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## Estudo de correlações não lineares entre variações do Índice da Bolsa de Valores de São Paulo (IBOVESPA) e variações de preço de ações; Nonlinear correlations among variations of São Paulo Exchange Index (IBOVESPA) and stock price variations

Pereira, José Rafael
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 30/08/2010 Português
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Estudos de correlação entre variações de preços de ações e variação de índices de mercado são importantes na compreensão da relação entre o retorno e o risco envolvido na alocação de recursos (investimentos). De acordo com o risco envolvido, deve haver um adequado retorno. Esta questão é abordada pelo modelo CAPM Capital Asset Pricing Model , que parte da premissa de que o risco sistemático de um ativo pode ser mensurado pela sua sensibilidade aos movimentos do mercado, e para isso se supõe que os retornos dos títulos são linearmente relacionados às flutuações de um índice de mercado amplo com um grau conhecido de sensibilidade. No entanto, pode haver relações não lineares entre os retornos dos títulos e as flutuações do índice de mercado. Sendo assim, o presente trabalho analisa uma medida de correlação global vinda da teoria da informação, que mensura qualquer tipo de relação entre duas variáveis, isto é, lineares e não lineares. O objetivo é mostrar a presença de correlações não lineares no mercado de capitais brasileiro. Demonstra-se que a correlação global é expressiva e maior ou igual à correlação linear em toda a amostra constituída de todas as ações que se mantiveram no Índice da Bolsa de Valores de São Paulo (IBOVESPA) de maio de 2001 a abril de 2008...

## A Common-Feature Approach for Testing Present-Value Restrictions with Financial Data

Hecq, Alain; Issler, João Victor
Fonte: Escola de Pós-Graduação em Economia da FGV Publicador: Escola de Pós-Graduação em Economia da FGV
Tipo: Relatório
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It is well known that cointegration between the level of two variables (labeled Yt and yt in this paper) is a necessary condition to assess the empirical validity of a present-value model (PV and PVM, respectively, hereafter) linking them. The work on cointegration has been so prevalent that it is often overlooked that another necessary condition for the PVM to hold is that the forecast error entailed by the model is orthogonal to the past. The basis of this result is the use of rational expectations in forecasting future values of variables in the PVM. If this condition fails, the present-value equation will not be valid, since it will contain an additional term capturing the (non-zero) conditional expected value of future error terms. Our article has a few novel contributions, but two stand out. First, in testing for PVMs, we advise to split the restrictions implied by PV relationships into orthogonality conditions (or reduced rank restrictions) before additional tests on the value of parameters. We show that PV relationships entail a weak-form common feature relationship as in Hecq, Palm, and Urbain (2006) and in Athanasopoulos, Guillén, Issler and Vahid (2011) and also a polynomial serial-correlation common feature relationship as in Cubadda and Hecq (2001)...

## 11.432J / 15.427J Real Estate Finance & Investments II: Macro-Level Analysis & Advanced Topics, Spring 2003; Real Estate Finance & Investments II: Macro-Level Analysis & Advanced Topics

Geltner, David, 1951-; Mcgrath, William Tod
Fonte: MIT - Massachusetts Institute of Technology Publicador: MIT - Massachusetts Institute of Technology
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The evolving organization and operation of real estate capital markets. Sources of real estate capital. Primary and secondary mortgage markets. The investment behavior of real estate assets. The development of REITs and securitized debt markets. Advanced pricing techniques for complex real estate securities. From the course home page: Course Description This course presents some of the major concepts, principles, analytical methods and tools useful for making investment and finance decisions regarding commercial real estate assets. As the second in a two-course sequence, this course focuses on more advanced topics and the "macro" level, which pertains to decisions about collections of many individual real estate assets, that is, portfolio or firm level decisions and investment management considerations. (More fundamental "micro" level analysis, pertaining to individual properties and deals, is covered in 11.431 taught in the fall semester). This course also introduces and surveys the major public capital market real estate vehicles, REITs and MBS. Other topics treated include a selection among such subjects as real options, land valuation, development project financial analysis, corporate real estate, capital structure, portfolio strategy...

## Valuation method for land pricing based on two cumulative distribution functions

Herrer??as-Velasco, Jos?? Manuel; Herrer??as-Pleguezuelo, Rafael
Fonte: Instituto Nacional de Investigaci??n y Tecnolog??a Agraria y Alimentaria (INIA) Publicador: Instituto Nacional de Investigaci??n y Tecnolog??a Agraria y Alimentaria (INIA)
Tipo: Artigo de Revista Científica
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This paper introduces the well-known valuation method based on two cumulative distribution functions (VMTCDF) that presents advantages with respect to other comparative techniques such as classical synthetic, which need a hypothesis of proportionality that is extremely simplifying and quite implausible, and econometric methods, which need databases contrary to VMTCDF that requires very little information. The VMTCDF use a single explicative variable, which summarizes in an index the different external signs that influence the market value of the asset to be assessed. The main aim of this paper is to extend the VMTCDF to find, under uncertainty, the market value of an asset from a two-dimensional vector of the characteristics of this asset. For this reason a new two-dimensional distribution is presented, Pyramidal distribution, which serves as a probabilistic model in the extended VMTCDF, and some of its statistical properties are studied. Finally, a practical application on land pricing illustrates the use of the extended VMTCDF as a tool for asset valuation. The main conclusion to be drawn from this paper is that it is the first step to extend the VMTCDF to the multidimensional case.; Este trabajo presenta el conocido m??todo de valoraci??n de las dos funciones de distribuci??n (VMTCDF) que presenta ventajas respecto a otras t??cnicas comparativas...

## Stochastic measures of financial markets efficiency and integration

Balbás, Alejandro; Muñoz-Bouzo, María José
Fonte: Universidade Carlos III de Madrid Publicador: Universidade Carlos III de Madrid
Tipo: Trabalho em Andamento Formato: application/pdf
Publicado em /12/1997 Português
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The notion of integration of different fmancial markets is often related to the absence of crossmarket arbitrage opportunities. Under the appropriated asswnptions and in absence of cross-market arbitrage opportunities, a riskneutral probability measure, shared by both markets, must exist. Some authors have considered this to provide some integration measures when the markets do not share any pricing rule, but always in static (or one period) asset pricing models. The purpose or this paper is to extend the refereed notions to a more general context. This is accomplished by introducing a methodology which may be applied in any intertemporal dynamic asset pricing model and without special asswnptions on the assets prices stochastic process. Then, the integration measures introduced here are stochastic processes testing different relative arbitrage profits and depending on the state of nature and on the date. The measures are introduced in a single fmancial market. When this market is not a global market from different ones, the measures simply test the degree of market efficiency. Transaction costs can be discounted in our model. Therefore, one can measure efficiency and integration in models with frictions. The main results are also interesting form a mathematical pint of view...

## Credit Pricing under Lévy Setting

CARIBONI Jessica; WIM Schoutens
Fonte: Centro Comum de Pesquisa da Comissão Européia Publicador: Centro Comum de Pesquisa da Comissão Européia
Tipo: Contributions to Conferences Formato: Printed
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The CreditGradesTM is a structural model extensively applied for estimating credit spreads. The model is built on the hypothesis that an event of default occurs when the asset value of a firm hits a barrier, which corresponds to the recovery value of the firm's debt. The asset value is described by a Geometric Brownian motion and the barrier is made stochastic to allow instantaneous defaults. It is verified that this model leads to higher short-term spreads than those produced without the barrier volatility. Moreover empirical evidence suggests that the underlying (log)normal distribution does not accurately describe the true behavior of the asset. We propose a new model, in line with the CreditGradesTM model, but under which we assume that the asset price process is described by an exponential of a (non-Brownian) Lévy process. In this way we take into account asymmetry and fat-tail behavior and, by including jumps in the process, we can produce instantaneous default with a deterministic barrier. Under the new model we show how to price a Credit Default Swap and work out the details in the case of a Variance Gamma Lévy process. The valuation is based on the solution of a Partial-Differential Integral Equation and the pricing of digital barrier option under the model considered.; JRC.G.9-Econometrics and statistical support to antifraud

## New Policies for Mandatory Defined Contribution Pensions : Industrial Organization Models and Investment Products

Impavido, Gregorio; Lasagabaster, Esperanza; Garcia-Huitron, Manuel
Fonte: World Bank Publicador: World Bank
Tipo: Publications & Research :: Publication; Publications & Research :: Publication
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The recent financial crisis is challenging the reform approach to mandated pension a scheme that has emerged over recent decades across the world. This reform approach is characterized by a move toward multi-pillar pension systems and includes the creation or extension of a mandatory funded pillar with defined contribution design. The rationale and viability of such a pillar is contingent on an enabling environment and the delivery of high risk-adjusted net rates of return that beat the natural benchmark, which is the internal rate of return that an unfunded mandated scheme is able to achieve. Two key aspects of mandated and funded defined contribution schemes have been under discussion and investigation since dedicated pension funds were created: (a) the high fees levied by privately organized pension funds and the consequence for the net rate of return; and (b) the investment products of these funds and their capability to address the investment risks and to deliver the expected retirement income in a life-cycle context. To this end...

## Moral hazard and nonlinear pricing in a general equilibrium model

Lisboa, Marcos de Barros
Fonte: Escola de Pós-Graduação em Economia da FGV Publicador: Escola de Pós-Graduação em Economia da FGV
Tipo: Relatório
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The paper analyzes a two period general equilibrium model with individual risk and moral hazard. Each household faces two individual states of nature in the second period. These states solely differ in the household's vector of initial endowments, which is strictly larger in the first state (good state) than in the second state (bad state). In the first period households choose a non-observable action. Higher leveis of action give higher probability of the good state of nature to occur, but lower leveIs of utility. Households have access to an insurance market that allows transfer of income across states of oature. I consider two models of financiaI markets, the price-taking behavior model and the nonlínear pricing modelo In the price-taking behavior model suppliers of insurance have a belief about each household's actíon and take asset prices as given. A variation of standard arguments shows the existence of a rational expectations equilibrium. For a generic set of economies every equilibrium is constraíned sub-optímal: there are commodity prices and a reallocation of financiaI assets satisfying the first period budget constraint such that, at each household's optimal choice given those prices and asset reallocation...

## Gestão activa versus gestão passiva: análise comparativa da performance dos exchange traded funds

Fonseca, Cláudia Sofia Gouveia
Fonte: Instituto Universitário de Lisboa Publicador: Instituto Universitário de Lisboa
Tipo: Dissertação de Mestrado
Publicado em //2012 Português
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Mestrado em Finanças; O estudo tem como objectivo analisar o comportamento dos Fundos de Investimento tradicionais face aos Exchange Traded Funds (ETF), instrumento recentemente introduzido no mercado e que tem vindo a assumir cada vez mais importância nas preferências dos investidores. Pretende-se verificar se a gestão activa, no caso dos fundos tradicionais, apresenta uma melhor performance face à gestão passiva, no caso dos ETF. A análise incide sobre o mercado Europeu e Americano e procura demonstrar qual das duas estratégias tem sido mais vantajosa para os investidores neste tipo de instrumento, para o período de 2005 a 2011. De forma a avaliar estes dois instrumentos foram utilizados os indicadores de performance tradicionais, tais como, Rendibilidade e Desvios-Padrão, Tracking Error, Índice de Treynor e de Índice de Sharpe, um Modelo de Factor Único baseado no Capital Asset Pricing (CAPM) e o Modelo do Três factores de Fama & French para avaliar as capacidades e qualidades dos gestores. Os resultados obtidos demonstraram que ambos os instrumentos não tiverem performances superiores ao benchmark. Os fundos tradicionais, no entanto, tiveram resultados mais favoráveis do que os ETF, apesar de não terem conseguido obter resultados significativos de rendibilidades em excesso. A análise com base no modelo de múltiplos factores veio comprovar que os resultados foram obtidos através de exposição a outros factores de risco...

## APT - evidencia emp??rica en el an??lisis del ROA en una empresa de servicios p??blicos domiciliarios de acueducto y alcantarillado

Cardona, Ra??l A.; Vel??squez, Ermilson; Vidal, Tatiana M.; Escobar, Ra??l A.
Fonte: Universidad EAFIT; Escuela de Econom??a y Finanzas Publicador: Universidad EAFIT; Escuela de Econom??a y Finanzas
Tipo: workingPaper; Documento de trabajo de investigaci??n; draf
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Con la metodolog??a APT desarrollada por ROSS, se evalu?? la Rentabilidad del Activo - ROA para una empresa de servicios p??blicos domiciliarios de acueducto y alcantarillado del departamento antioque??o. El sector de los servicios p??blicos domiciliarios de aguas es de naturaleza monop??lica y el m??todo de valoraci??n del costo de capital empleado para determinar las tarifas de las empresas que participan en ??ste, se encuentra regulado por un ??rgano del Estado colombiano. Este trabajo pretende evaluar una alternativa diferente o complementaria al m??todo CAPM empleado por el regulador, para encontrar el costo de capital que refleje las caracter??sticas de este mercado en Colombia. Para lograrlo, en este art??culo se incorpora el m??todo de componentes principales como medio de reducci??n de 19 variables observadas que se agrupan en diversas categor??as: macroecon??micas, financieras y t??cnico operativas de la empresa analizada. A partir de los datos se modelo el ROA, estableci??ndose de los resultados alcanzados que cinco componentes determinan la rentabilidad del activo de la empresa analizada, destac??ndose de ellas la cobertura geogr??fica y el rendimiento Operativo.; Using methodology developed by ROSS, the Return on Assets - ROA was assessed for a firm of public utilities for water and sewer department of Antioquia. The public utilities sector of water is monopolistic nature and the method of valuation of the cost of capital used to determine the rates of the companies involved in this...

## Valuation of capital protection options

Luo, Xiaolin; Shevchenko, Pavel V.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 04/08/2015 Português
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This paper presents numerical algorithm and results for pricing a capital protection option offered by many asset managers for investment portfolios to take advantage of market growth and protect savings. Under optimal withdrawal policyholder behaviour the pricing of such a product is an optimal stochastic control problem that cannot be solved using Monte Carlo method. In low dimension case, it can be solved using PDE based methods such as finite difference. In this paper, we develop a much more efficient Gauss-Hermite quadrature method with a one-dimensional cubic spline for calculation of the expectation between withdrawal/reset dates, and a bi-cubic spline interpolation for applying the jump conditions across withdrawal/reset dates. We show results for both static and dynamic withdrawals and for both the asset accumulation and the pension phases (different penalties for any excessive withdrawal) in the retirement investment cycle. To evaluate products with capital protection option, it is common industry practice to assume static withdrawals and use Monte Carlo method. As a result, the fair fee is underpriced if policyholder behaves optimally. We found that extra fee that has to be charged to counter the optimal policyholder behaviour is most significant at smaller interest rate and higher volatility levels...

## Dam Rain and Cumulative Gain

Brody, Dorje C.; Hughston, Lane P.; Macrina, Andrea
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 15/10/2007 Português
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We consider a financial contract that delivers a single cash flow given by the terminal value of a cumulative gains process. The problem of modelling and pricing such an asset and associated derivatives is important, for example, in the determination of optimal insurance claims reserve policies, and in the pricing of reinsurance contracts. In the insurance setting, the aggregate claims play the role of the cumulative gains, and the terminal cash flow represents the totality of the claims payable for the given accounting period. A similar example arises when we consider the accumulation of losses in a credit portfolio, and value a contract that pays an amount equal to the totality of the losses over a given time interval. An explicit expression for the value process is obtained. The price of an Arrow-Debreu security on the cumulative gains process is determined, and is used to obtain a closed-form expression for the price of a European-style option on the value of the asset. The results obtained make use of various remarkable properties of the gamma bridge process, and are applicable to a wide variety of financial products based on cumulative gains processes such as aggregate claims, credit portfolio losses, defined-benefit pension schemes...

## On the Solution of the Multi-asset Black-Scholes model: Correlations, Eigenvalues and Geometry

Contreras, Mauricio; Llanquihuén, Alejandro; Villena, Marcelo
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 09/10/2015 Português
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In this paper, we study the multi-asset Black-Scholes model in terms of the importance that the correlation parameter space (equivalent to an $N$ dimensional hypercube) has in the solution of the pricing problem. We show that inside of this hypercube there is a surface, called the Kummer surface $\Sigma_K$, where the determinant of the correlation matrix $\rho$ is zero, so the usual formula for the propagator of the $N$ asset Black-Scholes equation is no longer valid. Worse than that, in some regions outside this surface, the determinant of $\rho$ becomes negative, so the usual propagator becomes complex and divergent. Thus the option pricing model is not well defined for these regions outside $\Sigma_K$. On the Kummer surface instead, the rank of the $\rho$ matrix is a variable number. By using the Wei-Norman theorem, we compute the propagator over the variable rank surface $\Sigma_K$ for the general $N$ asset case. We also study in detail the three assets case and its implied geometry along the Kummer surface.

## Monte Carlo Methods and Path-Generation techniques for Pricing Multi-asset Path-dependent Options

Sabino, Piergiacomo
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 03/10/2007 Português
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We consider the problem of pricing path-dependent options on a basket of underlying assets using simulations. As an example we develop our studies using Asian options. Asian options are derivative contracts in which the underlying variable is the average price of given assets sampled over a period of time. Due to this structure, Asian options display a lower volatility and are therefore cheaper than their standard European counterparts. This paper is a survey of some recent enhancements to improve efficiency when pricing Asian options by Monte Carlo simulation in the Black-Scholes model. We analyze the dynamics with constant and time-dependent volatilities of the underlying asset returns. We present a comparison between the precision of the standard Monte Carlo method (MC) and the stratified Latin Hypercube Sampling (LHS). In particular, we discuss the use of low-discrepancy sequences, also known as Quasi-Monte Carlo method (QMC), and a randomized version of these sequences, known as Randomized Quasi Monte Carlo (RQMC). The latter has proven to be a useful variance reduction technique for both problems of up to 20 dimensions and for very high dimensions. Moreover, we present and test a new path generation approach based on a Kronecker product approximation (KPA) in the case of time-dependent volatilities. KPA proves to be a fast generation technique and reduces the computational cost of the simulation procedure.; Comment: 34 pages...

## Alpha Representation For Active Portfolio Management and High Frequency Trading In Seemingly Efficient Markets

Charles-Cadogan, Godfrey
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 12/06/2012 Português
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We introduce a trade strategy representation theorem for performance measurement and portable alpha in high frequency trading, by embedding a robust trading algorithm that describe portfolio manager market timing behavior, in a canonical multifactor asset pricing model. First, we present a spectral test for market timing based on behavioral transformation of the hedge factors design matrix. Second, we find that the typical trade strategy process is a local martingale with a background driving Brownian bridge that mimics portfolio manager price reversal strategies. Third, we show that equilibrium asset pricing models like the CAPM exists on a set with P-measure zero. So that excess returns, i.e. positive alpha, relative to a benchmark index is robust to no arbitrage pricing in turbulent capital markets. Fourth, the path properties of alpha are such that it is positive between suitably chosen stopping times for trading. Fifth, we demonstrate how, and why, econometric tests of portfolio performance tend to under report positive alpha.; Comment: 15 pages, 0 figures

## Nonparametric identification of positive eigenfunctions

Christensen, Timothy
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
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Important features of certain economic models may be revealed by studying positive eigenfunctions of appropriately chosen linear operators. Examples include long-run risk-return relationships in dynamic asset pricing models and components of marginal utility in external habit formation models. This paper provides identification conditions for positive eigenfunctions in nonparametric models. Identification is achieved if the operator satisfies two mild positivity conditions and a power compactness condition. Both existence and identification are achieved under a further non-degeneracy condition. The general results are applied to obtain new identification conditions for external habit formation models and for positive eigenfunctions of pricing operators in dynamic asset pricing models.

## Introduction into "Local Correlation Modelling"

Langnau, Alex
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
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In this paper we provide evidence that financial option markets for equity indices give rise to non-trivial dependency structures between its constituents. Thus, if the individual constituent distributions of an equity index are inferred from the single-stock option markets and combined via a Gaussian copula, for example, one fails to explain the steepness of the observed volatility skew of the index. Intuitively, index option prices are encoding higher correlations in cases where the option is particularly sensitive to stress scenarios of the market. As a result, more complex dependency structures emerge than the ones described by Gaussian copulas or (state-independent) linear correlation structures. In this paper we "decode" the index option market and extract this correlation information in order to extend the multi-asset version of Dupire's "local volatility" model by making correlations a dynamic variable of the market. A "local correlation" model (LCM) is introduced for the pricing of multi-asset derivatives. We show how consistency with the index volatility data can be achieved by construction. LCM achieves consistency with both the constituent- and index option markets by construction while preserving the efficiency and easy implementation of Dupire's model.; Comment: Keywords: implied correlation...

## How sensitive are equilibrium pricing models to real-world distortions?

Lamba, Harbir
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 30/09/2010 Português
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In both finance and economics, quantitative models are usually studied as isolated mathematical objects --- most often defined by very strong simplifying assumptions concerning rationality, efficiency and the existence of disequilibrium adjustment mechanisms. This raises the important question of how sensitive such models might be to real-world effects that violate the assumptions. We show how the consequences of rational behavior caused by perverse incentives, as well as various irrational tendencies identified by behavioral economists, can be systematically and consistently introduced into an agent-based model for a financial asset. This generates a class of models which, in the special case where such effects are absent, reduces to geometric Brownian motion --- the usual equilibrium pricing model. Thus we are able to numerically perturb a widely-used equilibrium pricing model market and investigate its stability. The magnitude of such perturbations in real markets can be estimated and the simulations imply that this is far outside the stability region of the equilibrium solution, which is no longer observed. Indeed the price fluctuations generated by endogenous dynamics, are in good general agreement with the excess kurtosis and heteroskedasticity of actual asset prices. The methodology is presented within the context of a financial market. However...

## Comportamento e estrutura a termo da volatilidade de empresas de grande e pequeno porte; Behavior and term structure of volatility for large and small companies

Rogers, Pablo; Securato, José Roberto; Ribeiro, Kárem Cristina de Sousa
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; ; ; ; ; ; Formato: application/pdf
Publicado em 01/01/2008 Português
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Em contraposição às hipóteses para sustentação dos modelos financeiros "clássicos", como o Capital Asset Pricing Model (CAPM) de Sharpe-Litner-Mossin, a literatura recente de Finanças tem documentado que algumas características das empresas se mostram relevantes para explicar retornos esperados. Este artigo tem por objetivo analisar se o tamanho da empresa no Brasil é uma característica importante para explicar uma outra dimensão da relação risco versus retorno: a volatilidade. Como metodologia, procedeu-se a uma reestruturação completa do índice IBrX da Bolsa de Valores de São Paulo (Bovespa), obtendo-se dois novos índices: um de empresas com grande porte e outro de empresas com pequeno porte. A partir dos índices construídos, analisaram-se o comportamento e a estrutura a termo da volatilidade, com ajustes dos modelos GARCH (1,1) e TARCH (1,1). Em linhas gerais, pode-se concluir que o comportamento e a estrutura a termo da volatilidade de empresas de grande e pequeno porte são diferentes, o que permite a incorporação da característica tamanho da empresa nas funções financeiras, tais como decisões de investimentos, precificação de títulos e gerenciamento de risco.; Recent finance literature states that certain company characteristics are relevant to explain the returns expected...

## Estimation of partial differential equations with applications in finance

Kristensen, Dennis
Fonte: Financial Markets Group, London School of Economics and Political Science Publicador: Financial Markets Group, London School of Economics and Political Science
Tipo: Monograph; NonPeerReviewed Formato: application/pdf
Publicado em /06/2004 Português
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Linear parabolic partial differential equations (PDE’s) and diffusion models are closely linked through the celebrated Feynman-Kac representation of solutions to PDE’s. In asset pricing theory, this leads to the representation of derivative prices as solutions to PDE’s. We give a number of examples of this, including the pricing of bonds and interest rate derivatives. Very often derivative prices are calculated given preliminary estimates of the diffusion model for the underlying variable. We demonstrate that the derivative prices are consistent and asymptotically normally distributed under general conditions. We apply this result to three leading cases of preliminary estimators: Nonparametric, semiparametric and fully parametric ones. In all three cases, the asymptotic distribution of the solution is derived. Our general results have other applications in asset pricing theory and in the estimation of diffusion models; these are also discussed.