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Resultados filtrados por Publicador: Universidade Cornell

## A Harmonic Analysis Solution to the Static Basket Arbitrage Problem

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 02/09/2003
Português

Relevância na Pesquisa

26.74%

We consider the problem of computing upper and lower bounds on the price of a
European basket call option, given prices on other similar baskets. We focus
here on an interpretation of this program as a generalized moment problem.
Recent results by Berg & Maserick (1984), Putinar & Vasilescu (1999) and
Lasserre (2001) on harmonic analysis on semigroups, the K-moment problem and
its applications to optimization, allow us to derive tractable necessary and
sufficient conditions for the absence of static arbitrage between basket
straddles, hence between basket calls and puts.; Comment: Preliminary version for IMA workshop "Risk Management and Model
Specifications Issues in Finance". Numerical results to be added later

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## Market viability via absence of arbitrage of the first kind

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

26.74%

#Quantitative Finance - Pricing of Securities#Mathematics - Probability#Quantitative Finance - Computational Finance

In a semimartingale financial market model, it is shown that there is
equivalence between absence of arbitrage of the first kind (a weak viability
condition) and the existence of a strictly positive process that acts as a
local martingale deflator on nonnegative wealth processes.; Comment: 15 pages. Updated, more self-contained version

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## Flexible least squares for temporal data mining and statistical arbitrage

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 25/09/2007
Português

Relevância na Pesquisa

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A number of recent emerging applications call for studying data streams,
potentially infinite flows of information updated in real-time. When multiple
co-evolving data streams are observed, an important task is to determine how
these streams depend on each other, accounting for dynamic dependence patterns
without imposing any restrictive probabilistic law governing this dependence.
In this paper we argue that flexible least squares (FLS), a penalized version
of ordinary least squares that accommodates for time-varying regression
coefficients, can be deployed successfully in this context. Our motivating
application is statistical arbitrage, an investment strategy that exploits
patterns detected in financial data streams. We demonstrate that FLS is
algebraically equivalent to the well-known Kalman filter equations, and take
advantage of this equivalence to gain a better understanding of FLS and suggest
a more efficient algorithm. Promising experimental results obtained from a
FLS-based algorithmic trading system for the S&P 500 Futures Index are
reported.; Comment: 28 pages, 6 figures, submitted to journal

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## Arbitrage and deflators in illiquid markets

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

26.74%

#Quantitative Finance - Pricing of Securities#Mathematics - Functional Analysis#Mathematics - Probability

This paper presents a stochastic model for discrete-time trading in financial
markets where trading costs are given by convex cost functions and portfolios
are constrained by convex sets. The model does not assume the existence of a
cash account/numeraire. In addition to classical frictionless markets and
markets with transaction costs or bid-ask spreads, our framework covers markets
with nonlinear illiquidity effects for large instantaneous trades. In the
presence of nonlinearities, the classical notion of arbitrage turns out to have
two equally meaningful generalizations, a marginal and a scalable one. We study
their relations to state price deflators by analyzing two auxiliary market
models describing the local and global behavior of the cost functions and
constraints.

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## Optimization of relative arbitrage

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

26.74%

#Quantitative Finance - Portfolio Management#Mathematics - Optimization and Control#Mathematics - Statistics Theory

In stochastic portfolio theory, a relative arbitrage is an equity portfolio
which is guaranteed to outperform a benchmark portfolio over a finite horizon.
When the market is diverse and sufficiently volatile, and the benchmark is the
market or a buy-and-hold portfolio, functionally generated portfolios
introduced by Fernholz provide a systematic way of constructing relative
arbitrages. In this paper we show that if the market portfolio is replaced by
the equal or entropy weighted portfolio among many others, no relative
arbitrages can be constructed under the same conditions using functionally
generated portfolios. We also introduce and study a shaped-constrained
optimization problem for functionally generated portfolios in the spirit of
maximum likelihood estimation of a log-concave density.; Comment: 33 pages, 5 figures, 2 tables; revised version

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## Maximizing expected utility in the Arbitrage Pricing Model

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 31/08/2015
Português

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We treat an infinite dimensional optimization problem arising in economic
theory. Under appropriate conditions, we show the existence of an optimal
strategy for an investor trading in the classical Arbitrage Pricing Model of S.
A. Ross. As a consequence, we derive the existence of equivalent risk-neutral
measures of a particular form which have favourable integrability properties.

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## Intuitive Proof of Black-Scholes Formula Based on Arbitrage and Properties of Lognormal Distribution

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 03/12/2006
Português

Relevância na Pesquisa

26.74%

Presented is intuitive proof of Black-Scholes formula for European call
options, which is based on arbitrage and properties of lognormal distribution.
Paper can help students and non-mathematicians to better understand economic
concepts behind one of the biggest achievements in modern financial theory.; Comment: 7 pages

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## Information, no-arbitrage and completeness for asset price models with a change point

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

26.74%

We consider a general class of continuous asset price models where the drift
and the volatility functions, as well as the driving Brownian motions, change
at a random time $\tau$. Under minimal assumptions on the random time and on
the driving Brownian motions, we study the behavior of the model in all the
filtrations which naturally arise in this setting, establishing martingale
representation results and characterizing the validity of the NA1 and NFLVR
no-arbitrage conditions.; Comment: 21 pages

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## Dynamic modeling of mean-reverting spreads for statistical arbitrage

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

26.74%

#Quantitative Finance - Statistical Finance#Quantitative Finance - Portfolio Management#Statistics - Applications#Statistics - Methodology

Statistical arbitrage strategies, such as pairs trading and its
generalizations, rely on the construction of mean-reverting spreads enjoying a
certain degree of predictability. Gaussian linear state-space processes have
recently been proposed as a model for such spreads under the assumption that
the observed process is a noisy realization of some hidden states. Real-time
estimation of the unobserved spread process can reveal temporary market
inefficiencies which can then be exploited to generate excess returns. Building
on previous work, we embrace the state-space framework for modeling spread
processes and extend this methodology along three different directions. First,
we introduce time-dependency in the model parameters, which allows for quick
adaptation to changes in the data generating process. Second, we provide an
on-line estimation algorithm that can be constantly run in real-time. Being
computationally fast, the algorithm is particularly suitable for building
aggressive trading strategies based on high-frequency data and may be used as a
monitoring device for mean-reversion. Finally, our framework naturally provides
informative uncertainty measures of all the estimated parameters. Experimental
results based on Monte Carlo simulations and historical equity data are
discussed...

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## No-arbitrage of second kind in countable markets with proportional transaction costs

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

26.74%

#Quantitative Finance - Computational Finance#Mathematics - Probability#Quantitative Finance - Pricing of Securities

Motivated by applications to bond markets, we propose a multivariate
framework for discrete time financial markets with proportional transaction
costs and a countable infinite number of tradable assets. We show that the
no-arbitrage of second kind property (NA2 in short), recently introduced by
Rasonyi for finite-dimensional markets, allows us to provide a closure property
for the set of attainable claims in a very natural way, under a suitable
efficient friction condition. We also extend to this context the equivalence
between NA2 and the existence of many (strictly) consistent price systems.; Comment: Published in at http://dx.doi.org/10.1214/11-AAP825 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org)

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## Trend arbitrage, bid-ask spread and market dynamics

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 10/07/2006
Português

Relevância na Pesquisa

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#Physics - Data Analysis, Statistics and Probability#Physics - Physics and Society#Quantitative Finance - Statistical Finance

Microstructure of market dynamics is studied through analysis of tick price
data. Linear trend is introduced as a tool for such analysis. Trend arbitrage
inequality is developed and tested. The inequality sets limiting relationship
between trend, bid-ask spread, market reaction and average update frequency of
price information. Average time of market reaction is measured from market
data. This parameter is interpreted as a constant value of the stock exchange
and is attributed to the latency of exchange reaction to actions of traders.
This latency and cost of trade are shown to be the main limit of bid-ask
spread. Data analysis also suggests some relationships between trend, bid-ask
spread and average frequency of price update process.; Comment: 21 pages, 15 figures, 3 tables, submitted to "Quantitative Finance"

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## Pricing rule based on non-arbitrage arguments for random volatility and volatility smile

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 10/05/2002
Português

Relevância na Pesquisa

26.74%

#Mathematics - Probability#Mathematics - Optimization and Control#Quantitative Finance - Pricing of Securities

We consider a generic market model with a single stock and with random
volatility. We assume that there is a number of tradable options for that stock
with different strike prices. The paper states the problem of finding a pricing
rule that gives Black-Scholes price for at-money options and such that the
market is arbitrage free for any number of tradable options, even if there are
two Brownian motions only: one drives the stock price, the other drives the
volatility process. This problem is reduced to solving a parabolic equation.; Comment: 18 pages

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## On Arbitrage and Duality under Model Uncertainty and Portfolio Constraints

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

26.74%

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

We consider the fundamental theorem of asset pricing (FTAP) and hedging
prices of options under non-dominated model uncertainty and portfolio
constrains in discrete time. We first show that no arbitrage holds if and only
if there exists some family of probability measures such that any admissible
portfolio value process is a local super-martingale under these measures. We
also get the non-dominated optional decomposition with constraints. From this
decomposition, we get duality of the super-hedging prices of European options,
as well as the sub- and super-hedging prices of American options. Finally, we
get the FTAP and duality of super-hedging prices in a market where stocks are
traded dynamically and options are traded statically.; Comment: Final version. To appear in Mathematical Finance

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## Non-Arbitrage Under Additional Information for Thin Semimartingale Models

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 05/05/2015
Português

Relevância na Pesquisa

26.74%

This paper completes the two studies undertaken in
\cite{aksamit/choulli/deng/jeanblanc2} and
\cite{aksamit/choulli/deng/jeanblanc3}, where the authors quantify the impact
of a random time on the No-Unbounded-Risk-with-Bounded-Profit concept (called
NUPBR hereafter) when the stock price processes are quasi-left-continuous (do
not jump on predictable stopping times). Herein, we focus on the NUPBR for
semimartingales models that live on thin predictable sets only and the
progressive enlargement with a random time. For this flow of information, we
explain how far the NUPBR property is affected when one stops the model by an
arbitrary random time or when one incorporates fully an honest time into the
model. This also generalizes \cite{choulli/deng} to the case when the jump
times are not ordered in anyway. Furthermore, for the current context, we show
how to construct explicitly local martingale deflator under the bigger
filtration from those of the smaller filtration.; Comment: This paper develops the part of thin and single jump processes
mentioned in our earlier version: "Non-arbitrage up to random horizon and
after honest times for semimartingale models", Available at:
arXiv:1310.1142v1. arXiv admin note: text overlap with arXiv:1404.0410

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## Calibration and simulation of arbitrage effects in a non-equilibrium quantum Black-Scholes model by using semiclassical methods

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 16/12/2015
Português

Relevância na Pesquisa

26.74%

An interacting Black-Scholes model for option pricing, where the usual
constant interest rate r is replaced by a stochastic time dependent rate r(t)
of the form r(t)=r+f(t) dW/dt, accounting for market imperfections and prices
non-alignment, was developed in [1]. The white noise amplitude f(t), called
arbitrage bubble, generates a time dependent potential U(t) which changes the
usual equilibrium dynamics of the traditional Black-Scholes model. The purpose
of this article is to tackle the inverse problem, that is, is it possible to
extract the time dependent potential U(t) and its associated bubble shape f(t)
from the real empirical financial data? In order to give an answer to this
question, the interacting Black-Scholes equation must be interpreted as a
quantum Schrodinger equation with hamiltonian operator H=H0+U(t), where H0 is
the equilibrium Black-Scholes hamiltonian and U(t) is the interaction term. If
the U(t) term is small enough, the interaction potential can be thought as a
perturbation, so one can compute the solution of the interacting Black-Scholes
equation in an approximate form by perturbation theory. In [2] by applying the
semi-classical considerations, an approximate solution of the non equilibrium
Black-Scholes equation for an arbitrary bubble shape f(t) was developed. Using
this semi-classical solution and the knowledge about the mispricing of the
financial data...

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