An Analysis of Currency Options and Exchange Rate Distributions

Chris Andrews

Abstract:

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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