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Handbook of Exchange Rates
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Handbook of Exchange Rates

by Jessica James, Ian Marsh, Lucio Sarno
July 2012
Beginner content levelBeginner
856 pages
27h 22m
English
Wiley
Content preview from Handbook of Exchange Rates

20.3 Scaling Laws

Scaling laws establish invariance of scale and play an important role in describing complex systems (Barabasi and Albert, 1999; Newman, 2005; West et al., 1997. In finance, there is one scaling law that has been widely reported (Ballocchi et al., 1999; Corsi et al., 2001; Dacorogna et al., 2001; Di Matteo et al., 2005; Galluccio et al., 1997; Mantegna and Stanley, 1995; Müller et al., 1990; Guillaume et al., 1997): the size of the average absolute price change (return) is scale-invariant to the time interval of its occurrence. This scaling law has been applied to risk management and volatility modeling (Di Matteo, 2007; Gabaix et al., 2003; Ghashghaie et al., 1996; Sornette, 2000), even though there has been no consensus among researchers for why the scaling law exists (Barndorff-Nielsen and Prause, 2001; Bouchaud, 2001; Farmer and Lillo, 2004; Joulin et al., 2008; Lux, 2006).

Searching for new scaling laws, we analyze the price data of the FX market, which is a complex network of interacting agents: corporations, institutional and retail traders, and brokers trading through market makers, who themselves form an intricate web of interdependence. We consider five years of tick-by-tick data for 13 exchange rates through November 2007 (see Glattfelder et al. (2010) for a description of the data set).

An exchange rate often moves by 10–20% within a year. However, since the seminal work of Mandelbrot (1963), we know about the fractal nature of price curves. The coastline, ...

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