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10
Market force, ecology, and evolution
, 2000
"... Markets have internal dynamics leading to excess volatility and other phenomena that are difficult to explain using rational expectations models. This paper studies these using a nonequilibrium price formation rule, developed in the context of trading with market orders. Because this is so much simp ..."
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Cited by 55 (8 self)
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Markets have internal dynamics leading to excess volatility and other phenomena that are difficult to explain using rational expectations models. This paper studies these using a nonequilibrium price formation rule, developed in the context of trading with market orders. Because this is so much simpler than a standard intertemporal equilibrium model, it is possible to study multiperiod markets analytically. There price dynamics have second order oscillatory terms. Value investing does not necessarily cause prices to track values. Trend following causes short term trends in prices, but also causes longerterm oscillations. When value investing and trend following are combined, even though there is little linear structure, there can be boombust cycles, excess and temporally correlated volatility, and fat tails in price fluctuations. The long term evolution of markets can be studied in terms of flows of money. Profits can be decomposed in terms of aggregate pairwise correlations. Under reinvestment of profits this leads to a capital allocation model that is equivalent to a standard model in population
Discrete random walk models for symmetric LévyFeller diffusion processes
, 1999
"... We propose a variety of models of random walk, discrete in space and time, suitable for simulating stable random variables of arbitrary index α (0 < α ≤ 2), in the symmetric case. We show that by properly scaled transition to vanishing space and time steps our random walk models converge to the c ..."
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Cited by 15 (6 self)
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We propose a variety of models of random walk, discrete in space and time, suitable for simulating stable random variables of arbitrary index α (0 < α ≤ 2), in the symmetric case. We show that by properly scaled transition to vanishing space and time steps our random walk models converge to the corresponding continuous Markovian stochastic processes, that we refer to as LévyFeller diffusion processes.
Fractional generalized random fields on bounded domains, Stochastic Anal
 Appl
"... Using the theory of generalized random fields on fractional Sobolev spaces on bounded domains, and the concept of dual generalized random field, this paper introduces a class of random fields with fractionalorder pure point spectra. The covariance factorization of an ageneralized random field havi ..."
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Cited by 5 (2 self)
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Using the theory of generalized random fields on fractional Sobolev spaces on bounded domains, and the concept of dual generalized random field, this paper introduces a class of random fields with fractionalorder pure point spectra. The covariance factorization of an ageneralized random field having a dual is established, leading to a whitenoise linearfilter representation, which reduces to the usual Markov representation in the ordinary case when a [ N and the covariance operator of the dual random field is local. Fractionalorder differential models commonly arising from anomalous diffusion in disordered media can be studied within this framework.
A twofactor asset pricing model and the fat tail distribution of firm sizes”, SSRN eLibrary
, 2007
"... Abstract We derive a theoretical twofactor model which has empirically a similar explanatory power as the FamaFrench threefactor model. In addition to the usual market risk, our model accounts for a diversification risk, proxied by the equallyweighted portfolio, and which results from an " ..."
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Cited by 2 (0 self)
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Abstract We derive a theoretical twofactor model which has empirically a similar explanatory power as the FamaFrench threefactor model. In addition to the usual market risk, our model accounts for a diversification risk, proxied by the equallyweighted portfolio, and which results from an "internal consistency factor" appearing for arbitrary large economies, as a consequence of the concentration of the market portfolio when the distribution of the capitalization of firms is sufficiently heavytailed as in real economies. Our model rationalizes the superior performance of the Fama and French threefactor model in explaining the cross section of stock returns: the size factor constitutes an alternative proxy of the diversification factor while the booktomarket effect is related to the increasing sensitivity of value stocks to this factor. JEL classification: G11, G12
On pricing of interest rate derivatives
, 2004
"... At present, there is an explosion of practical interest in the pricing of interest rate (IR) derivatives. Textbook pricing methods do not take into account the leptokurticity of the underlying IR process. In this paper, such a leptokurtic behaviour is illustrated using LIBOR data, and a possible mar ..."
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At present, there is an explosion of practical interest in the pricing of interest rate (IR) derivatives. Textbook pricing methods do not take into account the leptokurticity of the underlying IR process. In this paper, such a leptokurtic behaviour is illustrated using LIBOR data, and a possible martingale pricing scheme is discussed.
AN EMPIRICAL ANALYSIS OF MEDIUMTERM INTEREST RATES
, 2001
"... In the present paper, an empirical study of LIBOR (London Interbank Offered Rate) data is presented. In particular, a data set of interest rates from 1997 to 1999, for two different currencies and various maturities, is analyzed. It turns out that the random behavior of the daily increments for the ..."
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In the present paper, an empirical study of LIBOR (London Interbank Offered Rate) data is presented. In particular, a data set of interest rates from 1997 to 1999, for two different currencies and various maturities, is analyzed. It turns out that the random behavior of the daily increments for the interest rates series is nonGaussian and follows a leptokurtic distribution.
Using the Scaling Analysis to Characterize Financial Markets
"... The scaling properties encompass in a simple analysis many of the volatility characteristics of financial markets. That is why we use them to probe the different degree of markets development. We empirically study the scaling properties of daily Foreign Exchange rates, Stock Market indices and fixed ..."
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The scaling properties encompass in a simple analysis many of the volatility characteristics of financial markets. That is why we use them to probe the different degree of markets development. We empirically study the scaling properties of daily Foreign Exchange rates, Stock Market indices and fixed income instruments by using the generalized Hurst approach. The robustness of the results is tested by both MonteCarlo studies and a computation of the scaling in the frequencydomain. We show that the scaling exponents are associated with characteristics of the specific markets and can be used to differentiate markets in their stage of development.
CUBIC SPLINE COALESCENCE FRACTAL INTERPOLATION THROUGH MOMENTS
, 2006
"... This paper generalizes the classical cubic spline with the construction of the cubic spline coalescence hidden variable fractal interpolation function (CHFIF) through its moments, i.e. its second derivative at the mesh points. The second derivative of a cubic spline CHFIF is a typical fractal func ..."
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This paper generalizes the classical cubic spline with the construction of the cubic spline coalescence hidden variable fractal interpolation function (CHFIF) through its moments, i.e. its second derivative at the mesh points. The second derivative of a cubic spline CHFIF is a typical fractal function that is selfaffine or nonselfaffine depending on the parameters of the generalized iterated function system. The convergence results and effects of hidden variables are discussed for cubic spline CHFIFs.