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26
A Multifractal Model of Asset Returns
, 1997
"... This paper presents the multifractal model of asset returns (“MMAR”), based upon ..."
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Cited by 23 (2 self)
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This paper presents the multifractal model of asset returns (“MMAR”), based upon
Canonical momenta indicators of financial markets and neocortical
 EEG.” InInternational Conference on Neural Information Processing (ICONIP’96
, 1996
"... Abstract—A paradigm of statistical mechanics of financial markets (SMFM) is fit to multivariate financial markets using Adaptive Simulated Annealing (ASA), a global optimization algorithm, to perform maximum likelihood fits of Lagrangians defined by path integrals of multivariate conditional probabi ..."
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Cited by 16 (16 self)
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Abstract—A paradigm of statistical mechanics of financial markets (SMFM) is fit to multivariate financial markets using Adaptive Simulated Annealing (ASA), a global optimization algorithm, to perform maximum likelihood fits of Lagrangians defined by path integrals of multivariate conditional probabilities. Canonical momenta are thereby derived and used as technical indicators in a recursive ASA optimization process to tune trading rules. These trading rules are then used on outofsample data, to demonstrate that they can profit from the SMFM model, to illustrate that these markets are likely not efficient. This methodology can be extended to other systems, e.g., electroencephalography. This approach to complex systems emphasizes the utility of blending an intuitive and powerful mathematicalphysics formalism to generate indicators which are used by AItype rulebased models of management. 1.
Highresolution pathintegral development of financial options
 PHYSICA A
, 2000
"... The BlackScholes theory of option pricing has been considered for many years as an important but very approximate zerothorder description of actual market behavior. We generalize the functional form of the diffusion of these systems and also consider multifactor models including stochastic volati ..."
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Cited by 12 (10 self)
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The BlackScholes theory of option pricing has been considered for many years as an important but very approximate zerothorder description of actual market behavior. We generalize the functional form of the diffusion of these systems and also consider multifactor models including stochastic volatility. Daily Eurodollar futures prices and implied volatilities are fit to determine exponents of functional behavior of diffusions using methods of global optimization, Adaptive Simulated Annealing (ASA), to generate tight fits across moving time windows of Eurodollar contracts. These shorttime fitted distributions are then developed into longtime distributions using a robust nonMonte Carlo pathintegral algorithm, PATHINT, to generate prices and derivatives commonly used by option traders.
Data mining and knowledge discovery via statistical mechanics in nonlinear stochastic systems
 J MATHL COMPUTER MODELLING
, 1998
"... A modern calculus of multivariate nonlinear multiplicative GaussianMarkovian systems provides models of many complex systems faithful to their nature, e.g., by not prematurely applying quasilinear approximations for the sole purpose of easing analysis. To handle these complex algebraic construc ..."
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Cited by 11 (11 self)
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A modern calculus of multivariate nonlinear multiplicative GaussianMarkovian systems provides models of many complex systems faithful to their nature, e.g., by not prematurely applying quasilinear approximations for the sole purpose of easing analysis. To handle these complex algebraic constructs, sophisticated numerical tools have been developed, e.g., methods of adaptive simulated annealing (ASA) global optimization and of path integration (PATHINT). Indepth application to three quite different complex systems have yielded some insights into the benefits to be obtained by application of these algorithms and tools, in statistical mechanical descriptions of neocortex (shortterm memory and electroencephalography), financial markets (interestrate and trading models), and combat analysis (baselining simulations to exercise data).
2000): “Future Possibilities in Finance Theory and Finance Practice,” HBS Working Paper 01030
"... Working papers are in draft form. This working paper is distributed for purposes of comment and discussion only. It ..."
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Cited by 7 (1 self)
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Working papers are in draft form. This working paper is distributed for purposes of comment and discussion only. It
Optimization of Trading Physics Models of Markets
, 2001
"... We describe an endtoend realtime S&P futures trading system. Innershell stochastic nonlinear dynamic models are developed, and Canonical Momenta Indicators (CMI) are derived from a fitted Lagrangian used by outershell trading models dependent on these indicators. Recursive and adaptive optimiza ..."
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Cited by 7 (6 self)
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We describe an endtoend realtime S&P futures trading system. Innershell stochastic nonlinear dynamic models are developed, and Canonical Momenta Indicators (CMI) are derived from a fitted Lagrangian used by outershell trading models dependent on these indicators. Recursive and adaptive optimization using Adaptive Simulated Annealing (ASA) is used for fitting parameters shared across these shells of dynamic and trading models.
Tcheou, Scaling transformation and probability distributions for financial time series, preprint condmat/9905169
, 1999
"... The price of financial assets are, since [1], considered to be described by a (discrete or continuous) time sequence of random variables, i.e a stochastic process. Sharp scaling exponents or unifractal behavior of such processes has been reported in several works [2] [3] [4] [5] [6]. In this letter ..."
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Cited by 6 (0 self)
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The price of financial assets are, since [1], considered to be described by a (discrete or continuous) time sequence of random variables, i.e a stochastic process. Sharp scaling exponents or unifractal behavior of such processes has been reported in several works [2] [3] [4] [5] [6]. In this letter we investigate the question of scaling transformation of price processes by establishing a new connexion between nonlinear group theoretical methods and multifractal methods developed in mathematical physics. Using two sets of financial chronological time series, we show that the scaling transformation is a nonlinear group action on the moments of the price increments. Its linear part has a spectral decomposition that puts in evidence a multifractal behavior of the price increments. 1
A delayed Black and Scholes formula I
 J. Stoch. Anal. Appl
, 2007
"... In this article we develop an explicit formula for pricing European options when the underlying stock price follows a nonlinear stochastic differential delay equation (sdde). We believe that the proposed model is sufficiently flexible to fit real market data, and is yet simple enough to allow for a ..."
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Cited by 5 (0 self)
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In this article we develop an explicit formula for pricing European options when the underlying stock price follows a nonlinear stochastic differential delay equation (sdde). We believe that the proposed model is sufficiently flexible to fit real market data, and is yet simple enough to allow for a closedform representation of the option price. Furthermore, the model maintains the noarbitrage property and the completeness of the market. The derivation of the optionpricing formula is based on an equivalent martingale measure. 1