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## Uncertainty and absence of arbitrage opportunity

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 22/07/2013
Português

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It is shown that absence of arbitrage opportunity in financial markets is a
particular case of existence of uncertainty in decision system. Absence of
arbitrage opportunity is considered in the sense of the Arrow-Debreu model of
financial market with a riskless asset, while uncertainty (or ambiguity) is
defined on the basis of the principle of internal coherence of M. Allais.; Comment: 16 pages

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## On optimal arbitrage

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 21/10/2010
Português

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#Quantitative Finance - Computational Finance#Mathematics - Probability#Quantitative Finance - Portfolio Management

In a Markovian model for a financial market, we characterize the best
arbitrage with respect to the market portfolio that can be achieved using
nonanticipative investment strategies, in terms of the smallest positive
solution to a parabolic partial differential inequality; this is determined
entirely on the basis of the covariance structure of the model. The solution is
intimately related to properties of strict local martingales and is used to
generate the investment strategy which realizes the best possible arbitrage.
Some extensions to non-Markovian situations are also presented.; Comment: Published in at http://dx.doi.org/10.1214/09-AAP642 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org)

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## An example of short-term relative arbitrage

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 08/10/2015
Português

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Long-term relative arbitrage exists in markets where the excess growth rate
of the market portfolio is bounded away from zero. Here it is shown that under
a time-homogeneity hypothesis this condition will also imply the existence of
relative arbitrage over arbitrarily short intervals.; Comment: 4 pages

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## Arbitrage and duality in nondominated discrete-time models

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

26.99%

#Quantitative Finance - General Finance#Mathematics - Optimization and Control#Mathematics - Probability

We consider a nondominated model of a discrete-time financial market where
stocks are traded dynamically, and options are available for static hedging. In
a general measure-theoretic setting, we show that absence of arbitrage in a
quasi-sure sense is equivalent to the existence of a suitable family of
martingale measures. In the arbitrage-free case, we show that optimal
superhedging strategies exist for general contingent claims, and that the
minimal superhedging price is given by the supremum over the martingale
measures. Moreover, we obtain a nondominated version of the Optional
Decomposition Theorem.; Comment: Published in at http://dx.doi.org/10.1214/14-AAP1011 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 strategy

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 13/02/2010
Português

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An arbitrage strategy allows a financial agent to make certain profit out of
nothing, i.e., out of zero initial investment. This has to be disallowed on
economic basis if the market is in equilibrium state, as opportunities for
riskless profit would result in an instantaneous movement of prices of certain
financial instruments. The principle of not allowing for arbitrage
opportunities in financial markets has far-reaching consequences, most notably
the option-pricing and hedging formulas in complete markets.; Comment: 2 pages; a version of this paper will appear in the Encyclopaedia of
Quantitative Finance, John Wiley and Sons Inc

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## Asymptotic Exponential Arbitrage and Utility-based Asymptotic Arbitrage in Markovian Models of Financial Markets

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 20/06/2014
Português

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Consider a discrete-time infinite horizon financial market model in which the
logarithm of the stock price is a time discretization of a stochastic
differential equation. Under conditions different from those given in a
previous paper of ours, we prove the existence of investment opportunities
producing an exponentially growing profit with probability tending to $1$
geometrically fast. This is achieved using ergodic results on Markov chains and
tools of large deviations theory.
Furthermore, we discuss asymptotic arbitrage in the expected utility sense
and its relationship to the first part of the paper.; Comment: Forthcoming in Acta Applicandae Mathematicae

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## Statistical Arbitrage in the Black-Scholes Framework

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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26.99%

In this study we prove the existence of statistical arbitrage opportunities
in the Black-Scholes framework by considering trading strategies that consists
of borrowing from the risk free rate and taking a long position in the stock
until it hits a deterministic barrier level. We derive analytical formulas for
the expected value, variance, and probability of loss for the discounted
cumulative trading profits. No-statistical arbitrage condition is derived for
the Black-Scholes framework, which imposes a constraint on the Sharpe ratio of
the stock. Furthermore, we verify our theoretical results via extensive Monte
Carlo simulations.

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## Triangular arbitrage as an interaction among foreign exchange rates

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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#Condensed Matter - Statistical Mechanics#Condensed Matter - Disordered Systems and Neural Networks#Quantitative Finance - Trading and Market Microstructure

We first show that there are in fact triangular arbitrage opportunities in
the spot foreign exchange markets, analyzing the time dependence of the
yen-dollar rate, the dollar-euro rate and the yen-euro rate. Next, we propose a
model of foreign exchange rates with an interaction. The model includes effects
of triangular arbitrage transactions as an interaction among three rates. The
model explains the actual data of the multiple foreign exchange rates well.; Comment: 19 pages, 21 eps files embedded. Physica A, to be published

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## A note on the spot-forward no-arbitrage relations in a trading-production model for commodities

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

26.99%

In commodity markets, the convergence of futures towards spot prices as the
time to maturity of the contracts goes to zero is usually justified by
no-arbitrage arguments. In this paper we propose an alternative approach, that
relies on the expected profit maximization problem of an agent producing and
storing a commodity while trading in the associated futures contracts. In this
framework, the relation between the spot and the futures prices holds through
the well-posedness of the maximization problem. We show that the futures price
can still be seen as the risk-neutral expectation of the spot price at maturity
and we propose an explicit formula for the forward volatility. Moreover, we
provide an heuristic analysis of the optimal solution for the production /
storage / trading problem, in a Markovian setting. This approach is
particularly interesting in the case of energy commodity: it remains suitable
for commodities characterized by storability constraints, when standard
no-arbitrage arguments can not be safely applied.

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## A Multi-factor Adaptive Statistical Arbitrage Model

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 09/05/2014
Português

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This paper examines the implementation of a statistical arbitrage trading
strategy based on co-integration relationships where we discover candidate
portfolios using multiple factors rather than just price data. The portfolio
selection methodologies include K-means clustering, graphical lasso and a
combination of the two. Our results show that clustering appears to yield
better candidate portfolios on average than naively using graphical lasso over
the entire equity pool. A hybrid approach of using the combination of graphical
lasso and clustering yields better results still. We also examine the effects
of an adaptive approach during the trading period, by re-computing potential
portfolios once to account for change in relationships with passage of time.
However, the adaptive approach does not produce better results than the one
without re-learning. Our results managed to pass the test for the presence of
statistical arbitrage test at a statistically significant level. Additionally
we were able to validate our findings over a separate dataset for formation and
trading periods.; Comment: 16 pages

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## Arbitrage-free exchange rate ensembles over a general trade network

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 05/06/2014
Português

Relevância na Pesquisa

26.99%

#Quantitative Finance - Economics#Computer Science - Social and Information Networks#Quantitative Finance - Trading and Market Microstructure#91

It is assumed that under suitable economic and information-theoretic
conditions, market exchange rates are free from arbitrage. Commodity markets in
which trades occur over a complete graph are shown to be trivial. We therefore
examine the vector space of no-arbitrage exchange rate ensembles over an
arbitrary connected undirected graph. Consideration is given for the minimal
information for determination of an exchange rate ensemble. We conclude with a
topical discussion of exchanges in which our analyses may be relevant,
including the emergent but highly-regulated (and therefore not a complete
graph) market for digital currencies.; Comment: 6 pages

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## Fractional term structure models: No-arbitrage and consistency

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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#Quantitative Finance - Pricing of Securities#Mathematics - Probability#60H30 (Primary) 91B70 (Secondary)

In this work we introduce Heath-Jarrow-Morton (HJM) interest rate models
driven by fractional Brownian motions. By using support arguments we prove that
the resulting model is arbitrage free under proportional transaction costs in
the same spirit of Guasoni [Math. Finance 16 (2006) 569-582]. In particular, we
obtain a drift condition which is similar in nature to the classical HJM
no-arbitrage drift restriction. The second part of this paper deals with
consistency problems related to the fractional HJM dynamics. We give a fairly
complete characterization of finite-dimensional invariant manifolds for HJM
models with fractional Brownian motion by means of Nagumo-type conditions. As
an application, we investigate consistency of Nelson-Siegel family with respect
to Ho-Lee and Hull-White models. It turns out that similar to the Brownian case
such a family does not go well with the fractional HJM dynamics with
deterministic volatility. In fact, there is no nontrivial fractional interest
rate model consistent with the Nelson-Siegel family.; Comment: Published in at http://dx.doi.org/10.1214/08-AAP586 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org)

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## Do arbitrage-free prices come from utility maximization?

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

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In this paper we ask whether, given a stock market and an illiquid
derivative, there exists arbitrage-free prices at which an utility-maximizing
agent would always want to buy the derivative, irrespectively of his own
initial endowment of derivatives and cash. We prove that this is false for any
given investor if one considers all initial endowments with finite utility, and
that it can instead be true if one restricts to the endowments in the interior.
We show however how the endowments on the boundary can give rise to very odd
phenomena; for example, an investor with such an endowment would choose not to
trade in the derivative even at prices arbitrarily close to some arbitrage
price.; Comment: this version: streamlined the paper, fixed typos, cut discussions
when introducing the model, deleted Section 9 and part of Section 8, changed
bib style

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## Asymptotic arbitrage in the Heston model

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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In the context of the Heston model, we establish a precise link between the
set of equivalent martingale measures, the ergodicity of the underlying
variance process and the concept of asymptotic arbitrage proposed in
Kabanov-Kramkov and in Follmer-Schachermayer.; Comment: 13 pages. New definition of partial asymptotic arbitrage introduced.
Main theorems revised

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## No arbitrage without semimartingales

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 12/06/2009
Português

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We show that with suitable restrictions on allowable trading strategies, one
has no arbitrage in settings where the traditional theory would admit arbitrage
possibilities. In particular, price processes that are not semimartingales are
possible in our setting, for example, fractional Brownian motion.; Comment: Published in at http://dx.doi.org/10.1214/08-AAP554 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org)

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## Trajectory Based Models, Arbitrage and Continuity

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

26.99%

The paper develops no arbitrage results for trajectory based models by
imposing general constraints on the trading portfolios. The main condition
imposed, in order to avoid arbitrage opportunities, is a local continuity
requirement on the final portfolio value considered as a functional on the
trajectory space. The paper shows this to be a natural requirement by proving
that a large class of practical trading strategies, defined by means of
trajectory based stopping times, give rise to locally continuous functionals.
The theory is illustrated, with some detail, for two specific trajectory models
of practical interest. The implications for stochastic models which are not
semimartingales are described. The present paper extends some of the results in
[1] by incorporating in the formalism a larger set of trading portfolios.

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## Arbitrage in Fractal Modulated Markets When the Volatility is Stochastic

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 22/01/2005
Português

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#Computer Science - Information Theory#Computer Science - Computational Engineering, Finance, and Science

In this paper an arbitrage strategy is constructed for the modified
Black-Scholes model driven by fractional Brownian motion or by a time changed
fractional Brownian motion, when the volatility is stochastic. This latter
property allows the heavy tailedness of the log returns of the stock prices to
be also accounted for in addition to the long range dependence introduced by
the fractional Brownian motion. Work has been done previously on this problem
for the case with constant `volatility' and without a time change; here these
results are extended to the case of stochastic volatility models when the
modulator is fractional Brownian motion or a time change of it. (Volatility in
fractional Black-Scholes models does not carry the same meaning as in the
classic Black-Scholes framework, which is made clear in the text.)
Since fractional Brownian motion is not a semi-martingale, the Black-Scholes
differential equation is not well-defined sense for arbitrary predictable
volatility processes. However, it is shown here that any almost surely
continuous and adapted process having zero quadratic variation can act as an
integrator over functions of the integrator and over the family of continuous
adapted semi-martingales. Moreover it is shown that the integral also has zero
quadratic variation...

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## No-arbitrage pricing under cross-ownership

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 05/05/2010
Português

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#Quantitative Finance - Pricing of Securities#Quantitative Finance - General Finance#91B24, 91B25, 91B52, 91G20, 91G40, 91G50

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

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## Arbitrage-Free Pricing Before and Beyond Probabilities

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 03/10/2013
Português

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"Fundamental theorem of asset pricing" roughly states that absence of
arbitrage opportunity in a market is equivalent to the existence of a
risk-neutral probability. We give a simple counterexample to this
oversimplified statement. Prices are given by linear forms which do not always
correspond to probabilities. We give examples of such cases. We also show that
arbitrage freedom is equivalent to the continuity of the pricing linear form in
the relevant topology. Finally we analyze the possible loss of martingality of
asset prices with lognormal stochastic volatility. For positive correlation
martingality is lost when the financial process is modelled through standard
probability theory. We show how to recover martingality using the appropriate
mathematical tools.; Comment: 5 pages

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## Arbitrage-Free Pricing of XVA -- Part I: Framework and Explicit Examples

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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We develop a novel framework for computing the total valuation adjustment
(XVA) of a European claim accounting for funding costs, counterparty credit
risk, and collateralization. Based on no-arbitrage arguments, we derive the
nonlinear backward stochastic differential equations (BSDEs) associated with
the replicating portfolios of long and short positions in the claim. This leads
to the definition of buyer's and seller's XVA which in turn identify a
no-arbitrage interval. When borrowing and lending rates coincide we provide a
fully explicit expression for the uniquely determined price of XVA, expressed
as a percentage of the price of the traded claim, and for the corresponding
replication strategies. This extends the result of Piterbarg by incorporating
the effect of premature contract termination due to default risk of the trader
and of his counterparty.; Comment: 34 pages, 7 figures

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