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## Deterministic criteria for the absence of arbitrage in one-dimensional diffusion models

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 11/05/2010
Português

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We obtain a deterministic characterisation of the \emph{no free lunch with
vanishing risk}, the \emph{no generalised arbitrage} and the \emph{no relative
arbitrage} conditions in the one-dimensional diffusion setting and examine how
these notions of no-arbitrage relate to each other.; Comment: 20 pages; most results in this paper were contained in the first
version of submission 0905.3701; to appear in Finance & Stochastics

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## Asymptotic arbitrage and num\'eraire portfolios in large financial markets

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 27/02/2007
Português

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This paper deals with the notion of a large financial market and the concepts
of asymptotic arbitrage and strong asymptotic arbitrage (both of the first
kind), introduced by Yu.M. Kabanov and D.O. Kramkov. We show that the arbitrage
properties of a large market are completely determined by the asymptotic
behavior of the sequence of the num\'eraire portfolios, related to the small
markets. The obtained criteria can be expressed in terms of contiguity, entire
separation and Hellinger integrals, provided these notions are extended to
sub-probability measures. As examples we consider market models on finite
probability spaces, semimartingale and diffusion models. Also a discrete-time
infinite horizon market model with one log-normal stock is examined.; Comment: 18 pages

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## Generalised arbitrage-free SVI volatility surfaces

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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In this article we propose a generalisation of the recent work of Gatheral
and Jacquier on explicit arbitrage-free parameterisations of implied volatility
surfaces. We also discuss extensively the notion of arbitrage freeness and
Roger Lee's moment formula using the recent analysis by Roper. We further
exhibit an arbitrage-free volatility surface different from Gatheral's SVI
parameterisation.; Comment: 20 pages, 4 figures. Section 2 more precise. Added a section on
non-smooth implied volatilities

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## Arbitrage Opportunities in Misspecified Stochastic volatility Models

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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#Quantitative Finance - Pricing of Securities#Quantitative Finance - General Finance#Quantitative Finance - Statistical Finance#91G20, 60J60

There is vast empirical evidence that given a set of assumptions on the
real-world dynamics of an asset, the European options on this asset are not
efficiently priced in options markets, giving rise to arbitrage opportunities.
We study these opportunities in a generic stochastic volatility model and
exhibit the strategies which maximize the arbitrage profit. In the case when
the misspecified dynamics is a classical Black-Scholes one, we give a new
interpretation of the classical butterfly and risk reversal contracts in terms
of their (near) optimality for arbitrage strategies. Our results are
illustrated by a numerical example including transaction costs.; Comment: Several typos in section 5 have been corrected in this new version
(with thanks to Amy Y. Zhou from MIT)

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## Derivative pricing with virtual arbitrage

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 03/02/1999
Português

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In this paper we derive an effective equation for derivative pricing which
accounts for the presence of virtual arbitrage opportunities and their
elimination by the market. We model the arbitrage return by a stochastic
process and find an equation for the average derivative price. This is an
integro-differential equation which, in the absence of the virtual arbitrage or
for an infinitely fast market reaction, reduces to the Black-Scholes equation.
Explicit formulas are obtained for European call and put vanilla options.; Comment: Latex, 10 pages

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## A note on arbitrage, approximate arbitrage and the fundamental theorem of asset pricing

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 27/11/2013
Português

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We provide a critical analysis of the proof of the fundamental theorem of
asset pricing given in the paper "Arbitrage and approximate arbitrage: the
fundamental theorem of asset pricing" by B. Wong and C.C. Heyde (Stochastics,
2010) in the context of incomplete It\^o-process models. We show that their
approach can only work in the known case of a complete financial market model
and give an explicit counterexample.; Comment: 10 pages

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## Credit Risk in a Geometric Arbitrage Perspective

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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Geometric Arbitrage Theory, where a generic market is modelled with a
principal fibre bundle and arbitrage corresponds to its curvature, is applied
to credit markets to model default risk and recovery, leading to closed form no
arbitrage characterizations for corporate bonds.; Comment: arXiv admin note: substantial text overlap with arXiv:0910.1671

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## Static versus Dynamic Arbitrage Bounds on Multivariate Option Prices

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 10/07/2004
Português

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We compare static arbitrage price bounds on basket calls, i.e. bounds that
only involve buy-and-hold trading strategies, with the price range obtained
within a multi-variate generalization of the Black-Scholes model. While there
is no gap between these two sets of prices in the univariate case, we observe
here that contrary to our intuition about model risk for at-the-money calls,
there is a somewhat large gap between model prices and static arbitrage prices,
hence a similarly large set of prices on which a multivariate Black-Scholes
model cannot be calibrated but where no conclusion can be drawn on the presence
or not of a static arbitrage opportunity.; Comment: Submitted to IMA series

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## Non-Arbitrage up to Random Horizon for Semimartingale Models

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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This paper addresses the question of how an arbitrage-free semimartingale
model is affected when stopped at a random horizon. We focus on
No-Unbounded-Profit-with-Bounded-Risk (called NUPBR hereafter) concept, which
is also known in the literature as the first kind of non-arbitrage. For this
non-arbitrage notion, we obtain two principal results. The first result lies in
describing the pairs of market model and random time for which the resulting
stopped model fulfills NUPBR condition. The second main result characterises
the random time models that preserve the NUPBR property after stopping for any
market model. These results are elaborated in a very general market model, and
we also pay attention to some particular and practical models. The analysis
that drives these results is based on new stochastic developments in
semimartingale theory with progressive enlargement. Furthermore, we construct
explicit martingale densities (deflators) for some classes of local martingales
when stopped at random time.; Comment: 40 pages. This version develops in details the ideas and the results
of the previous version and fixes a glitch in the quasi-left-continuous case

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## No-arbitrage conditions and absolutely continuous changes of measure

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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We study the stability of several no-arbitrage conditions with respect to
absolutely continuous, but not necessarily equivalent, changes of measure. We
first consider models based on continuous semimartingales and show that
no-arbitrage conditions weaker than NA and NFLVR are always stable. Then, in
the context of general semimartingale models, we show that an absolutely
continuous change of measure does never introduce arbitrages of the first kind
as long as the change of measure density process can reach zero only
continuously.; Comment: 14 pages. Arbitrage, Credit and Informational Risks (C. Hillairet, M.
Jeanblanc and Y. Jiao, eds.), Peking University Series in Mathematics, Vol.
6, World Scientific, 2014

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## Arbitrage-free prediction of the implied volatility smile

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 21/07/2014
Português

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This paper gives an arbitrage-free prediction for future prices of an
arbitrary co-terminal set of options with a given maturity, based on the
observed time series of these option prices. The statistical analysis of such a
multi-dimensional time series of option prices corresponding to $n$ strikes
(with $n$ large, e.g. $n\geq 40$) and the same maturity, is a difficult task
due to the fact that option prices at any moment in time satisfy non-linear and
non-explicit no-arbitrage restrictions. Hence any $n$-dimensional time series
model also has to satisfy these implicit restrictions at each time step, a
condition that is impossible to meet since the model innovations can take
arbitrary values. We solve this problem for any $n\in\NN$ in the context of
Foreign Exchange (FX) by first encoding the option prices at each time step in
terms of the parameters of the corresponding risk-neutral measure and then
performing the time series analysis in the parameter space. The option price
predictions are obtained from the predicted risk-neutral measure by effectively
integrating it against the corresponding option payoffs. The non-linear
transformation between option prices and the risk-neutral parameters applied
here is \textit{not} arbitrary: it is the standard mapping used by market
makers in the FX option markets (the SABR parameterisation) and is given
explicitly in closed form. Our method is not restricted to the FX asset class
nor does it depend on the type of parameterisation used. Statistical analysis
of FX market data illustrates that our arbitrage-free predictions outperform
the naive random walk forecasts...

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## Periodic Sequences of Arbitrage: A Tale of Four Currencies

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 26/12/2011
Português

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#Quantitative Finance - General Finance#Mathematics - Dynamical Systems#Quantitative Finance - Trading and Market Microstructure#91B26, 91B60

This paper investigates arbitrage chains involving four currencies and four
foreign exchange trader-arbitrageurs. In contrast with the three-currency case,
we find that arbitrage operations when four currencies are present may appear
periodic in nature, and not involve smooth convergence to a "balanced" ensemble
of exchange rates in which the law of one price holds. The goal of this article
is to understand some interesting features of sequences of arbitrage
operations, features which might well be relevant in other contexts in finance
and economics.; Comment: 35 pages, 48 bibliography references, submitted to Metroeconomica

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## An Hilbert space approach for a class of arbitrage free implied volatilities models

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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We present an Hilbert space formulation for a set of implied volatility
models introduced in \cite{BraceGoldys01} in which the authors studied
conditions for a family of European call options, varying the maturing time and
the strike price $T$ an $K$, to be arbitrage free. The arbitrage free
conditions give a system of stochastic PDEs for the evolution of the implied
volatility surface ${\hat\sigma}_t(T,K)$. We will focus on the family obtained
fixing a strike $K$ and varying $T$. In order to give conditions to prove an
existence-and-uniqueness result for the solution of the system it is here
expressed in terms of the square root of the forward implied volatility and
rewritten in an Hilbert space setting. The existence and the uniqueness for the
(arbitrage free) evolution of the forward implied volatility, and then of the
the implied volatility, among a class of models, are proved. Specific examples
are also given.; Comment: 21 pages

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## Black-Scholes equation from Gauge Theory of Arbitrage

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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#High Energy Physics - Theory#Condensed Matter - Statistical Mechanics#High Energy Physics - Lattice#Physics - Physics and Society#Quantitative Finance - Pricing of Securities

We apply Gauge Theory of Arbitrage (GTA) {hep-th/9710148} to derivative
pricing. We show how the standard results of Black-Scholes analysis appear from
GTA and derive correction to the Black-Scholes equation due to a virtual
arbitrage and speculators reaction on it. The model accounts for both violation
of the no-arbitrage constraint and non-Brownian price walks which resemble real
financial data. The correction is nonlocal and transform the differential
Black-Scholes equation to an integro-differential one.; Comment: Latex, 19 pages

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