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## Rare Disasters and Asset Markets in the Twentieth Century

Fonte: MIT Press
Publicador: MIT Press

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The potential for rare economic disasters explains a lot of asset-pricing puzzles. I calibrate disaster probabilities from the twentieth century global history, especially the sharp contractions associated with World War I, the Great Depression, and World War II. The puzzles that can be explained include the high equity premium, low risk-free rate, and volatile stock returns. Another mystery that may be resolved is why expected real interest rates were low in the United States during major wars, such as World War II. The model, an extension of work by Rietz, maintains the tractable framework of a representative agent, time-additive and isoelastic preferences, and complete markets. The results hold with i.i.d. shocks to productivity growth in a Lucas-tree type economy and also with the inclusion of capital formation.; Economics

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## Idiosyncratic volatility, aggregate volatility risk, and the cross-section of returns

Fonte: University of Rochester
Publicador: University of Rochester

Tipo: Tese de Doutorado
Formato: Number of Pages:ix, 145 leaves

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#Empirical asset pricing#New issues puzzle#Aggregate volatility#Anomolies#Value effect#Idiosyncratic volatility

Thesis (Ph. D.)--University of Rochester. William E. Simon Graduate School of Business Administration, 2008.; The first chapter presents a simple real options model that explains why in cross-section high idiosyncratic volatility implies low future returns and why the value effect is stronger for high volatility firms. In the model, high idiosyncratic volatility makes growth options a hedge against aggregate volatility risk. Growth options become less sensitive to the underlying asset value as idiosyncratic volatility goes up. It cuts their betas and saves them from losses in volatile times that are usually recessions. Growth options value also positively depends on volatility. It makes them a natural hedge against volatility increases. In empirical tests, the aggregate volatility risk factor explains the idiosyncratic volatility discount and why it is stronger for growth firms. The aggregate volatility risk factor also partly explains the stronger value effect for high volatility firms. I also find that high volatility and growth firms have much lower betas in recessions than in booms. In the second chapter I show that the aggregate volatility risk factor (the BVIX factor) explains the well-known underperformance of small growth firms. The BVIX factor also reduces the underperformance of IPOs and SEOs by 45% and makes it statistically insignificant. The BVIX factor is unrelated to the investment factor proposed by Lyandres...

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## Stochastic Volatility.

Fonte: Université de Montréal
Publicador: Université de Montréal

Tipo: Artigo de Revista Científica
Formato: 3941208 bytes; application/pdf

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#[JEL:C00] Mathematical and Quantitative Methods - General - General#[JEL:G10] Financial Economics - General Financial Markets - General#[JEL:G11] Financial Economics - General Financial Markets - Portfolio Choice#Investment Decisions#[JEL:G12] Financial Economics - General Financial Markets - Asset Pricing#Trading volume#Bond Interest Rates#[JEL:C00] Mathématiques et méthodes quantitatives - Généralités#[JEL:G10] Économie financière - Marchés financiers généraux - Généralités#[JEL:G11] Économie financière - Marchés financiers généraux - Choix de portefeuille#[JEL:G12] Économie financière - Marchés financiers généraux - Prix des actifs

This paper prepared for the Handbook of Statistics (Vol.14: Statistical Methods in Finance), surveys the subject of stochastic volatility. the following subjects are covered: volatility in financial markets (instantaneous volatility of asset returns, implied volatilities in option prices and related stylized facts), statistical modelling in discrete and continuous time and, finally, statistical inference (methods of moments, quasi-maximum likelihood, likelihood-based and bayesian methods and indirect inference).

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## VaR and expected shortfall: A non-normal regime switching framework

Fonte: IOP Publishing Ltd.
Publicador: IOP Publishing Ltd.

Tipo: Artigo de Revista Científica

Publicado em //2009
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We have developed a regime switching framework to compute the Value at Risk and Expected Shortfall measures. Although Value at Risk as a risk measure has been criticized by some researchers for lack of subadditivity, it is still a central tool in banking regulations and internal risk management in the finance industry. In contrast, Expected Shortfall is coherent and convex, so it is a better measure of risk than Value at Risk. Expected Shortfall is widely used in the insurance industry and has the potential to replace Value at Risk as a standard risk measure in the near future. We have proposed regime switching models to measure value at risk and expected shortfall for a single financial asset as well as financial portfolios. Our models capture the volatility clustering phenomenon and variance-independent variation in the higher moments by assuming the returns follow Student-t distributions.; Robert J. Elliott and Hong Miao

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## Asset Prices in a Time Series Model with Perpetually Disparately Informed, Competitive Traders

Fonte: Universidade de Indiana
Publicador: Universidade de Indiana

Tipo: Trabalho em Andamento
Formato: 296970 bytes; application/pdf

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This paper develops a dynamic asset pricing model with persistent heterogeneous beliefs. The model features competitive traders who receive idiosyncratic signals about an underlying fundamentals process. We adapt Futia’s (1981) frequency domain methods to derive conditions on the fundamentals that guarantee noninvertibility of the mapping between observed market data and the underlying shocks to agents’ information sets. When these conditions are satisfied, agents must ‘forecast the forecasts of others’. The paper provides an explicit analytical characterization of the resulting higher-order belief dynamics. These additional dynamics can explain apparent violations of variance bounds and rejections of cross-equation restrictions.

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## On the economic link between asset prices and real activity

Fonte: Universidade Carlos III de Madrid
Publicador: Universidade Carlos III de Madrid

Tipo: Trabalho em Andamento
Formato: application/pdf

Publicado em /05/2006
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This paper presents a model linking two financial markets (stocks and bonds) with the real business cycle, in the framework of the Consumption Capital Asset Pricing Model with Generalized Isoelastic Preferences. Besides interest rate term spread, the model includes a new variable to forecast economic activity: stock market term spread, which constitutes the slope of expected stock market returns. The empirical evidence documented in this paper suggests systematic relationships between the state of the business cycle and the shapes of two yield curves (interest rates and expected stock returns). Results are robust to changes in measures of economic growth, stock prices, interest rates and expectation-generating mechanisms.

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## On the economic link between asset prices and real activity

Fonte: Wiley-Blackwell
Publicador: Wiley-Blackwell

Tipo: info:eu-repo/semantics/publishedVersion; info:eu-repo/semantics/article
Formato: application/pdf

Publicado em /07/2007
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This paper presents a model linking two financial markets (stocks and bonds) with
real business cycle, in the framework of the Consumption Capital Asset Pricing Model with
Generalized Isoelastic Preferences. Besides interest rate term spread, the model includes a new
variable to forecast economic activity: stock market term spread. This is the slope of expected
stock market returns. The empirical evidence documented in this paper suggests systematic
relationships between business cycle’s state and the shapes of two yield curves (interest rates and
expected stock returns). Results are robust to changes in measures of economic growth, stock
prices, interest rates and expectations generating mechanisms.; The authors are from Universidad Carlos III de Madrid. Partial financial support was provided by DGICYT grants PB98-0030, BEC2002-0279 and SEC2003-06457. Seminar participants at various universities and conferences provided useful comments. The authors thank the anonymous referee who provided astute comments that considerably improved the study. The usual disclaimer applies. (Paper received March 2005, revised version accepted August 2006. Online publication December 2006)

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## New simulation schemes for the Heston model

Fonte: Université de Montréal
Publicador: Université de Montréal

Tipo: Thèse ou Mémoire numérique / Electronic Thesis or Dissertation

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#Volatilité stochastique#Stochastic volatility#Algorithmes de simulation#Simulation schemes#Tarification de produits dérivés#Asset pricing#MCMC#Algorithme de Metropolis-Hastings#Metropolis-Hastings algorithm#Modèle de Heston#Heston model

Les titres financiers sont souvent modélisés par des équations différentielles stochastiques (ÉDS). Ces équations peuvent décrire le comportement de l'actif, et aussi parfois certains paramètres du modèle. Par exemple, le modèle de Heston (1993), qui s'inscrit dans la catégorie des modèles à volatilité stochastique, décrit le comportement de l'actif et de la variance de ce dernier.
Le modèle de Heston est très intéressant puisqu'il admet des formules semi-analytiques pour certains produits dérivés, ainsi qu'un certain réalisme. Cependant, la plupart des algorithmes de simulation pour ce modèle font face à quelques problèmes lorsque la condition de Feller (1951) n'est pas respectée.
Dans ce mémoire, nous introduisons trois nouveaux algorithmes de simulation pour le modèle de Heston. Ces nouveaux algorithmes visent à accélérer le célèbre algorithme de Broadie et Kaya (2006); pour ce faire, nous utiliserons, entre autres, des méthodes de Monte Carlo par chaînes de Markov (MCMC) et des approximations.
Dans le premier algorithme, nous modifions la seconde étape de la méthode de Broadie et Kaya afin de l'accélérer. Alors, au lieu d'utiliser la méthode de Newton du second ordre et l'approche d'inversion...

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## Asset Prices and Exchange Rates

Fonte: MIT - Massachusetts Institute of Technology
Publicador: MIT - Massachusetts Institute of Technology

Tipo: Trabalho em Andamento
Formato: 712125 bytes; application/pdf

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This paper develops a simple two-country, two-good model, in which the real
exchange rate, stock and bond prices are jointly determined. The model predicts that
stock market prices are correlated internationally even though their dividend processes
are independent, providing a theoretical argument in favor of financial contagion. The
foreign exchange market serves as a propagation channel from one stock market to
the other. The model identifies interconnections between stock, bond and foreign
exchange markets and characterizes their joint dynamics as a three-factor model.
Contemporaneous responses of each market to changes in the factors are shown to
have unambiguous signs. These implications enjoy strong empirical support. Estimation
of various versions of the model reveals that most of the signs predicted by the model
indeed obtain in the data, and the point estimates are in line with the implications of our
theory. Furthermore...

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## Fractional G-White Noise Theory, Wavelet Decomposition for Fractional G-Brownian Motion, and Bid-Ask Pricing Application to Finance Under Uncertainty

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 18/06/2013
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#Quantitative Finance - Pricing of Securities#Mathematics - Probability#60E05, 60H40, 60K, 60G18, 60G22

G-framework is presented by Peng [41] for measure risk under uncertainty. In
this paper, we define fractional G-Brownian motion (fGBm). Fractional
G-Brownian motion is a centered G-Gaussian process with zero mean and
stationary increments in the sense of sub-linearity with Hurst index $H\in
(0,1)$. This process has stationary increments, self-similarity, and long rang
dependence properties in the sense of sub-linearity. These properties make the
fractional G-Brownian motion a suitable driven process in mathematical finance.
We construct wavelet decomposition of the fGBm by wavelet with compactly
support. We develop fractional G-white noise theory, define G-It\^o-Wick
stochastic integral, establish the fractional G-It\^o formula and the
fractional G-Clark-Ocone formula, and derive the G-Girsanov's Theorem. For
application the G-white noise theory, we consider the financial market modelled
by G-Wick-It\^o type of SDE driven by fGBm. The financial asset price modelled
by fGBm has volatility uncertainty, using G-Girsanov's Theorem and
G-Clark-Ocone Theorem, we derive that sublinear expectation of the discounted
European contingent claim is the bid-ask price of the claim.

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## Non-Equivalent Beliefs and Subjective Equilibrium Bubbles

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 21/06/2013
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This paper develops a dynamic equilibrium model where agents exhibit a strong
form of belief heterogeneity: they disagree about zero probability events. It
is shown that, somewhat surprisingly, equilibrium exists in this setting, and
that the disagreement about nullsets naturally leads to equilibrium asset
pricing bubbles. The bubbles are subjective in the sense that they are
perceived by some but not necessarily all agents. In contrast to existing
models, bubbles arise with no restrictions on trade beyond a standard solvency
constraint.; Comment: 30 pages

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## No-arbitrage pricing under cross-ownership

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 05/05/2010
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#Quantitative Finance - Pricing of Securities#Quantitative Finance - General Finance#91B24, 91B25, 91B52, 91G20, 91G40, 91G50

We generalize Merton's asset valuation approach to systems of multiple
financial firms where cross-ownership of equities and liabilities is present.
The liabilities, which may include debts and derivatives, can be of differing
seniority. We derive equations for the prices of equities and recovery claims
under no-arbitrage. An existence result and a uniqueness result are proven.
Examples and an algorithm for the simultaneous calculation of all no-arbitrage
prices are provided. A result on capital structure irrelevance for groups of
firms regarding externally held claims is discussed, as well as financial
leverage and systemic risk caused by cross-ownership.; Comment: Excerpts and ideas from this paper have been presented at the
Scientific Conference of the German Association for Actuarial and Financial
Mathematics (DGVFM), Bremen, April 30, 2010. Some methods and systems derived
from this work have been subject to a provisional (successful) patent filing

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## Error analysis in Fourier methods for option pricing

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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We provide a bound for the error committed when using a Fourier method to
price European options when the underlying follows an exponential \levy
dynamic. The price of the option is described by a partial integro-differential
equation (PIDE). Applying a Fourier transformation to the PIDE yields an
ordinary differential equation that can be solved analytically in terms of the
characteristic exponent of the \levy process. Then, a numerical inverse Fourier
transform allows us to obtain the option price. We present a novel bound for
the error and use this bound to set the parameters for the numerical method. We
analyse the properties of the bound for a dissipative and pure-jump example.
The bound presented is independent of the asymptotic behaviour of option prices
at extreme asset prices. The error bound can be decomposed into a product of
terms resulting from the dynamics and the option payoff, respectively. The
analysis is supplemented by numerical examples that demonstrate results
comparable to and superior to the existing literature.; Comment: 21 pages, 3 figures, 1 table

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## Robust pricing and hedging of double no-touch options

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 06/01/2009
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Double no-touch options, contracts which pay out a fixed amount provided an
underlying asset remains within a given interval, are commonly traded,
particularly in FX markets. In this work, we establish model-free bounds on the
price of these options based on the prices of more liquidly traded options
(call and digital call options). Key steps are the construction of super- and
sub-hedging strategies to establish the bounds, and the use of Skorokhod
embedding techniques to show the bounds are the best possible.
In addition to establishing rigorous bounds, we consider carefully what is
meant by arbitrage in settings where there is no {\it a priori} known
probability measure. We discuss two natural extensions of the notion of
arbitrage, weak arbitrage and weak free lunch with vanishing risk, which are
needed to establish equivalence between the lack of arbitrage and the existence
of a market model.; Comment: 32 pages, 5 figures

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## Moment Explosions and Long-Term Behavior of Affine Stochastic Volatility Models

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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We consider a class of asset pricing models, where the risk-neutral joint
process of log-price and its stochastic variance is an affine process in the
sense of Duffie, Filipovic and Schachermayer [2003]. First we obtain conditions
for the price process to be conservative and a martingale. Then we present some
results on the long-term behavior of the model, including an expression for the
invariant distribution of the stochastic variance process. We study moment
explosions of the price process, and provide explicit expressions for the time
at which a moment of given order becomes infinite. We discuss applications of
these results, in particular to the asymptotics of the implied volatility
smile, and conclude with some calculations for the Heston model, a model of
Bates and the Barndorff-Nielsen-Shephard model.; Comment: minor revision

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## Option Pricing and Hedging with Small Transaction Costs

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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#Quantitative Finance - Pricing of Securities#Mathematics - Optimization and Control#Mathematics - Probability#Quantitative Finance - Portfolio Management

An investor with constant absolute risk aversion trades a risky asset with
general It\^o-dynamics, in the presence of small proportional transaction
costs. In this setting, we formally derive a leading-order optimal trading
policy and the associated welfare, expressed in terms of the local dynamics of
the frictionless optimizer. By applying these results in the presence of a
random endowment, we obtain asymptotic formulas for utility indifference prices
and hedging strategies in the presence of small transaction costs.; Comment: 20 pages, to appear in "Mathematical Finance"

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## Consistent price systems and face-lifting pricing under transaction costs

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 31/03/2008
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#Quantitative Finance - Pricing of Securities#Mathematics - Probability#91B28 (Primary) 60G15, 60G44 (Secondary)

In markets with transaction costs, consistent price systems play the same
role as martingale measures in frictionless markets. We prove that if a
continuous price process has conditional full support, then it admits
consistent price systems for arbitrarily small transaction costs. This result
applies to a large class of Markovian and non-Markovian models, including
geometric fractional Brownian motion. Using the constructed price systems, we
show, under very general assumptions, the following ``face-lifting'' result:
the asymptotic superreplication price of a European contingent claim $g(S_T)$
equals $\hat{g}(S_0)$, where $\hat{g}$ is the concave envelope of $g$ and $S_t$
is the price of the asset at time $t$. This theorem generalizes similar results
obtained for diffusion processes to processes with conditional full support.; Comment: Published in at http://dx.doi.org/10.1214/07-AAP461 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org)

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## Hedging of claims with physical delivery under convex transaction costs

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 11/10/2008
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#Quantitative Finance - Pricing of Securities#Mathematics - Functional Analysis#Mathematics - Probability#26B25#49J53#60G42#46A20

We study superhedging of contingent claims with physical delivery in a
discrete-time market model with convex transaction costs. Our model extends
Kabanov's currency market model by allowing for nonlinear illiquidity effects.
We show that an appropriate generalization of Schachermayer's robust no
arbitrage condition implies that the set of claims hedgeable with zero cost is
closed in probability. Combined with classical techniques of convex analysis,
the closedness yields a dual characterization of premium processes that are
sufficient to superhedge a given claim process. We also extend the fundamental
theorem of asset pricing for general conical models.

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## Functionals of Exponential Brownian Motion and Divided Differences

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 10/06/2010
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#Mathematics - Numerical Analysis#Mathematics - Probability#Quantitative Finance - Computational Finance#Quantitative Finance - Pricing of Securities#41A10, 65D05, 60J65

We provide a surprising new application of classical approximation theory to
a fundamental asset-pricing model of mathematical finance. Specifically, we
calculate an analytic value for the correlation coefficient between exponential
Brownian motion and its time average, and we find the use of divided
differences greatly elucidates formulae, providing a path to several new
results. As applications, we find that this correlation coefficient is always
at least $1/\sqrt{2}$ and, via the Hermite--Genocchi integral relation,
demonstrate that all moments of the time average are certain divided
differences of the exponential function. We also prove that these moments agree
with the somewhat more complex formulae obtained by Oshanin and Yor.

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## Pricing the European call option in the model with stochastic volatility driven by Ornstein--Uhlenbeck process. Exact formulas

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 07/10/2015
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We consider the Black--Scholes model of financial market modified to capture
the stochastic nature of volatility observed at real financial markets. For
volatility driven by the Ornstein--Uhlenbeck process, we establish the
existence of equivalent martingale measure in the market model. The option is
priced with respect to the minimal martingale measure for the case of
uncorrelated processes of volatility and asset price, and an analytic
expression for the price of European call option is derived. We use the inverse
Fourier transform of a characteristic function and the Gaussian property of the
Ornstein--Uhlenbeck process.; Comment: Published at http://dx.doi.org/10.15559/15-VMSTA36CNF in the Modern
Stochastics: Theory and Applications (https://www.i-journals.org/vtxpp/VMSTA)
by VTeX (http://www.vtex.lt/)

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