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## Intertemporal arbitrage, speculative balances, and the liquidity effect

Fonte: Universidade Rice
Publicador: Universidade Rice

Português

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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...

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

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 23/06/2015
Português

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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

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## Characterization of arbitrage-free markets

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 23/03/2005
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#Mathematics - Probability#Quantitative Finance - Computational Finance#60H05,, 90A09 (Primary) . (Secondary)

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)

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## Double Exponential Instability of Triangular Arbitrage Systems

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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#Quantitative Finance - General Finance#Mathematics - Dynamical Systems#Mathematics - Rings and Algebras#Quantitative Finance - Trading and Market Microstructure#91B26, 91B54, 91B64, 15A60

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

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## Universal Arbitrage Aggregator in Discrete Time Markets under Uncertainty

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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#Quantitative Finance - Mathematical Finance#Mathematics - Probability#Primary 60G42, 91B24, 91G99, 60H99 Secondary 46A20, 46E27

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.

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## Volatility smile and stochastic arbitrage returns

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 27/05/2004
Português

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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

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## Arbitrage theory without a num\'eraire

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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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

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## Diversity and no arbitrage

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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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

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## Statistical Arbitrage Mining for Display Advertising

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 11/06/2015
Português

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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...

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## The Mirage of Triangular Arbitrage in the Spot Foreign Exchange Market

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 04/12/2008
Português

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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.

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

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 30/01/2014
Português

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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.

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## Virtual Arbitrage Pricing Theory

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 03/02/1999
Português

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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

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## Simple arbitrage

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 19/10/2012
Português

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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)

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## Stochastic arbitrage return and its implications for option pricing

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 30/03/2004
Português

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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

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

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 30/07/2014
Português

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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...

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## Gauge Invariance, Geometry and Arbitrage

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 20/08/2009
Português

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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

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## Arbitrage Opportunities and their Implications to Derivative Hedging

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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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

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## Market models with optimal arbitrage

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 17/12/2013
Português

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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.

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## Geometric Arbitrage Theory and Market Dynamics

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

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#Quantitative Finance - Computational Finance#Mathematics - Differential Geometry#Mathematics - Probability#Quantitative Finance - General Finance#91G80

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.

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## The dynamics of financially constrained arbitrage

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

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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.

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