This paper explores the use of a measure of chaotic behavior, the correlation dimension, in explaining the unpredictable fluctuations in foreign exchange rates. The resulting calculations indicate that the Singapore dollar has a smaller correlation dimension than four European currencies, consistent with the view that the Singapore dollar is a highly managed currency. We also utilize the correlation dimension to determine the impact of the stock market crash of October 19, 1987 on the five currencies. The four European currencies exhibit a statistically significant decrease in their correlation dimensions, while the Singapore dollar displays no significant change. This is consistent with a hypothesis of a an intervention in the management of the European currencies.
We present an algorithm producing a dynamic non-self-financing hedging strategy in an incomplete market corresponding to investor-relevant risk criterion. The optimization is a twostage process that first determines market calibrated model parameters that correspond to the market price of the option being hedged. In the second stage, an optimal set of model parameters is chosen from the market calibrated set. This choice is based on stock price simulations using a time-series model for stock price jump evolution. Results are presented for options traded on the New York Stock Exchange.
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