Mercik, Szymon and Weron, Rafal (2002): Origins of scaling in FX markets.

PDF
MPRA_paper_2294.pdf Download (255kB)  Preview 
Abstract
Typical data sets employed by economists and financial analysts do not exceed a few hundred or thousand observations per series. However, in the last decade data sets containing tickbytick observations have become available. The studies of these data have turned up new and interesting facts about the pricing of assets.
In this article we show that foreign exchange (FX) rate returns satisfy scaling with an exponent significantly different from that of a random walk. But what is more important, we also show that the conditionally exponential decay (CED) model can be used to solve a long standing problem in the analysis of intradaily data, i.e. it can be used to identify the mathematical structure of the distributions of FX returns corresponding to the empirical scaling laws.
Item Type:  MPRA Paper 

Institution:  Hugo Steinhaus Center, Wroclaw University of Technology 
Original Title:  Origins of scaling in FX markets 
Language:  English 
Keywords:  FX market; scaling law; volatility; CED model; high frequency data 
Subjects:  C  Mathematical and Quantitative Methods > C4  Econometric and Statistical Methods: Special Topics > C46  Specific Distributions ; Specific Statistics F  International Economics > F3  International Finance > F31  Foreign Exchange C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C13  Estimation: General 
Item ID:  2294 
Depositing User:  Rafal Weron 
Date Deposited:  17. Mar 2007 
Last Modified:  16. Apr 2015 15:15 
References:  [1] T.G. Andersen, Some reflections on analysis of highfrequency data, J. Business & Economic Statistics 18 (2000) 146153. [2] H. Aoyama, W. Souma, Y. Nagahara, M.P. Okazaki, H. Takayasu, M. Takayasu, Pareto’s law for income of individuals and debt of bankrupt companies, Fractals 8 (2000) 293300. [3] O.E. BarndorffNielsen, Processes of the normal inverse Gaussian type, Finance & Stochastics 2 (1998) 4168. [4] R.C. Blattberg, N.J. Gonedes, A comparison of the stable and Student distributions as statistical models for stock prices, J. Business 47 (1974) 244280. [5] J.P. Bouchaud, Power laws in economics and finance: some ideas from physics, Quantitative Finance 1 (2001) 105112. [6] G. Casella, R.L. Berger, Statistical Inference, 2nd ed., Duxbury, Pacific Grove, 2001. [7] P.K. Clark, A subordinated stochastic process model with finite variance for speculative prices, Econometrica 41 (1973) 135156. [8] M.M. Dacorogna, R. Gencay, U.A. M¨uller, R.B. Olsen, O.V. Pictet, An Introduction to HighFrequency Finance, Academic Press, San Diego, 2001. [9] L. Devroye, A Course on Density Estimation, Birkhauser, Boston, 1987. [10] E. Eberlein, U. Keller, Hyperbolic distributions in finance, Bernoulli 1 (1995) 281299. [11] E. Fama, Mandelbrot and the stable Paretian hypothesis, J. Business 35 (1963) 420429. [12] E. Fama, The behavior of stock market prices, J. Business 38 (1965) 34105. [13] W. Feller, An Introduction to Probability Theory and Its Applications, 2nd edn. Wiley, New York, 1971. [14] S. Galluccio, G. Caldarelli, M. Marsili, Y.C. Zhang, Scaling in currency exchange, Physica A 245 (1997) 423436. [15] I. Gleria, R.Matsushita, S. Da Silva, Scaling power laws in the Sao Paulo Stock Exchange, Economics Bulletin 7(3) (2002) 112.. [16] D.M. Guillaume, M.M. Dacorogna, R.R. Dave, U.A. Mueller, R.B. Olsen, O.V. Pictet, From the bird’s eye to the microscope: A survey of new stylized facts of the intradaily foreign exchange markets, Finance & Stochastics 1 (1997) 95129. [17] S.R. Hurst, E. Platen, S.T. Rachev, Subordinated market index models: A comparison, Financial Engineering & Japanese Markets 4 (1997) 97124. [18] A. Janicki, A. Weron, Simulation and Chaotic Behavior of alphaStable Stochastic Processes, Marcel Dekker, New York, 1994. [19] A. Jurlewicz, A. Weron, K. Weron, Asymptotic behavior of stochastic systems with conditionally exponential decay property, Applicationes Mathematicae 23 (1996) 379394. [20] S.J. Kon, Models of stock returns  A comparison, J. Finance 39 (1984) 147165. [21] U. Kuechler, K. Neumann, M. Sørensen, A. Streller, Stock returns and hyperbolic distributions, Mathematical & Computer Modelling 29 (1999) 115. [22] J.C. Lagarias, J. A. Reeds, M. H. Wright, P. E. Wright, Convergence properties of the NelderMead simplex method in low dimensions, SIAM Journal of Optimization 9 (1998) 112147. [23] T. Lux, M. Ausloos, Market fluctuations I: Scaling, multiscaling and their possible origins, in A. Bunde, H.J. Schellnhuber eds., Theories of disasters, Springer, Berlin, 2001. [24] B.B. Mandelbrot, The variation of certain speculative prices, J. Business 36 (1963) 394419. [25] B.B. Mandelbrot, Fractals and Scaling in Finance: Discontinuity, Concentration, Risk, SpringerVerlag, New York, 1997. [26] R.N. Mantegna, H.E. Stanley, An Introduction to Econophysics: Correlations and Complexity in Finance, Cambridge University Press, Cambridge, 1999. [27] S. Mercik, R. Weron, Scaling in currency exchange: A Conditionally Exponential Decay approach, Physica A 267 (1999) 239250. [28] S. Mittnik, S.T. Rachev, Modeling asset returns with alternative stable distributions, Econometric Rev. 12 (1993) 261329. [29] U.A. M¨uller, M.M. Dacorogna, R.D. Dave, O.V. Pictet, R.B. Olsen, J.R. Ward, Unpublished manuscript, Olsen & Associates, Z¨urich, 1993. [30] U.A. M¨uller, M.M. Dacorogna, R.B. Olsen, O.V. Pictet, M. Schwarz, C. Morgenegg, Statistical study of foreign exchange rates, empirical evidence of a price change scaling law, and intraday analysis, J. Banking & Finance 14 (1990) 11891208. [31] E.E. Peters, Fractal Market Analysis: Applying Chaos Theory to Investment and Economics, Wiley & Sons, New York, 1994. [32] S.T. Rachev, S. Mittnik, Stable Paretian Models in Finance, Wiley, 2000. [33] S.T. Rachev, A. Weron, K. Weron, Conditionally exponential dependence model for asset returns, Appl. Math. Lett. 10 (1997) 59. [34] A.L. Tucker, L. Bond, The probability distribution of foreign exchange price changes: Tests of candidate processes, Rev. Economics & Statistics 70 (1988) 638647. [35] A. Weron, S. Mercik, R. Weron, Origins of the scaling behaviour in the dynamics of financial data, Physica A 264 (1999) 562569. [36] A. Weron, R. Weron, Financial Engineering: Derivatives Pricing, Computer Simulations, Market Statistics, (in Polish) WNT, Warsaw, 1998. [37] K. Weron, A. Jurlewicz, Two forms of selfsimilarity as a fundamental feature of the powerlaw dielectric relaxation, J. Physics A: Mathematical & General 26 (1993) 395410. [38] R. Weron, K. Weron, A. Weron, A conditionally exponential decay approach to scaling in finance, Physica A 264 (1999) 551561. 
URI:  http://mpra.ub.unimuenchen.de/id/eprint/2294 