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## Arbitrage-free Self-organizing Markets with GARCH Properties: Generating them in the Lab with a Lattice Model

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 11/12/2011
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We extend our studies of a quantum field model defined on a lattice having
the dilation group as a local gauge symmetry. The model is relevant in the
cross-disciplinary area of econophysics. A corresponding proposal by Ilinski
aimed at gauge modeling in non-equilibrium pricing is realized as a numerical
simulation of the one-asset version. The gauge field background enforces
minimal arbitrage, yet allows for statistical fluctuations. The new feature
added to the model is an updating prescription for the simulation that drives
the model market into a self-organized critical state. Taking advantage of some
flexibility of the updating prescription, stylized features and dynamical
behaviors of real-world markets are reproduced in some detail.; Comment: 19 pages, 11 figures compiled from 33 eps files

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## A Systematic Approach to Constructing Market Models With Arbitrage

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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This short note provides a systematic construction of market models without
unbounded profits but with arbitrage opportunities.; Comment: Very minor changes

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## Arbitrage of the first kind and filtration enlargements in semimartingale financial models

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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In a general semimartingale financial model, we study the stability of the No
Arbitrage of the First Kind (NA1) (or, equivalently, No Unbounded Profit with
Bounded Risk) condition under initial and under progressive filtration
enlargements. In both cases, we provide a simple and general condition which is
sufficient to ensure this stability for any fixed semimartingale model.
Furthermore, we give a characterisation of the NA1 stability for all
semimartingale models.; Comment: 27 pages

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## Discrete, Non Probabilistic Market Models. Arbitrage and Pricing Intervals

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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The paper develops general, discrete, non-probabilistic market models and
minmax price bounds leading to price intervals for European options. The
approach provides the trajectory based analogue of martingale-like properties
as well as a generalization that allows a limited notion of arbitrage in the
market while still providing coherent option prices. Several properties of the
price bounds are obtained, in particular a connection with risk neutral pricing
is established for trajectory markets associated to a continuous-time
martingale model.; Comment: Version 2, from June 12, 2015, supersedes the version of July 7 2014.
The changes are numerous and substantial. Version3, November 4, 2015, much
polished version, notation and notions consistent with sequel paper
(appearing as reference [12] in this version)

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## Diversity and Arbitrage in a Regulatory Breakup Model

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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In 1999 Robert Fernholz observed an inconsistency between the normative
assumption of existence of an equivalent martingale measure (EMM) and the
empirical reality of diversity in equity markets. We explore a method of
imposing diversity on market models by a type of antitrust regulation that is
compatible with EMMs. The regulatory procedure breaks up companies that become
too large, while holding the total number of companies constant by imposing a
simultaneous merge of other companies. The regulatory events are assumed to
have no impact on portfolio values. As an example, regulation is imposed on a
market model in which diversity is maintained via a log-pole in the drift of
the largest company. The result is the removal of arbitrage opportunities from
this market while maintaining the market's diversity.; Comment: 21 pages

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## Arbitrage and Hedging in model-independent markets with frictions

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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#Quantitative Finance - Mathematical Finance#60B05, 28B20, 60G42, 46A20, 28A05, 91B70, 91B24, 91G99, 60H99

We provide a Fundamental Theorem of Asset Pricing and a Superhedging Theorem
for a model independent discrete time financial market with proportional
transaction costs. We consider a probability-free version of the No Robust
Arbitrage condition introduced in Schachermayer ['04] and show that this is
equivalent to the existence of Consistent Price Systems. Moreover, we prove
that the superhedging price for a claim g coincides with the frictionless
superhedging price of g for a suitable process in the bid-ask spread.

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## Second-order Price Dynamics: Approach to Equilibrium with Perpetual Arbitrage

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 27/02/2012
Português

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The notion that economies should normally be in equilibrium is by now
well-established; equally well-established is that economies are almost never
precisely in equilibrium. Using a very general formulation, we show that under
dynamics that are second-order in time a price system can remain away from
equilibrium with permanent and repeating opportunities for arbitrage, even when
a damping term drives the system towards equilibrium. We also argue that
second-order dynamic equations emerge naturally when there are heterogeneous
economic actors, some behaving as active and knowledgeable arbitrageurs, and
others using heuristics. The essential mechanism is that active arbitrageurs
are able to repeatedly benefit from the suboptimal heuristics that govern most
economic behavior.

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## Optimal control of storage for arbitrage, with applications to energy systems

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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We study the optimal control of storage which is used for arbitrage, i.e. for
buying a commodity when it is cheap and selling it when it is expensive. Our
particular concern is with the management of energy systems, although the
results are generally applicable. We consider a model which may account for
nonlinear cost functions, market impact, input and output rate constraints and
inefficiencies or losses in the storage process. We develop an algorithm which
is maximally efficient in then sense that it incorporates the result that, at
each point in time, the optimal management decision depends only a finite, and
typically short, time horizon. We give examples related to the management of a
real-world system.; Comment: 7 pages, 6 figures

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## The fractional volatility model: No-arbitrage, leverage and completeness

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 13/05/2012
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Based on a criterion of mathematical simplicity and consistency with
empirical market data, a stochastic volatility model has been obtained with the
volatility process driven by fractional noise. Depending on whether the
stochasticity generators of log-price and volatility are independent or are the
same, two versions of the model are obtained with different leverage behavior.
Here, the no-arbitrage and completeness properties of the models are studied.; Comment: 13 pages Latex. arXiv admin note: substantial text overlap with
arXiv:1007.2817

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## Inflation securities valuation with macroeconomic-based no-arbitrage dynamics

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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We develop a model to price inflation and interest rates derivatives using
continuous-time dynamics that have some links with macroeconomic monetary DSGE
models equipped with a Taylor rule: in particular, the reaction function of the
central bank, the bond market liquidity, inflation and growth expectations play
an important role. The model can explain the effects of non-standard monetary
policies (like quantitative easing or its tapering) and shed light on how
central bank policy can affect the value of inflation and interest rates
derivatives.
The model is built under standard no-arbitrage assumptions. Interestingly,
the model yields short rate dynamics that are consistent with a time-varying
Hull-White model, therefore making the calibration to the nominal interest
curve and options straightforward. Further, we obtain closed forms for both
zero-coupon and year-on-year inflation swap and options. The calibration
strategy we propose is fully separable, which means that the calibration can be
carried out in subsequent simple steps that do not require heavy computation. A
market calibration example is provided.
The advantages of such structural inflation modelling become apparent when
one starts doing risk analysis on an inflation derivatives book: because the
model explicitly takes into account economic variables...

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## No arbitrage and local martingale deflators

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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A supermartingale deflator (resp., local martingale deflator)
multiplicatively transforms nonnegative wealth processes into supermartingales
(resp., local martingales). The supermartingale numeraire (resp., local
martingale numeraire) is the wealth processes whose reciprocal is a
supermartingale deflator (resp., local martingale deflator). It has been
established in previous literature that absence of arbitrage of the first kind
(NA1) is equivalent to existence of the supermartingale numeraire, and further
equivalent to existence of a strictly positive local martingale deflator;
however, under NA1, the local martingale numeraire may fail to exist. In this
work, we establish that, under NA1, any total-variation neighbourhood of the
original probability has an equivalent probability under which the local
martingale numeraire exists. This result, available previously only for single
risky-asset models, is in striking resemblance with the fact that any
total-variation neighbourhood of a separating measure contains an equivalent
$\sigma$-martingale measure. The presentation of our main result is relatively
self-contained, including a proof of existence of the supermartingale numeraire
under NA1. We further show that, if the Levy measures of the asset-price
process have finite support...

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## Model-independent no-arbitrage conditions on American put options

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 23/01/2013
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#Quantitative Finance - Pricing of Securities#Mathematics - Optimization and Control#Mathematics - Probability#91G20 (Primary) 60G40, 60G44 (Secondary)

We consider the pricing of American put options in a model-independent
setting: that is, we do not assume that asset prices behave according to a
given model, but aim to draw conclusions that hold in any model. We incorporate
market information by supposing that the prices of European options are known.
In this setting, we are able to provide conditions on the American Put prices
which are necessary for the absence of arbitrage. Moreover, if we further
assume that there are finitely many European and American options traded, then
we are able to show that these conditions are also sufficient. To show
sufficiency, we construct a model under which both American and European
options are correctly priced at all strikes simultaneously. In particular, we
need to carefully consider the optimal stopping strategy in the construction of
our process.; Comment: 32 pages, 3 figures

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## Comparisons for backward stochastic differential equations on Markov chains and related no-arbitrage conditions

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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#Quantitative Finance - Computational Finance#Mathematics - Probability#60H10 (Primary) 91B70 (Secondary)

Most previous contributions to BSDEs, and the related theories of nonlinear
expectation and dynamic risk measures, have been in the framework of continuous
time diffusions or jump diffusions. Using solutions of BSDEs on spaces related
to finite state, continuous time Markov chains, we develop a theory of
nonlinear expectations in the spirit of [Dynamically consistent nonlinear
evaluations and expectations (2005) Shandong Univ.]. We prove basic properties
of these expectations and show their applications to dynamic risk measures on
such spaces. In particular, we prove comparison theorems for scalar and vector
valued solutions to BSDEs, and discuss arbitrage and risk measures in the
scalar case.; Comment: Published in at http://dx.doi.org/10.1214/09-AAP619 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org)

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## Arbitrage free cointegrated models in gas and oil future markets

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 20/12/2007
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#Quantitative Finance - Statistical Finance#Mathematics - Probability#Quantitative Finance - Risk Management

In this article we present a continuous time model for natural gas and crude
oil future prices. Its main feature is the possibility to link both energies in
the long term and in the short term. For each energy, the future returns are
represented as the sum of volatility functions driven by motions. Under the
risk neutral probability, the motions of both energies are correlated Brownian
motions while under the historical probability, they are cointegrated by a
Vectorial Error Correction Model. Our approach is equivalent to defining the
market price of risk. This model is free of arbitrage: thus, it can be used for
risk management as well for option pricing issues. Calibration on European
market data and numerical simulations illustrate well its behavior.

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## Online Convex Optimization Against Adversaries with Memory and Application to Statistical Arbitrage

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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The framework of online learning with memory naturally captures learning
problems with temporal constraints, and was previously studied for the experts
setting. In this work we extend the notion of learning with memory to the
general Online Convex Optimization (OCO) framework, and present two algorithms
that attain low regret. The first algorithm applies to Lipschitz continuous
loss functions, obtaining optimal regret bounds for both convex and strongly
convex losses. The second algorithm attains the optimal regret bounds and
applies more broadly to convex losses without requiring Lipschitz continuity,
yet is more complicated to implement. We complement our theoretic results with
an application to statistical arbitrage in finance: we devise algorithms for
constructing mean-reverting portfolios.; Comment: 22 pages, 2 figures

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## Price discrimination and limits to arbitrage: An analysis of global LNG markets

Fonte: Elsevier
Publicador: Elsevier

Tipo: Article; accepted version

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This is the author accepted manuscript. The final version can be found published in Energy Economics and be found here: http://www.sciencedirect.com/science/article/pii/S0140988314001704#.; Gas prices around the world vary widely despite being connected by international trade of liquefied natural gas (LNG). Some industry observers argue that major exporters have acted irrationally by not arbitraging prices. This is also difficult to reconcile with a competitive model in which regional price differences exist solely because of transport costs. We show that a model which incorporates market power can rationalize observed prices and trade flows. We highlight how different features of the LNG market limit the ability and/or incentive of other players to engage in arbitrage, including constraints in LNG shipping. We also present some rough estimates of market power in short-term sales by Qatar (to Japan and the UK, respectively), and discuss the potential impact of US LNG exports.

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## Bayesian Estimation of Risk-Premia in an APT Context

Fonte: Universidade de Cambridge
Publicador: Universidade de Cambridge

Tipo: Trabalho em Andamento
Formato: 278908 bytes; application/pdf; application/pdf

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Recognizing the problems of estimation error in computing risk premia via arbitrage pricing, this paper provides a Bayesian methodology for estimating factor risk premia and hence equity risk premia for both traded and non-traded factors. Some illustrative calculations based on UK equity are also provided.

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## Improving the Estimates of the Risk Premia - Application in the UK Financial Market

Fonte: Universidade de Cambridge
Publicador: Universidade de Cambridge

Tipo: Trabalho em Andamento
Formato: 179383 bytes; application/pdf; application/pdf

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#Non-linear seemingly unrelated regression#Risk premium#Classification-JEL: G12, C13, C19#Arbitrage pricing theory

We develop a methodology for improving the estimate of the risk premia calculated jointly with the asset sensitivities, extending the McElroy-Burmeister approach for estimating the Arbitrage Pricing Theory (Ross 1976) as a restricted nonlinear multivariate regression model using observed macroeconomic risk factors. This allows us to use multiple samples of stocks to estimate and test common risk premia. This simpler expression for the variance-covariance matrix of the estimated parameter allows easier estimate and testing. With large number of stocks and a small number of observations, we use different samples of stocks to estimate vectors of risk premia which are then combined so that a final improved estimate of the risk premium vector is asymptotically unbiased and has minimum variance. We also derive the variance -covariance matrix of the final estimate of the risk premium. We apply the methodology to UK data, using FTSE-350 assets and observed macroeconomic risk factors.

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## Regulating financial conglomerates

Fonte: CFAP, Cambridge Judge Business School, University of Cambridge
Publicador: CFAP, Cambridge Judge Business School, University of Cambridge

Tipo: Working Paper; published version

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We investigate the optimal regulation of financial conglomerates which combine a bank and a non-bank financial institution. The conglomerate?s risk-taking incentives depend upon the level of market discipline it faces, which in turn is determined by the conglomerate?s liability structure. We examine optimal capital requirements for stand-alone institutions, for integrated financial conglomerates, and for financial conglomerates that are structured as holding companies. For a given risk profile, integrated conglomerates have a lower probability of failure than either their stand-alone or decentralized equivalent. However, when risk profiles are endogenously selected, conglomeration may extend the reach of the deposit insurance safety net and hence provide incentives for increased risk-taking. As a result, integrated conglomerates may optimally attract higher capital requirements. In contrast, decentralised conglomerates are able to hold assets in the socially most efficient place. Their optimal capital requirements encourage this. Hence, the practice of ?regulatory arbitrage?, or of transferring assets from one balance sheet to another, is welfare-increasing. We discuss the policy implications of our finding in the context not only of the present debate on the regulation of financial conglomerates but also in the light of existing US bank holding company regulation.

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## Arbitrage pricing theory as a restricted nonlinear multivariate regression model: Iterated nonlinear seemingly unrelated regression estimates

Fonte: Journal of Business & Economic Statistics
Publicador: Journal of Business & Economic Statistics

Tipo: Artigo de Revista Científica
Formato: 376508 bytes; application/pdf

Publicado em //1988
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#Asset pricing models#Capital Asset Pricing Model#expected asset returns#linear factor model#macroeconomic factors#nonlinear seemingly unrelated regression

By replacing the unknown random factors of factor analysis with observed macroeconomic variables, the arbitrage pricing theory (APT) is recast as a multivariate nonlinear regression model with across-equation restrictions. An explicit theoretical justification for the inclusion of an arbitrary, well-diversified market index is given. Using monthly returns on 70 stocks, iterated nonlinear seemingly unrelated regression techniques are employed to obtain joint estimates of asset sensitivities and their associated APT risk “prices.” Without the assumption of normally distributed errors, these estimators are strongly consistent and asymptotically normal. With the additional assumption of normal errors, they are also full-information maximum likelihood estimators. Classical asymptotic nonlinear nested hypothesis tests are supportive of the APT with measured macroeconomic factors.

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