An Analysis of Currency Options and Exchange Rate Distributions
This paper investigates several aspects of
the pricing of currency and currency options.
In section 2 a standard model for the behavior of stocks
will be applied to currency exchange rates. This model will be used
to value European call options on currencies in section 3.
Market values for various
exchange rates and currency options will be used to analyze the accuracy
of the model. Data for this paper was collected from the Financial
Analysis and Securities Traders' Lab at the Graduate School of
Industrial Administration at Carnegie Mellon University. The Japanese
Yen, the British Pound, and several other currencies were monitored.
Most attention in section 4 will be focused on the
``volatility'' of the stochastic process of the exchange rate.
The implied volatility of European call options will be calculated
and shown to be non-constant and associated with other variables
in the model.
In section 5 the true distribution of exchange rate will be
inferred from the observed currency options and the observed exchange rate.
The behavior of domestic and foreign interest rates and their effects
on exchange rates also will be discussed briefly in Appendix A.
Some deviations from the exchange rate model assumptions will be shown
and possible improvements to the model will be suggested.
The final sections summarize the findings of this paper
and suggest extensions of and refinements to the analysis.
Keywords: Black-Scholes model; currency options; foreign exchange;
implied volatility; risk neutral valuation; pricing; valuation;
at the money.
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