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

Dupoyet, B.; Fiebig, H. R.; Musgrove, D. P.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 11/12/2011 Português
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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

A Systematic Approach to Constructing Market Models With Arbitrage

Ruf, Johannes; Runggaldier, Wolfgang
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
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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

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

Acciaio, Beatrice; Fontana, Claudio; Kardaras, Constantinos
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
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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

Discrete, Non Probabilistic Market Models. Arbitrage and Pricing Intervals

Ferrando, Sebastian E.; Gonzalez, Alfredo L.; Degano, Ivan L.; Rahsepar, Massoome
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
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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)

Diversity and Arbitrage in a Regulatory Breakup Model

Strong, Winslow; Fouque, Jean-Pierre
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
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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

Arbitrage and Hedging in model-independent markets with frictions

Burzoni, Matteo
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
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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.

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

Kemp-Benedict, Eric
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.

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

Cruise, James; Gibbens, Richard; Zachary, Stan
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

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

Mendes, R. Vilela; Oliveira, M. J.; Rodrigues, A. M.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 13/05/2012 Português
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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

Inflation securities valuation with macroeconomic-based no-arbitrage dynamics

Sarais, Gabriele; Brigo, Damiano
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...

No arbitrage and local martingale deflators

Kabanov, Yuri; Kardaras, Constantinos; Song, Shiqi
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...

Model-independent no-arbitrage conditions on American put options

Cox, Alexander M. G.; Hoeggerl, Christoph
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 23/01/2013 Português
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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

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

Cohen, Samuel N.; Elliott, Robert J.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
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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)

Arbitrage free cointegrated models in gas and oil future markets

Benmenzer, Grégory; Gobet, Emmanuel; Jérusalem, Céline
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 20/12/2007 Português
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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.

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

Anava, Oren; Hazan, Elad; Mannor, Shie
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

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

Ritz, Robert A.
Fonte: Elsevier Publicador: Elsevier
Tipo: Article; accepted version
Português
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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.

Bayesian Estimation of Risk-Premia in an APT Context

Darsinos, Theofanis; Satchell, Stephen E.
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.

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

Pitsillis, M.; Satchell, Stephen E.
Fonte: Universidade de Cambridge Publicador: Universidade de Cambridge
Tipo: Trabalho em Andamento Formato: 179383 bytes; application/pdf; application/pdf
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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.

Regulating financial conglomerates

Freixas, Xavier; L?r?nth, Gy?ngyi; Morrison, Alan D
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.

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

McElroy, Marjorie; Burmeister, Edwin
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 Português
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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.