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Intertemporal arbitrage, speculative balances, and the liquidity effect

Fortowsky, Elaine Barbara
Fonte: Universidade Rice Publicador: Universidade Rice
Português
Relevância na Pesquisa
27.32%
This thesis explores money manager intertemporal arbitrage as an explanation of the liquidity effect. We develop a theoretical model of optimal portfolio adjustment by professional money managers, and show that they engage in intertemporal asset price arbitrage; they reduce their holdings of financial assets when they expect asset prices to fall, and increase their holdings when they expect prices to rise. Since a reduction in financial assets can only be accomplished through an increase in money holdings, a connection exists between intertemporal price arbitrage and speculative balances. We show that in equilibrium, money manager behavior causes market liquidity shocks to be accompanied by a form of asset price overshooting in which asset prices first rise above their long-run value and then slowly return as speculative balances are lent out to borrowers and absorbed into transactions balances. Such asset price overshooting is precisely the liquidity effect, stated in terms of asset prices rather than interest rates. This shadows the result established by Hartley (1990), who showed that the combination of sector-specific liquidity shocks and trading rigidities across sectors will cause general price overshooting in those sectors closest to the money supply injection. The second part of this thesis attempts to identify an empirical relationship between speculative balances and asset prices as a means of verifying the hypothesis that money manager intertemporal price arbitrage generates the liquidity effect. It is not possible to estimate this relationship on an aggregate level because no means exist to identify speculative balances relative to the total money supply. However...

Nonparametric and arbitrage-free construction of call surfaces using l1-recovery

Blacque-Florentin, Pierre M.; Missaoui, Badr
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 23/06/2015 Português
Relevância na Pesquisa
27.32%
This paper is devoted to the application of an l1-minimisation technique to construct an arbitrage-free call-option surface. We propose a novel approach to obtaining model-free call option surfaces that are perfectly consistent with market quotes and free of static arbitrage. The approach is inspired from the compressed-sensing framework that is used in signal processing to deal with under-sampled signals. We address the problem of fitting the call-option surface to sparse option data. To illustrate the methodology, we first apply the methodology to a slice of the call-option surface of the S&P500 to recover a finer slice free of butterfly arbitrage and matching the market quotes. We then proceed to the construction of the whole call-price surface of the S&P500 options, taking into account the arbitrage possibilities in the time direction. The resulting object is a surface free of both butterfly and calendar-spread arbitrage that matches the original market points.; Comment: 16 pages, 9 figures

Characterization of arbitrage-free markets

Strasser, Eva
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 23/03/2005 Português
Relevância na Pesquisa
27.32%
The present paper deals with the characterization of no-arbitrage properties of a continuous semimartingale. The first main result, Theorem \refMainTheoremCharNA, extends the no-arbitrage criterion by Levental and Skorohod [Ann. Appl. Probab. 5 (1995) 906-925] from diffusion processes to arbitrary continuous semimartingales. The second main result, Theorem 2.4, is a characterization of a weaker notion of no-arbitrage in terms of the existence of supermartingale densities. The pertaining weaker notion of no-arbitrage is equivalent to the absence of immediate arbitrage opportunities, a concept introduced by Delbaen and Schachermayer [Ann. Appl. Probab. 5 (1995) 926-945]. Both results are stated in terms of conditions for any semimartingales starting at arbitrary stopping times \sigma. The necessity parts of both results are known for the stopping time \sigma=0 from Delbaen and Schachermayer [Ann. Appl. Probab. 5 (1995) 926-945]. The contribution of the present paper is the proofs of the corresponding sufficiency parts.; Comment: Published at http://dx.doi.org/10.1214/105051604000000558 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)

Double Exponential Instability of Triangular Arbitrage Systems

Cross, Rod; Kozyakin, Victor
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
27.32%
If financial markets displayed the informational efficiency postulated in the efficient markets hypothesis (EMH), arbitrage operations would be self-extinguishing. The present paper considers arbitrage sequences in foreign exchange (FX) markets, in which trading platforms and information are fragmented. In Kozyakin et al. (2010) and Cross et al. (2012) it was shown that sequences of triangular arbitrage operations in FX markets containing 4 currencies and trader-arbitrageurs tend to display periodicity or grow exponentially rather than being self-extinguishing. This paper extends the analysis to 5 or higher-order currency worlds. The key findings are that in a 5-currency world arbitrage sequences may also follow an exponential law as well as display periodicity, but that in higher-order currency worlds a double exponential law may additionally apply. There is an "inheritance of instability" in the higher-order currency worlds. Profitable arbitrage operations are thus endemic rather that displaying the self-extinguishing properties implied by the EMH.; Comment: 22 pages, 22 bibliography references, expanded Introduction and Conclusion, added bibliohraphy references

Universal Arbitrage Aggregator in Discrete Time Markets under Uncertainty

Burzoni, Matteo; Frittelli, Marco; Maggis, Marco
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
27.42%
In a model independent discrete time financial market, we discuss the richness of the family of martingale measures in relation to different notions of Arbitrage, generated by a class $\mathcal{S}$ of significant sets, which we call Arbitrage de la classe $\mathcal{S}$. The choice of $\mathcal{S}$ reflects into the intrinsic properties of the class of polar sets of martingale measures. In particular: for S=${\Omega}$ absence of Model Independent Arbitrage is equivalent to the existence of a martingale measure; for $\mathcal{S}$ being the open sets, absence of Open Arbitrage is equivalent to the existence of full support martingale measures. These results are obtained by adopting a technical filtration enlargement and by constructing a universal aggregator of all arbitrage opportunities. We further introduce the notion of market feasibility and provide its characterization via arbitrage conditions. We conclude providing a dual representation of Open Arbitrage in terms of weakly open sets of probability measures, which highlights the robust nature of this concept.

Volatility smile and stochastic arbitrage returns

Fedotov, Sergei; Panayides, Stephanos
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 27/05/2004 Português
Relevância na Pesquisa
27.32%
The purpose of this work is to explore the role that random arbitrage opportunities play in pricing financial derivatives. We use a non-equilibrium model to set up a stochastic portfolio, and for the random arbitrage return, we choose a stationary ergodic random process rapidly varying in time. We exploit the fact that option price and random arbitrage returns change on different time scales which allows us to develop an asymptotic pricing theory involving the central limit theorem for random processes. We restrict ourselves to finding pricing bands for options rather than exact prices. The resulting pricing bands are shown to be independent of the detailed statistical characteristics of the arbitrage return. We find that the volatility ``smile'' can also be explained in terms of random arbitrage opportunities.; Comment: 15 pages, 3 figures. The paper was accepted for publication in Physica A

Arbitrage theory without a num\'eraire

Tehranchi, Michael R.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
27.32%
This note develops an arbitrage theory for a discrete-time market model without the assumption of the existence of a num\'eraire asset. Fundamental theorems of asset pricing are stated and proven in this context. The distinction between the notions of investment-consumption arbitrage and pure-investment arbitrage provide a discrete-time analogue of the distinction between the notions of absolute arbitrage and relative arbitrage in the continuous-time theory. Applications to the modelling of bubbles is discussed.; Comment: 27 pages

Diversity and no arbitrage

Herczegh, Attila; Prokaj, Vilmos; Rásonyi, Miklós
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
27.32%
A stock market is called diverse if no stock can dominate the market in terms of relative capitalization. On one hand, this natural property leads to arbitrage in diffusion models under mild assumptions. On the other hand, it is also easy to construct diffusion models which are both diverse and free of arbitrage. Can one tell whether an observed diverse market admits arbitrage? In the present paper we argue that this may well be impossible by proving that the known examples of diverse markets in the literature (which do admit arbitrage) can be approximated uniformly (on the logarithmic scale) by models which are both diverse and arbitrage-free.; Comment: 14 pages, final version

Statistical Arbitrage Mining for Display Advertising

Zhang, Weinan; Wang, Jun
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 11/06/2015 Português
Relevância na Pesquisa
27.32%
We study and formulate arbitrage in display advertising. Real-Time Bidding (RTB) mimics stock spot exchanges and utilises computers to algorithmically buy display ads per impression via a real-time auction. Despite the new automation, the ad markets are still informationally inefficient due to the heavily fragmented marketplaces. Two display impressions with similar or identical effectiveness (e.g., measured by conversion or click-through rates for a targeted audience) may sell for quite different prices at different market segments or pricing schemes. In this paper, we propose a novel data mining paradigm called Statistical Arbitrage Mining (SAM) focusing on mining and exploiting price discrepancies between two pricing schemes. In essence, our SAMer is a meta-bidder that hedges advertisers' risk between CPA (cost per action)-based campaigns and CPM (cost per mille impressions)-based ad inventories; it statistically assesses the potential profit and cost for an incoming CPM bid request against a portfolio of CPA campaigns based on the estimated conversion rate, bid landscape and other statistics learned from historical data. In SAM, (i) functional optimisation is utilised to seek for optimal bidding to maximise the expected arbitrage net profit...

The Mirage of Triangular Arbitrage in the Spot Foreign Exchange Market

Fenn, Daniel J.; Howison, Sam D.; McDonald, Mark; Williams, Stacy; Johnson, Neil F.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 04/12/2008 Português
Relevância na Pesquisa
27.38%
We investigate triangular arbitrage within the spot foreign exchange market using high-frequency executable prices. We show that triangular arbitrage opportunities do exist, but that most have short durations and small magnitudes. We find intra-day variations in the number and length of arbitrage opportunities, with larger numbers of opportunities with shorter mean durations occurring during more liquid hours. We demonstrate further that the number of arbitrage opportunities has decreased in recent years, implying a corresponding increase in pricing efficiency. Using trading simulations, we show that a trader would need to beat other market participants to an unfeasibly large proportion of arbitrage prices to profit from triangular arbitrage over a prolonged period of time. Our results suggest that the foreign exchange market is internally self-consistent and provide a limited verification of market efficiency.

Transit Fare Arbitrage: Case Study of San Francisco Bay Area Rapid Transit (BART) System

Haque, Asif
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 30/01/2014 Português
Relevância na Pesquisa
27.32%
Transit fare arbitrage is the scenario when two or more commuters agree to swap tickets during travel in such a way that total cost is lower than otherwise. Such arbitrage allows pricing inefficiencies to be explored and exploited, leading to improved pricing models. In this paper we discuss the basics of fare arbitrage through an intuitive pricing framework involving population density. We then analyze the San Francisco Bay Area Rapid Transit (BART) system to understand underlying inefficiencies. We also provide source code and comprehensive list of pairs of trips with significant arbitrage gain at github.com/asifhaque/transit-arbitrage. Finally, we point towards a uniform payment interface for different kinds of transit systems.

Virtual Arbitrage Pricing Theory

Ilinski, Kirill
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 03/02/1999 Português
Relevância na Pesquisa
27.32%
We generalize the Arbitrage Pricing Theory (APT) to include the contribution of virtual arbitrage opportunities. We model the arbitrage return by a stochastic process. The latter is incorporated in the APT framework to calculate the correction to the APT due to the virtual arbitrage opportunities. The resulting relations reduce to the APT for an infinitely fast market reaction or in the case where the virtual arbitrage is absent. Corrections to the Capital Asset Pricing Model (CAPM) are also derived.; Comment: Latex, 12 pages

Simple arbitrage

Bender, Christian
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 19/10/2012 Português
Relevância na Pesquisa
27.38%
We characterize absence of arbitrage with simple trading strategies in a discounted market with a constant bond and several risky assets. We show that if there is a simple arbitrage, then there is a 0-admissible one or an obvious one, that is, a simple arbitrage which promises a minimal riskless gain of \epsilon, if the investor trades at all. For continuous stock models, we provide an equivalent condition for absence of 0-admissible simple arbitrage in terms of a property of the fine structure of the paths, which we call "two-way crossing." This property can be verified for many models by the law of the iterated logarithm. As an application we show that the mixed fractional Black-Scholes model, with Hurst parameter bigger than a half, is free of simple arbitrage on a compact time horizon. More generally, we discuss the absence of simple arbitrage for stochastic volatility models and local volatility models which are perturbed by an independent 1/2-H\"{o}lder continuous process.; Comment: Published in at http://dx.doi.org/10.1214/11-AAP830 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)

Stochastic arbitrage return and its implications for option pricing

Fedotov, Sergei; Panayides, Stephanos
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 30/03/2004 Português
Relevância na Pesquisa
27.32%
The purpose of this work is to explore the role that arbitrage opportunities play in pricing financial derivatives. We use a non-equilibrium model to set up a stochastic portfolio, and for the random arbitrage return, we choose a stationary ergodic random process rapidly varying in time. We exploit the fact that option price and random arbitrage returns change on different time scales which allows us to develop an asymptotic pricing theory involving the central limit theorem for random processes. We restrict ourselves to finding pricing bands for options rather than exact prices. The resulting pricing bands are shown to be independent of the detailed statistical characteristics of the arbitrage return. We find that the volatility "smile" can also be explained in terms of random arbitrage opportunities.; Comment: 14 pages, 3 fiqures

Critical transaction costs and 1-step asymptotic arbitrage in fractional binary markets

Cordero, Fernando; Perez-Ostafe, Lavinia
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 30/07/2014 Português
Relevância na Pesquisa
27.46%
We study the arbitrage opportunities in the presence of transaction costs in a sequence of binary markets approximating the fractional Black-Scholes model. This approximating sequence was constructed by Sottinen and named fractional binary markets. Since, in the frictionless case, these markets admit arbitrage, we aim to determine the size of the transaction costs needed to eliminate the arbitrage from these models. To gain more insight, we first consider only 1-step trading strategies and we prove that arbitrage opportunities appear when the transaction costs are of order $o(1/\sqrt{N})$. Next, we characterize the asymptotic behavior of the smallest transaction costs $\lambda_c^{(N)}$, called "critical" transaction costs, starting from which the arbitrage disappears. Since the fractional Black-Scholes model is arbitrage-free under arbitrarily small transaction costs, one could expect that $\lambda_c^{(N)}$ converges to zero. However, the true behavior of $\lambda_c^{(N)}$ is opposed to this intuition. More precisely, we show, with the help of a new family of trading strategies, that $\lambda_c^{(N)}$ converges to one. We explain this apparent contradiction and conclude that it is appropriate to see the fractional binary markets as a large financial market and to study its asymptotic arbitrage opportunities. Finally...

Gauge Invariance, Geometry and Arbitrage

Vazquez, Samuel E.; Farinelli, Simone
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 20/08/2009 Português
Relevância na Pesquisa
27.38%
In this work, we identify the most general measure of arbitrage for any market model governed by It\^o processes. We show that our arbitrage measure is invariant under changes of num\'{e}raire and equivalent probability. Moreover, such measure has a geometrical interpretation as a gauge connection. The connection has zero curvature if and only if there is no arbitrage. We prove an extension of the Martingale pricing theorem in the case of arbitrage. In our case, the present value of any traded asset is given by the expectation of future cash-flows discounted by a line integral of the gauge connection. We develop simple strategies to measure arbitrage using both simulated and real market data. We find that, within our limited data sample, the market is efficient at time horizons of one day or longer. However, we provide strong evidence for non-zero arbitrage in high frequency intraday data. Such events seem to have a decay time of the order of one minute.; Comment: 45 pages, 15 figures

Arbitrage Opportunities and their Implications to Derivative Hedging

Panayides, Stephanos
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
27.32%
We explore the role that random arbitrage opportunities play in hedging financial derivatives. We extend the asymptotic pricing theory presented by Fedotov and Panayides [Stochastic arbitrage return and its implication for option pricing, Physica A 345 (2005), 207-217] for the case of hedging a derivative when arbitrage opportunities are present in the market. We restrict ourselves to finding hedging confidence intervals that can be adapted to the amount of arbitrage risk an investor will permit to be exposed to. The resulting hedging bands are independent of the detailed statistical characteristics of the arbitrage opportunities.; Comment: 10 pages, 2 figures added references, corrected typos

Market models with optimal arbitrage

Chau, Huy N.; Tankov, Peter
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 17/12/2013 Português
Relevância na Pesquisa
27.49%
We construct and study market models admitting optimal arbitrage. We say that a model admits optimal arbitrage if it is possible, in a zero-interest rate setting, starting with an initial wealth of 1 and using only positive portfolios, to superreplicate a constant c>1. The optimal arbitrage strategy is the strategy for which this constant has the highest possible value. Our definition of optimal arbitrage is similar to the one in Fernholz and Karatzas (2010), where optimal relative arbitrage with respect to the market portfolio is studied. In this work we present a systematic method to construct market models where the optimal arbitrage strategy exists and is known explicitly. We then develop several new examples of market models with arbitrage, which are based on economic agents' views concerning the impossibility of certain events rather than ad hoc constructions. We also explore the concept of fragility of arbitrage introduced in Guasoni and Rasonyi (2012), and provide new examples of arbitrage models which are not fragile in this sense.

Geometric Arbitrage Theory and Market Dynamics

Farinelli, Simone
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
27.38%
We have embedded the classical theory of stochastic finance into a differential geometric framework called Geometric Arbitrage Theory and show that it is possible to: --Write arbitrage as curvature of a principal fibre bundle. --Parameterize arbitrage strategies by its holonomy. --Give the Fundamental Theorem of Asset Pricing a differential homotopic characterization. --Characterize Geometric Arbitrage Theory by five principles and show they they are consistent with the classical theory of stochastic finance. --Derive for a closed market the equilibrium solution for market portfolio and dynamics in the cases where: -->Arbitrage is allowed but minimized. -->Arbitrage is not allowed. --Prove that the no-free-lunch-with-vanishing-risk condition implies the zero curvature condition. The converse is in general not true and additionally requires the Novikov condition for the instantaneous Sharpe Ratio Dynamics to be satisfied.

The dynamics of financially constrained arbitrage

Gromb, Denis; Vayanos, Dimitri
Fonte: The London School of Economics and Political Science Systematic Risk Centre Publicador: The London School of Economics and Political Science Systematic Risk Centre
Tipo: Monograph; NonPeerReviewed Formato: application/pdf
Publicado em 25/02/2015 Português
Relevância na Pesquisa
27.32%
We develop a model of financially constrained arbitrage, and use it to study the dynamics of arbitrage capital, liquidity, and asset prices. Arbitrageurs exploit price discrepancies between assets traded in segmented markets, and in doing so provide liquidity to investors. A collateral constraint limits their positions as a function of capital. We show that the dynamics of arbitrage activity are self-correcting: following a shock that depletes arbitrage capital, profitability increases, and this allows capital to be gradually replenished. Spreads increase more and recover faster for more volatile trades, although arbitrageurs cut their positions in these trades the least. When arbitrage capital is more mobile across markets, liquidity in each market generally becomes less volatile, but the reverse may hold for aggregate liquidity because of mobility-induced contagion.