deficiency of the GBM model, it also introduces a new formulation that utilizes a large and flexible parametric family of jump models (i.e., Lévy processes). To validate this claim, data related to traffic demand and land prices were collected and analyzed to reveal that their distributions, heavy-tailed and asymmetric, do not match well with the GBM model. As a remedy, this research used the Merton, Kou, and negative inverse Gaussian Lévy processes as possible alternatives.
Though the results show indifference in relation to final decisions among the models, mathematically, they improve the precision of uncertainty models and the decision-making process. This furthers the quest for optimality in highway projects and beyond.