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Aplicações da expansão de Edgeworth à precificação de derivativos financeiros; Testing option pricing with the Edgeworth expansion

Balieiro Filho, Ruy Gabriel
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Dissertação de Mestrado Formato: application/pdf
Publicado em 19/02/2003 Português
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O Objetivo deste trabalho é usar uma ferramenta matemática conhecida como expansão de Edgeworth em conjunto com a moderna teoria de análise de derivativos financeiros que utilizam o método de precificação neutra ao risco. Tal expansão permite obter uma função densidade de probabilidade com assimetria e curtose arbitrárias a partir de uma densidade normal. Desta forma, podemos usar esta nova distribuição como a state price density do ativo-objeto procurando corrigir o sorriso da volatilidade através da definição de funções de probabilidade com assimetrias positivas ou negativas e curtose maior de que três. Além disso esperamos também chegar a uma nova maneira de realizar o delta hedge de uma carteira de replicação de modo mais eficiente do que a de Black-Scholes.; There is a well-developed framework, the Black?Scholes theory, for the pricing of contracts based on the future prices of certain assets, called options. This theory assumes that the probability distribution of the returns of the underlying asset is a Gaussian distribution. However, it is observed in the market that this hypothesis is 2awed, leading to the introduction of a fudge factor, the so-called volatility smile. Therefore, it would be interesting to explore extensions of the Black?Scholes theory to non-Gaussian distributions. In this paper...

Estudo de três metodologias para determinação do custo de capital internacional : análise comparativa e validação dos modelos; Assessment of three methodologies to determine the international cost of capital : comparative analysis and validation

Rossi, Luiz Egydio Malamud
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Tese de Doutorado Formato: application/pdf
Publicado em 12/11/2007 Português
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O processo de globalização integrou mercados, aumentou o fluxo de capitais entre os países e, apesar da maior abundância de capitais, aumentou a disputa entre países emergentes e desenvolvidos por recursos oriundos do exterior. Em decorrência dessa maior dependência de recursos externos, a capacidade de atrair investimentos se tornou um fator importante para determinar a competitividade do país no cenário internacional. Os investidores consideram a relação entre risco percebido e retorno esperado ao alocar seus recursos internacionalmente e, dessa forma, a correta mensuração do risco incorrido deve ser compatível com a remuneração esperada pelo investimento. Possíveis efeitos da incorreta percepção de risco pelos investidores são a redução do valor dos ativos locais, a maior saída de recursos em decorrência de altos dividendos ou juros e a redução na entrada de recursos do exterior por inibir investidores que buscam opções de baixo risco. Devido a esses efeitos na economia dos países dependentes de recursos, estudaram-se nesta tese três metodologias usualmente empregadas pelos investidores no apreçamento do custo de capital internacional. Essas metodologias de apreçamento analisadas se baseiam em medidas de risco distintas...

Uma análise da utilização do coeficiente Beta no setor elétrico brasileiro; An analysis of the coefficient beta in the context of the Brazilian electricity industry

Pinto, Rinaldo Caldeira
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Dissertação de Mestrado Formato: application/pdf
Publicado em 30/06/2008 Português
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O coeficiente beta, definido no contexto do modelo de avaliação de ativos denominado Capital Asset Pricing Model, tem sido amplamente utilizado no Setor Elétrico Brasileiro. Sua aplicação tem sido importante não apenas no âmbito das revisões tarifárias conduzidas pelo órgão regulador, mas também para análise das empresas do setor pelos investidores em mercado de capitais. Embora a aplicação do modelo CAPM seja simples, ele é construído sobre hipóteses rigorosas, que nem sempre são observáveis no mercado real, principalmente em países emergentes. Inserido no referencial teórico deste Modelo, o presente trabalho tem como o objetivo analisar a utilização do coeficiente beta no setor elétrico brasileiro, identificando potenciais distorções que decorram de sua aplicação. Adicionalmente, este trabalho busca analisar o comportamento desse coeficiente de mercado ao longo do período de 1999 a 2007, identificando possíveis tendências. Para isso, lança-se mão de dados que são amplamente utilizados pelos agentes do mercado de capitais, oriundos de uma amostra de empresas que, por possuírem dados disponibilizados em bolsa de valores tornam viável gerar este coeficiente. Das análises realizadas é possível concluir que o coeficiente beta obtido com dados do mercado brasileiro apresentou valores bem próximos aos coeficientes obtidos em mercados desenvolvidos. Também foi possível constatar que os segmentos de distribuição e geração apresentam...

Aplicação do CAPM para a determinação do custo de capital próprio no Brasil; Application of the CAPM for determining the cost of equity in Brazil

Bellizia, Nathalia Wurzler
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Dissertação de Mestrado Formato: application/pdf
Publicado em 18/08/2009 Português
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O desenvolvimento acelerado do mercado de capitais brasileiro e o aumento de sua importância no cenário econômico internacional, assim como o de outros mercados emergentes, colocaram em evidência um tema muito controvertido no campo de finanças: a precificação de ativos em mercados emergentes. Diante da ausência de consenso em relação ao tema, o objetivo desta dissertação consistiu em testar e comparar a aplicação de quatro modelos de precificação de ativos no mercado de capitais brasileiro: o CAPM Local, o CAPM Global, o Modelo Goldman e o modelo proposto por Solnik (2000). Para tal, a metodologia de Fama e MacBeth (1973) foi aplicada à uma amostra composta por todas as ações listadas na BOVESPA, no período compreendido entre janeiro de 1998 e dezembro de 2007. Os resultados obtidos sugerem a existência de fatores não especificados nos modelos com poder explanatório sobre o prêmio pelo risco das carteiras, e a inexistência de um prêmio pelo risco de mercado positivo no Brasil. Tais resultados, juntamente com o baixo coeficiente de determinação ajustado dos modelos, indicam que estes não são válidos no mercado de capitais brasileiro. No entanto, quando os modelos são testados com a exclusão dos interceptos...

Mercado e desempenho operacional contábil de longo prazo

Rosa, Meg Sarkis Simão
Fonte: Universidade de Brasília Publicador: Universidade de Brasília
Tipo: Dissertação
Português
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Dissertação (mestrado)-Universidade de Brasília, Departamento de Ciências Contábeis, Programa de Pós-Graduação em Ciências Contábeis, 2011.; Pesquisas sobre relevância da informação contábil para o valor da empresa, geralmente, avaliam o impacto do desempenho, medido por informações contábeis, no valor de mercado das empresas. Seguindo essa linha de pesquisa, este estudo propôs verificar se o mercado diferencia as empresas de alto, médio e baixo desempenho operacional de longo prazo, medido por informações contábeis de rentabilidade, variação de vendas e endividamento, tendo como base teórica os estudos sobre relevância para o valor, a Hipótese de Eficiência do Mercado, o Capital Asset Pricing Model e a Teoria da Divulgação. Os objetos de estudo foram as Demonstrações Contábeis Societárias Anuais Individuais divulgadas no período de 1996 a 2009 juntamente com os preços das ações das empresas listadas na Bolsa de Valores e de Mercadorias e Futuros de São Paulo – BM&FBOVESPA, compondo uma amostra de 142 empresas não-financeiras, utilizando janelas móveis de cinco anos, que resultaram em dez períodos quinquenais. Após a apuração dos índices de cada empresa, as variáveis contábeis foram unificadas em um Índice Síntese de Desempenho...

The convolution method for pricing american options under Lévy processes

Oliveira, Pedro Simões
Fonte: Universidade de Lisboa Publicador: Universidade de Lisboa
Tipo: Dissertação de Mestrado
Publicado em //2014 Português
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Tese de mestrado em Matemática Financeira, apresentada à Universidade de Lisboa, através da Faculdade de Ciências, 2014; Um método flexível, rápido e exacto para avaliação de opções, desde as mais simples às mais complexas com provisões de exercício antecipado, é apresentado. Este método baseia-se na Fast Fourier Transform (FFT) e depende, naturalmente, das transformadas de Fourier. A ideia principal baseia-se em reconhecer que a fórmula usual de avaliação neutra ao risco pode ser calculada como uma convolução. Esta característica, é extremamente útil, dado que convoluções no domínio do tempo podem ser transformadas facilmente em multiplicações no domínio de Fourier, o que permite aplicar a FFT e beneficiar da sua capacidade computacional. Este recente método de avaliação, proposto por Lord et al. (2008), foi apelidado de método da convolução, e é aplicável a uma grande variedade de payoffs necessitando apenas do conhecimento da função característica do modelo. Desta forma, o método é aplicável a vários modelos afins, entre os quais está a classe de modelos exponenciais de Levy. O método apresentado é capaz de estender os métodos anteriores, baseados na FFT para o cálculo de opções Europeias...

Analysis of employee stock options and guaranteed withdrawal benefits for life

Shah, Premal (Premal Y.)
Fonte: Massachusetts Institute of Technology Publicador: Massachusetts Institute of Technology
Tipo: Tese de Doutorado Formato: 224 p.
Português
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In this thesis we study three problems related to financial modeling. First, we study the problem of pricing Employee Stock Options (ESOs) from the point of view of the issuing company. Since an employee cannot trade or eectively hedge ESOs, she exercises them to maximize a subjective criterion of value. Modeling this exercise behavior is key to pricing ESOs. We argue that ESO exercises should not be modeled on a one by one basis, as is commonly done, but at a portfolio level because exercises related to different ESOs that an employee holds would be coupled. Using utility based models we also show that such coupled exercise behavior leads to lower average ESO costs for the commonly used utility functions such as power and exponential utilities. Unfortunately, utility based models do not lead to tractable solutions for finding costs associated with ESOs. We propose a new risk management based approach to model exercise behavior based on mean-variance portfolio maximization. The resulting exercise behavior is both intuitive and leads to a computationally tractable model for finding ESO exercises and pricing ESOs as a portfolio. We also study a special variant of this risk-management based exercise model, which leads to a decoupling of the ESO exercises and then obtain analytical bounds on the implied cost of an ESO for the employer in this case. Next...

Aging Population, Pension Funds, and Financial Markets : Regional Perspectives and Global Challenges for Central, Eastern, and Southern Europe

Holzmann, Robert
Fonte: World Bank Publicador: World Bank
Português
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Population aging is a worldwide phenomenon, but it is particularly advanced in highly developed northern countries. The retirement of the baby-boom generation in these rich countries will impose additional, albeit temporary, pressure on their pension systems. To cope with this pressure, reforms have been introduced that have lessened the generosity of publicly provided pension benefits. By design and by implication, this change increases the importance of mandatory and voluntary funded retirement schemes in smoothing consumption across the life cycle. The first three chapters of this book investigate questions germane to pension systems in the Central, Eastern, and Southern Europe (CESE) economies: the extent to which pension systems were prepared to deal with multi pillar pension reform, how to foster the development of financial systems so that they can better support funded systems, and how ready the systems are for the approaching payout of benefits as the first participants in the funded pillar approach retirement age. The remaining three chapters investigate broader questions facing pension systems in both developed and emerging countries: the capacity of the financial markets to deliver sufficiently high net rates of return...

Pakistan : Issues Related to the Government Securities Market and Government Debt Management

World Bank
Fonte: Washington, DC Publicador: Washington, DC
Português
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The government of Pakistan borrows in the domestic market through a range of instruments, and this market is a critical source of funding for both shorter-term cash management and longer-term deficit-financing. The government has taken actions over the past 18 months that have enhanced the effectiveness of the market as a source of funding, as well as its efficiency. These include the movement toward more predictable, volume-based, market-determined pricing of government securities. Taking account of the dynamics of demand will be important as the government continues to develop its medium-term debt management strategy. Doing so will help identify potential constraints that may impede the implementation of the chosen strategy. Specific actions that the government is recommended to take include: a) reducing the number of tenors issued, b) consolidating the debt stock so as to improve liquidity in individual bonds, c) reducing time delays in auction processing, and d) developing and investor-relations function...

A New "Availability-Payment" Model for Pricing Performance-Based Logistics Contracts

Sandborn, Peter; Kashani-Pour, Amir Reza; Zhu, Xinyuan; Cui, Qingbin
Fonte: Escola de Pós-Graduação Naval Publicador: Escola de Pós-Graduação Naval
Tipo: Relatório
Português
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Annual Acquisition Research Symposium batch 1; Acquisition Research Program Sponsored Report Series; Approved for public release; distribution is unlimited.; This report describes the adoption and extension of “availability payment” concepts currently in use for civil infrastructure Public-Private Partnerships (PPPs) to contract design and pricing for Performance-Based Logistics (PBL) contracts. Availability payment models for civil infrastructure PPPs require the private sector to take responsibility for designing, building, financing, operating and maintaining an asset (most commonly highways). Under the “availability payment” concept, once the asset is available for use, the private sector begins receiving an annual payment for a contracted number of years based on meeting performance requirements. The challenge in PPPs is to determine a payment plan (amount and length of time) that protects the public interest, i.e., does not overpay the private sector, but also minimizes that risk that the asset will become unsupported. In this report we focus on availability as the key required outcome and introduce a stochastic availability requirement into PBL contract structures. The model developed in this report uses an affine controller to drive a discrete event simulator (Petri net) that produces availability and cost measures. The model is used to explore the optimum availability assessment window (length of time over which availability should be assessed) for a PBL contract.

Financial Globalization in Emerging Countries : Diversification vs. Offshoring

Ceballos, Francisco; Didier, Tatiana; Schmukler, Sergio L.
Fonte: World Bank, Washington, DC Publicador: World Bank, Washington, DC
Tipo: Publications & Research :: Policy Research Working Paper; Publications & Research
Português
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Financial globalization has gathered attention since the early 1990s because of its macro-financial implications and growing importance. But financial globalization has taken shape via different forms over time. This paper examines two important, concurrent dimensions of financial globalization: diversification and offshoring. The diversification dimension refers to the increase in foreign assets and liabilities in countries' portfolios. Offshoring is related to the reallocation of financial activities to international markets. The former focuses on who holds the assets, the latter on where transactions take place. The authors find that globalization via the diversification channel expanded throughout the world during the 2000s, as domestic residents invested more abroad and foreigners increased their investments at home, generating more cross-border holdings. However, financial globalization via offshoring displays more mixed patterns, with variations across markets and countries. The paper also shows that the nature of financing through both diversification and offshoring has improved for emerging countries.

Unlocking Land Values for Urban Infrastructure Finance : International Experience--Considerations for Indian Policy

Peterson, George E.
Fonte: World Bank, Washington, DC Publicador: World Bank, Washington, DC
Tipo: Publications & Research :: Policy Research Working Paper; Publications & Research
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Despite strong economic growth, investment in basic urban infrastructure -- water supply, wastewater removal and treatment, roads, and other capital-intensive systems -- has failed to keep pace with urban growth, leaving a critical urban infrastructure deficit. At the same time, urban lands in these many developing countries are among the most expensive in the world. Much of this land is owned by public authorities. Significant parts of it lie vacant, unused for public service provision or inappropriate for conversion to higher-valued economic activity. A composite public-sector balance sheet for India's urban areas would show an asset mix strong on public-sector landholdings but weak on infrastructure. This raises the following questions: Can some excess public-sector land be exchanged for infrastructure, in a manner that is politically acceptable and economically efficient? Can public land sales be a realistic source of finance for critically needed urban infrastructure investment? This paper considers the policy context that has shaped different land-disposal and earmarking initiatives...

Capital Market Integration and MiFID Implementation : The Bulgarian Experience

World Bank
Fonte: Washington, DC Publicador: Washington, DC
Tipo: Economic & Sector Work :: Commodities Study; Economic & Sector Work
Português
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Bulgaria's financial integration with Europe has been essential in financing economic transition and spurring economic growth. As the sovereign debt turmoil in Europe casts a cloud over the financial sector, the development of capital markets over the medium term may offer a beneficial diversification of the financial system. Bulgaria began aligning its regulation of securities markets to European Union (EU) standards when its EU accession process began and introduced the Markets in Financial Instruments Directive (MiFID) in November 2007 along with other EU countries. This report aims to assess the implementation of MiFID in Bulgaria, to provide an initial view on the impact it had on the Bulgarian securities markets, and to draw lessons about the experience. The report not only offers concrete suggestions for stimulating development of the capital market to the benefit of firms and investors, but it also aims to stimulate further debate about how to organize the securities market infrastructure for long-term development.

Credit Risk, Fraud Risk, and Corporate Bond Spreads

Zhang, QI
Fonte: Quens University Publicador: Quens University
Tipo: Tese de Doutorado
Português
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Exploring the main factors that determine bond spreads with respect to Treasury rates is one of the most critical issues in the corporate debt market. Credit risk has long been perceived as the most important determinant of bond spreads (Fisher, 1959). One of the most critical parameters in credit risk models is asset volatility, which includes idiosyncratic and systematic components. However, these models do not distinguish between them. Chapter 2 investigates the impact of idiosyncratic volatility on bond portfolio spreads between 2000 and 2010. While the prediction of traditional asset pricing models is that firm-specific risk should be diversified away at aggregate level, I find idiosyncratic volatility plays an incremental role in explaining bond portfolio spreads beyond the market factors. Recovery is an important measurement of credit risk additional to default probability. Chapter 3 focuses on the estimation of firm recovery after bankruptcy using the Leland and Toft (1996) model. Using a large sample of Chapter 11 filings from 1996 to 2007, I find that the recovery derived from the Leland and Toft model has strong explanatory power on the debt recovery observed in the market. Recent literature finds that all extant credit risk models significantly underestimate bond spreads...

Does specialization in security analysis and portfolio management explain deviations from the CAPM?

Keyser, Leonid
Fonte: Massachusetts Institute of Technology Publicador: Massachusetts Institute of Technology
Tipo: Tese de Doutorado Formato: 45 p.; 2379923 bytes; 2381696 bytes; application/pdf; application/pdf
Português
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The Capital Asset Pricing Model (CAPM), which relates the risk of an individual security to its expected return, is frequently cited in investments textbooks and the academic literature as a centerpiece of modem finance theory. The main prediction of the CAPM is that investors are compensated in the form of expected return only for bearing systematic or market risk, which is the portion of a security's risk that cannot be diversified away. That investors demand reparation for and only for systematic risk is a consequence from the pivotal assumption that all investors have identical information for the entire universe of publicly traded securities. In actuality, professional active money managers rarely invest in a portfolio broad enough to be considered the market portfolio. Instead, the asset management industry has self-organized over time according to a top-down investment process, where asset allocators provide capital to security selectors who specialize in high-yield bonds, large-cap value stocks, and the like. Any losses in diversification benefits resulting from this theoretically suboptimal two-phase investment strategy are deemed an unavoidable cost of obtaining accurate forecasts through specialization in security analysis and portfolio management.; (cont.) This research paper extends the ideas of the CAPM to formulate an equilibrium security pricing model that attempts to account for the top-down approach followed by investors in the real-world.; by Leonid Keyser.; Thesis (M.B.A.)--Massachusetts Institute of Technology...

Volatility derivatives in market models with jumps

Mijatovic, A.; Lo, H.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 20/05/2009 Português
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It is well documented that a model for the underlying asset price process that seeks to capture the behaviour of the market prices of vanilla options needs to exhibit both diffusion and jump features. In this paper we assume that the asset price process $S$ is Markov with cadlag paths and propose a scheme for computing the law of the realized variance of the log returns accrued while the asset was trading in a prespecified corridor. We thus obtain an algorithm for pricing and hedging volatility derivatives and derivatives on the corridor-realized variance in such a market. The class of models under consideration is large, as it encompasses jump-diffusion and Levy processes. We prove the weak convergence of the scheme and describe in detail the implementation of the algorithm in the characteristic cases where $S$ is a CEV process (continuous trajectories), a variance gamma process (jumps with independent increments) or an infinite activity jump-diffusion (discontinuous trajectories with dependent increments).; Comment: 27 pages, 3 figures

Price Discovery in Financial markets: the case of the CAPM

Bossaerts, Peter; Kleiman, Daniel; Plott, Charles
Fonte: Edward Elgar Publicador: Edward Elgar
Tipo: Book Section; PeerReviewed Formato: application/pdf
Publicado em 19/04/1999 Português
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We report on experiments of simple, repeated asset markets in two risky securities and one risk-free security, set up to test the Capital Asset Pricing Model (CAPM), which embeds the two most essential principles of modern asset pricing theory, namely, (i) financial markets equilibrate, (ii) in equilibrium risk premia are solely determined by covariance with aggregate risk. Slow, but steady convergence towards the CAPM is discovered. The convergence process, however, halts before reaching the actual equilibrium. There is ample evidence that subjects gradually move up in mean-variance space, in accordance with the CAPM. Yet, adjustment stops as if the remaining trading time was insufficient to complete all the transactions that are needed to guarantee improvements in positions. We conjecture that this is due to subjects' hesitance in the face of market thinness. Because the convergence process halts, statistical tests reject the CAPM.

Three Essays on High-Frequency and High-Dimensional Financial Data Analysis

Li, Zhengzi
Fonte: Universidade Duke Publicador: Universidade Duke
Tipo: Dissertação
Publicado em //2013 Português
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In recent decades, financial market data has become available with increasingly higher frequency and higher dimension. This rapidly growing amount of financial data has created many research opportunities and challenges. In this dissertation, I address several important issues in the areas of asset pricing, financial econometrics, and computational statistics using large-scale financial data techniques. In terms of asset pricing (Chapter 2), I investigate the relationship between the cross-section of expected stock returns and the associated market risks. In terms of financial econometrics (Chapter 3), I uncover the sources of extreme dependence risks between assets. In terms of computational statistics (Chapter 4), I design novel algorithms for efficiently estimating large-scale covariance matrices.

In Chapter 2, using a large novel high-frequency dataset, I investigate how individual stock returns respond to two different market changes: continuous and discontinuous (jump) movements. I also explore whether the different systematic risks associated with those two distinct movements are priced in the cross-section of expected stock returns. I show that the cross-section of expected stock returns reflects a risk premium for the systematic discontinuous risk but not for the systematic continuous risk. An investment strategy that goes long stocks in the highest discontinuous beta decile and shorts stocks in the lowest discontinuous beta decile produces average excess returns of 17% per annum. I estimate the risk premium for the systematic discontinuous risk is approximately 3% per annum after controlling for the usual firm characteristic variables including size...

Cost of capital in Brazil: a methodological approach; Una propuesta metodológica para el cálculo del costo de capital en Brasil; Uma proposta metodológica para o cálculo do custo de capital no Brasil

Assaf Neto, Alexandre; Lima, Fabiano Guasti; Araújo, Adriana Maria Procópio de
Fonte: Universidade de São Paulo. Faculdade de Economia, Administração e Contabilidade Publicador: Universidade de São Paulo. Faculdade de Economia, Administração e Contabilidade
Tipo: info:eu-repo/semantics/article; info:eu-repo/semantics/publishedVersion; Artigo Avaliado pelos Pares Formato: application/pdf
Publicado em 01/03/2008 Português
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O Capital Asset Princig Model (CAPM) oferece conceitos válidos e aceitos na definição do risco dos ativos. Essa metodologia de cálculo é medida pela relação entre a covariância dos retornos de mercado e da companhia e a variância dos retornos da empresa. Por tratar-se de uma metodologia aplicada em mercados estáveis, as conclusões favoráveis ao CAPM precisam, no entanto, ser reavaliadas em mercados emergentes, como o brasileiro. São discutidos os principais indicadores financeiros do mercado brasileiro e justificada, por meio de fundamentos estatísticos, a inconsistência dos resultados. No estudo, mostrou-se a necessidade de apurar o custo de oportunidade dos investidores brasileiros utilizando o benchmark de uma economia mais estável. O objetivo neste trabalho é sugerir um modelo que utiliza padrões de benchmark, sendo descritos os diversos ajustes necessários ao cálculo do custo de oportunidade dos acionistas das companhias brasileiras. De forma original, o modelo sugerido do custo de capital incorpora, além do risco-país, a volatilidade do mercado acionário brasileiro, demonstrando, portanto, a compatibilidade no desenvolvimento de uma metodologia de cálculo do custo do capital no Brasil.; The Capital Asset Pricing Model (CAPM) offers valid and accepted concepts in the definition of the assets risks. This is measured by the relation between the market return covariance and the company return variance. The methodology applied for the CAPM model is based on stable markets...

Derivatives pricing in a Markov chain jump-diffusion setting.

Nathan, Shaoul
Fonte: London School of Economics and Political Science Thesis Publicador: London School of Economics and Political Science Thesis
Tipo: Thesis; NonPeerReviewed Formato: application/pdf
Publicado em //2005 Português
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In this work we develop a Markov Chain Jump-Diffusion (MCJD) model, where we have a financial market in which there are several possible states. Asset prices in the market follow a generalised geometric Brownian motion, with drift and volatility depending on the state of the market. So for example, one state may represent a bull market where drifts are high, whilst another state may represent a bear market where where drifts are low. The state the market is in is governed by a continuous time Markov chain. We add to this diffusion process jumps in the asset price which occur when the market changes state, and the jump sizes are dependent on the states the market is transiting to and transiting from. We also allow the market to transit to the same state, which corresponds to a jump in the asset price with no change to the drift or volatility. We will develop conditions of no arbitrage in such a market, and methods for pricing derivatives of assets whose prices follow MCJD processes. We will also consider Term-Structure models where the short rate (or forward rate) follows an MCJD process.