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Uncertainty and absence of arbitrage opportunity

Ivanenko, Yaroslav; Pasichnichenko, Illya
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 22/07/2013 Português
Relevância na Pesquisa
26.99%
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

On optimal arbitrage

Fernholz, Daniel; Karatzas, Ioannis
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 21/10/2010 Português
Relevância na Pesquisa
26.99%
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)

An example of short-term relative arbitrage

Fernholz, Robert
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 08/10/2015 Português
Relevância na Pesquisa
26.99%
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

Arbitrage and duality in nondominated discrete-time models

Bouchard, Bruno; Nutz, Marcel
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
26.99%
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)

Arbitrage strategy

Kardaras, Constantinos
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 13/02/2010 Português
Relevância na Pesquisa
26.99%
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

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

Bidima, Martin Le Doux Mbele; Rásonyi, Miklós
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 20/06/2014 Português
Relevância na Pesquisa
26.99%
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

Statistical Arbitrage in the Black-Scholes Framework

Goncu, Ahmet
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
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.

Triangular arbitrage as an interaction among foreign exchange rates

Aiba, Yukihiro; Hatano, Naomichi; Takayasu, Hideki; Marumo, Kouhei; Shimizu, Tokiko
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
26.99%
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

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

Aïd, René; Campi, Luciano; Lautier, Delphine
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.

A Multi-factor Adaptive Statistical Arbitrage Model

Zhang, Wenbin; Dai, Zhen; Pan, Bindu; Djabirov, Milan
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 09/05/2014 Português
Relevância na Pesquisa
26.99%
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

Arbitrage-free exchange rate ensembles over a general trade network

Palasek, Stan
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 05/06/2014 Português
Relevância na Pesquisa
26.99%
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

Fractional term structure models: No-arbitrage and consistency

Ohashi, Alberto
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
26.99%
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)

Do arbitrage-free prices come from utility maximization?

Siorpaes, Pietro
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
26.99%
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

Asymptotic arbitrage in the Heston model

Haba, Fatma; Jacquier, Antoine
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
26.99%
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

No arbitrage without semimartingales

Jarrow, Robert A.; Protter, Philip; Sayit, Hasanjan
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 12/06/2009 Português
Relevância na Pesquisa
26.99%
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)

Trajectory Based Models, Arbitrage and Continuity

Alvarez, Alexander; Ferrando, Sebastian
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.

Arbitrage in Fractal Modulated Markets When the Volatility is Stochastic

Bayraktar, Erhan; Poor, H. Vincent
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 22/01/2005 Português
Relevância na Pesquisa
26.99%
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...

No-arbitrage pricing under cross-ownership

Fischer, Tom
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 05/05/2010 Português
Relevância na Pesquisa
26.99%
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

Arbitrage-Free Pricing Before and Beyond Probabilities

Paulot, Louis
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 03/10/2013 Português
Relevância na Pesquisa
26.99%
"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

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

Bichuch, Maxim; Capponi, Agostino; Sturm, Stephan
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
26.99%
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