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## Stochastic relaxational dynamics applied to finance: towards non-equilibrium option pricing theory

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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#Condensed Matter - Statistical Mechanics#Quantitative Finance - Computational Finance#Quantitative Finance - Pricing of Securities

Non-equilibrium phenomena occur not only in physical world, but also in
finance. In this work, stochastic relaxational dynamics (together with path
integrals) is applied to option pricing theory. A recently proposed model (by
Ilinski et al.) considers fluctuations around this equilibrium state by
introducing a relaxational dynamics with random noise for intermediate
deviations called ``virtual'' arbitrage returns. In this work, the model is
incorporated within a martingale pricing method for derivatives on securities
(e.g. stocks) in incomplete markets using a mapping to option pricing theory
with stochastic interest rates. Using a famous result by Merton and with some
help from the path integral method, exact pricing formulas for European call
and put options under the influence of virtual arbitrage returns (or
intermediate deviations from economic equilibrium) are derived where only the
final integration over initial arbitrage returns needs to be performed
numerically. This result is complemented by a discussion of the hedging
strategy associated to a derivative, which replicates the final payoff but
turns out to be not self-financing in the real world, but self-financing {\it
when summed over the derivative's remaining life time}. Numerical examples are
given which underline the fact that an additional positive risk premium (with
respect to the Black-Scholes values) is found reflecting extra hedging costs
due to intermediate deviations from economic equilibrium.; Comment: 21 pages...

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## An application of Malliavin Calculus to Finance

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 29/11/2001
Português

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In this article, we give a brief informal introduction to Malliavin Calculus
for newcomers. We apply these ideas to the simulation of Greeks in Finance.
First to European-type options where formulas can be computed explicitly and
therefore can serve as testing ground. Later we study the case of Asian options
where close formulas are not available. The Greeks are computed through Monte
Carlo simulation.; Comment: 12 pages, 3 figures, coference proceedins

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## The financial framework of the sustainability of health universal coverage in Italy. A quantitative financial model for the assessment of the italian stability and reform program of public health financing

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 26/07/2012
Português

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Italy and the Eurozone are heading in the year 2012 into a financial
depression of unprecedented magnitude, with a forthcoming multitude of often
contradictory public economic and financial stability emergency interventions
whose ultimate endogenous and exogenous effects on public and private health
spending and on the sustainability of universal coverage are difficult to
predict ex ante. The research question is to assess whether it is possible to
synthesise into a single and simple quantitative index such multitude of public
economic and financial stability interventions and assess their magnitude and
direction towards increasing or decreasing sustainability of publicly funded
health care and universal coverage. We have analyzed the Italian Economic and
Stability Reform Program 2011-2014 and we have proposed a quantitative
synthetic sustainability index {\sigma} based on simple partial and absolute
differential equations. The sustainability index {\sigma} highlights that in
case the growth of the GDP in the period 2011-2014 be insufficient - as is
already the case in the first semester of 2012 - all the assumptions on which
the Italian Economic and Stability Reform Program 2011-2014 rests will fall,
and Universal Coverage will become unsustainable. Health and Public Health
professionals should intervene immediately with Italian and Eurozone national
budgets planners and financial health regulators before unselective exogenously
induced health financing and provision shortages produce irreparable
epidemiological effects.; Comment: 28 pages

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## To the problem of turbulence in quantitative easing transmission channels and transactions network channels at quantitative easing policy implementation by central banks

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

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In agreement with the recent research findings in the econophysics, we
propose that the nonlinear dynamic chaos can be generated by the turbulent
capital flows in both the quantitative easing transmission channels and the
transaction networks channels, when there are the laminar turbulent capital
flows transitions in the financial system. We demonstrate that the capital
flows in both the quantitative easing transmission channels and the transaction
networks channels in the financial system can be accurately characterized by
the Reynolds numbers. We explain that the transition to the nonlinear dynamic
chaos regime can be realized through the cascade of the Landau, Hopf
bifurcations in the turbulent capital flows in both the quantitative easing
transmission channels and the transaction networks channels in the financial
system. We completed the computer modeling, using both the Nonlinear Dynamic
Stochastic General Equilibrium Theory (NDSGET) and the Hydrodynamics Theory
(HT), to accurately characterize the US economy in the conditions of the QE
policy implementation by the US Federal Reserve. We found that the ability of
the US financial system to adjust to the different levels of liquidity depends
on the nonlinearities appearance in the QE transmission channels...

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## Multifractal fluctuations in finance

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 21/02/2001
Português

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

We consider the structure functions S^(q)(T), i.e. the moments of order q of
the increments X(t+T)-X(t) of the Foreign Exchange rate X(t) which give clear
evidence of scaling (S^(q)(T)~T^z(q)). We demonstrate that the nonlinearity of
the observed scaling exponent z(q) is incompatible with monofractal additive
stochastic models usually introduced in finance: Brownian motion, Levy
processes and their truncated versions. This nonlinearity corresponds to
multifractal intermittency yielded by multiplicative processes. The
non-analycity of z(q) corresponds to universal multifractals, which are
furthermore able to produce ``hyperbolic'' pdf tails with an exponent q_D >2.
We argue that it is necessary to introduce stochastic evolution equations which
are compatible with this multifractal behaviour.; Comment: 4 pages, 2 figures

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## Why Quantitative Structuring?

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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#Quantitative Finance - General Finance#Quantitative Finance - Economics#Quantitative Finance - Statistical Finance

Wherever we look, we see numerous success stories of quality-designed
products. Wouldn't it be great if the quality of financial products became just
as apparent? This paper is a fast introduction to Quantitative Structuring -- a
technology of manufacturing quality financial products. More detailed
discussions are presented as a set of appendices. A short summary with
references provide further depth and also cover applications beyond product
design: from model risk to economics.; Comment: 10 pages

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## Some applications of first-passage ideas to finance

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 13/06/2013
Português

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

Many problems in finance are related to first passage times. Among all of
them, we chose three on which we contributed personally. Our first example
relates Kolmogorov-Smirnov like goodness-of-fit tests, modified in such a way
that tail events and core events contribute equally to the test (in the
standard Kolmogorov-Smirnov, the tails contribute very little to the measure of
goodness-of-fit). We show that this problem can be mapped onto that of a random
walk inside moving walls. The second example is the optimal time to sell an
asset (modelled as a random walk with drift) such that the sell time is as
close as possible to the time at which the asset reaches its maximum value. The
last example concerns optimal trading in the presence of transaction costs. In
this case, the optimal strategy is to wait until the predictor reaches (plus or
minus) a threshold value before buying or selling. The value of this threshold
is found by mapping the problem onto that of a random walk between two walls.; Comment: 30 pages. To appear in the special volume "First-Passage Phenomena
and Their Applications", Eds. R. Metzler, G. Oshanin, S. Redner. World
Scientific (2013)

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## Coupled continuous time random walks in finance

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 29/08/2006
Português

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

Continuous time random walks (CTRWs) are used in physics to model anomalous
diffusion, by incorporating a random waiting time between particle jumps. In
finance, the particle jumps are log-returns and the waiting times measure delay
between transactions. These two random variables (log-return and waiting time)
are typically not independent. For these coupled CTRW models, we can now
compute the limiting stochastic process (just like Brownian motion is the limit
of a simple random walk), even in the case of heavy tailed (power-law) price
jumps and/or waiting times. The probability density functions for this limit
process solve fractional partial differential equations. In some cases, these
equations can be explicitly solved to yield descriptions of long-term price
changes, based on a high-resolution model of individual trades that includes
the statistical dependence between waiting times and the subsequent
log-returns. In the heavy tailed case, this involves operator stable space-time
random vectors that generalize the familiar stable models. In this paper, we
will review the fundamental theory and present two applications with
tick-by-tick stock and futures data.; Comment: 7 pages, 2 figures. Paper presented at the Econophysics Colloquium...

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## Robust Quantitative Comparative Statics for a Multimarket Paradox

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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#Computer Science - Computer Science and Game Theory#Quantitative Finance - General Finance#91B66#J.4.1

We introduce a quantitative approach to comparative statics that allows to
bound the maximum effect of an exogenous parameter change on a system's
equilibrium. The motivation for this approach is a well known paradox in
multimarket Cournot competition, where a positive price shock on a monopoly
market may actually reduce the monopolist's profit. We use our approach to
quantify for the first time the worst case profit reduction for multimarket
oligopolies exposed to arbitrary positive price shocks. For markets with affine
price functions and firms with convex cost technologies, we show that the
relative profit loss of any firm is at most 25% no matter how many firms
compete in the oligopoly. We further investigate the impact of positive price
shocks on total profit of all firms as well as on social welfare. We find tight
bounds also for these measures showing that total profit and social welfare
decreases by at most 25% and 16.6%, respectively. Finally, we show that in our
model, mixed, correlated and coarse correlated equilibria are essentially
unique, thus, all our bounds apply to these game solutions as well.; Comment: 23 pages, 1 figure

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## Some applications and methods of large deviations in finance and insurance

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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#Mathematics - Probability#Quantitative Finance - Statistical Finance#60F10, 62P05, 65C05, 91B28, 91B30

In these notes, we present some methods and applications of large deviations
to finance and insurance. We begin with the classical ruin problem related to
the Cramer's theorem and give en extension to an insurance model with
investment in stock market. We then describe how large deviation approximation
and importance sampling are used in rare event simulation for option pricing.
We finally focus on large deviations methods in risk management for the
estimation of large portfolio losses in credit risk and portfolio performance
in market investment.

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## A New Kind of Finance

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 04/10/2012
Português

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Finance has benefited from the Wolfram's NKS approach but it can and will
benefit even more in the future, and the gains from the influence may actually
be concentrated among practitioners who unintentionally employ those principles
as a group.; Comment: 13 pages; Forthcoming in "Irreducibility and Computational
Equivalence: 10 Years After Wolfram's A New Kind of Science," Hector Zenil,
ed., Springer Verlag, 2013

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## The Quantitative Relations between Stock Prices and Quantities of Tradable Stock Shares and Its Applications

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 31/03/2005
Português

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This paper analyzes the quantitative relations between stock prices and
quantities of tradable stock shares in Chinese stock markets at six time points
by means of Exploratory Data Analysis (EDA) method. It is found the resulting
formulae have the same structure but different parameters. This paper also uses
these relationships in order to analyse the feasibility of policies for Chinese
Government to sell the state-owned shares in Chinese stock markets.; Comment: 13 pages,7 figures, 3 tables

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## Agent-based Versus Macroscopic Modeling of Competition and Business Processes in Economics and Finance

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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We present examples of agent-based and stochastic models of competition and
business processes in economics and finance. We start from as simple as
possible models, which have microscopic, agent-based, versions and macroscopic
treatment in behavior. Microscopic and macroscopic versions of herding model
proposed by Kirman and Bass diffusion of new products are considered in this
contribution as two basic ideas. Further we demonstrate that general herding
behavior can be considered as a background of nonlinear stochastic model of
financial fluctuations.; Comment: 20 pages, 8 figures

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## Efficient Markets, Behavioral Finance and a Statistical Evidence of the Validity of Technical Analysis

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 05/02/2013
Português

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This work tried to detect the existence of a relationship between the graphic
signals - or patterns - observed day by day in the Brazilian stock market and
the trends which happen after these signals, within a period of 8 years, for a
number of securities. The results obtained from this study show evidence of the
existence of such a relationship, suggesting the validity of the Technical
Analysis as an instrument to predict the trend of security prices in the
Brazilian stock market within that period.; Comment: 20 pages; Keywords: Efficient Markets, Behavioral Finance, Technical
Analysis

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## Quantitative easing is an incomplete strategy that must be accompanied by the nullification of debt

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

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Compound interest as well as inflation grows exponentially with time, whereas
other means to repay debt grow polynomially. For this and other, mostly
political, reasons, debt without inflation is unsustainable. We suggest a
discontinuous way to eliminate debt by nullifying it. This scenario is
preferable to current central bank strategies of quantitative easing because it
allows the disposal of debt without hyperinflation or bloated balance sheets.; Comment: 8 pages, some revisions

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## Applications of physics to economics and finance: Money, income, wealth, and the stock market

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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Several problems arising in Economics and Finance are analyzed using concepts
and quantitative methods from Physics. Here is the abridged abstact:
Chapter 1: By analogy with energy, the equilibrium probability distribution
of money must follow the exponential Boltzmann-Gibbs law characterized by an
effective temperature equal to the average amount of money per economic agent.
A thermal machine which extracts a monetary profit can be constructed between
two economic systems with different temperatures.
Chapter 2: Using data from several sources, it is found that the distribution
of income is described for the great majority of population by an exponential
distribution, whereas the high-end tail follows a power law. The Lorenz curve
and Gini coefficient were calculated and are shown to be in good agreement with
both income and wealth data sets.
Chapter 3: The Heston model where stock-price dynamics is governed by a
geometrical (multiplicative) Brownian motion with stochastic variance is
studied. The corresponding Fokker-Planck equation is solved exactly.
Integrating out the variance, an analytic formula for the time-dependent
probability distribution of stock price changes (returns) is found. The formula
is in excellent agreement with the Dow-Jones index for the time lags from 1 to
250 trading days.; Comment: 30 pages...

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## Quantitative relations between corruption and economic factors

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 01/05/2007
Português

Relevância na Pesquisa

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

We report quantitative relations between corruption level and economic
factors, such as country wealth and foreign investment per capita, which are
characterized by a power law spanning multiple scales of wealth and investments
per capita. These relations hold for diverse countries, and also remain stable
over different time periods. We also observe a negative correlation between
level of corruption and long-term economic growth. We find similar results for
two independent indices of corruption, suggesting that the relation between
corruption and wealth does not depend on the specific measure of corruption.
The functional relations we report have implications when assessing the
relative level of corruption for two countries with comparable wealth, and for
quantifying the impact of corruption on economic growth and foreign
investments.; Comment: 10 pages, 9 figures

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## Additive versus multiplicative parameters - applications in economics and finance

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 20/06/2013
Português

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In this paper, we pay our attention to geometric parameters and their
applications in economics and finance. We discuss the multiplicative models in
which a geometric mean and a geometric standard deviation are more natural than
arithmetic ones. We give two examples from Warsaw Stock Exchange in 1995--2009
and from a bid of 52-week treasury bills in 1992--2009 in Poland as an
illustrative example. For distributions having applications in finance and
insurance we give their multiplicative parameters as well as their estimations.
We consider, among others, heavy-tailed distributions such as lognormal and
Pareto distribution, applied to modelling of large losses.

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## Quantitative comparisons between finitary posterior distributions and Bayesian posterior distributions

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 08/07/2008
Português

Relevância na Pesquisa

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#Quantitative Finance - Statistical Finance#Mathematics - Probability#Mathematics - Statistics Theory#Statistics - Methodology#62C10, 62F15, 60G09

The main object of Bayesian statistical inference is the determination of
posterior distributions. Sometimes these laws are given for quantities devoid
of empirical value. This serious drawback vanishes when one confines oneself to
considering a finite horizon framework. However, assuming infinite
exchangeability gives rise to fairly tractable {\it a posteriori} quantities,
which is very attractive in applications. Hence, with a view to a
reconciliation between these two aspects of the Bayesian way of reasoning, in
this paper we provide quantitative comparisons between posterior distributions
of finitary parameters and posterior distributions of allied parameters
appearing in usual statistical models.

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## Bridging stylized facts in finance and data non-stationarities

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

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Employing a recent technique which allows the representation of nonstationary
data by means of a juxtaposition of locally stationary patches of different
length, we introduce a comprehensive analysis of the key observables in a
financial market: the trading volume and the price fluctuations. From the
segmentation procedure we are able to introduce a quantitative description of a
group of statistical features (stylizes facts) of the trading volume and price
fluctuations, namely the tails of each distribution, the U-shaped profile of
the volume in a trading session and the evolution of the trading volume
autocorrelation function. The segmentation of the trading volume series
provides evidence of slow evolution of the fluctuating parameters of each
patch, pointing to the mixing scenario. Assuming that long-term features are
the outcome of a statistical mixture of simple local forms, we test and compare
different probability density functions to provide the long-term distribution
of the trading volume, concluding that the log-normal gives the best agreement
with the empirical distribution. Moreover, the segmentation of the magnitude
price fluctuations are quite different from the results for the trading volume,
indicating that changes in the statistics of price fluctuations occur at a
faster scale than in the case of trading volume.; Comment: 13 pages...

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