Multifractality of US Dollar/Deutsche Mark Exchange Rates - Studies2

a broad range of sampling frequencies (two hours to six months).
In modelling financial prices, multifractality generates long memory in squared returns, long
tails, and allows substantial flexibility in modelling either martingale or long-memory behavior in
returns. Repeated simulations show that, among existing models of financial prices, the MMAR is
most like typical financial data in its appearance. Further, the MMAR is best able to replicate the
scaling law found in DM/USD returns.
The conclusion we draw is that multifractality is a promising new tool in economics. In the near
future, it should be possible to use the MMAR in the evaluation of risk. With assumptions on a
pricing model, we also envision pricing derivative assets through simulation methods. Naturally, this
will require further work on estimation methods for multifractal processes, including convergence
properties, simulation methods, and inference procedures. Another component of this research
program is empirical study of other data sets. Given that all of these areas are relatively unexplored,
there is considerable potential for new discovery.
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