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

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

An application of Malliavin Calculus to Finance

Kohatsu-Higa, Arturo; Montero, Miquel
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

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

Olgiati, Stefano; Danovi, Alessandro
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 26/07/2012 Português
Relevância na Pesquisa
57.1707%
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

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

Ledenyov, Dimitri O.; Ledenyov, Viktor O.
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...

Multifractal fluctuations in finance

Schmitt, F.; Schertzer, D.; Lovejoy, S.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 21/02/2001 Português
Relevância na Pesquisa
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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

Why Quantitative Structuring?

Soklakov, Andrei N.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
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57.55866%
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

Some applications of first-passage ideas to finance

Chicheportiche, Rémy; Bouchaud, Jean-Philippe
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 13/06/2013 Português
Relevância na Pesquisa
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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)

Coupled continuous time random walks in finance

Meerschaert, Mark M.; Scalas, Enrico
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 29/08/2006 Português
Relevância na Pesquisa
57.030957%
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...

Robust Quantitative Comparative Statics for a Multimarket Paradox

Harks, Tobias; von Falkenhausen, Philipp
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
57.09918%
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

Some applications and methods of large deviations in finance and insurance

Pham, Huyen
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
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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.

A New Kind of Finance

Maymin, Philip Z.
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

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

Gou, Chengling
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 31/03/2005 Português
Relevância na Pesquisa
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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

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

Kononovicius, Aleksejus; Gontis, Vygintas; Daniunas, Valentas
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
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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

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

Penteado, Marco Antonio
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 05/02/2013 Português
Relevância na Pesquisa
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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

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

Svozil, Karl
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
57.09918%
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

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

Dragulescu, Adrian A.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
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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...

Quantitative relations between corruption and economic factors

Shao, Jia; Ivanov, Plamen Ch.; Podobnik, Boris; Stanley, H. Eugene
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 01/05/2007 Português
Relevância na Pesquisa
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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

Additive versus multiplicative parameters - applications in economics and finance

Jasiulewicz, Helena; Kordecki, Wojciech
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 20/06/2013 Português
Relevância na Pesquisa
57.100605%
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.

Quantitative comparisons between finitary posterior distributions and Bayesian posterior distributions

Bassetti, Federico
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 08/07/2008 Português
Relevância na Pesquisa
57.09918%
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.

Bridging stylized facts in finance and data non-stationarities

Camargo, Sabrina; Queiros, Silvio M. Duarte; Anteneodo, Celia
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
57.150024%
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...