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10.1 Overview

The foreign exchange market is one of the largest markets in the world. In late 1993, the total value of currency trading was close to one trillion dollars per day! The growth of this market has come from the increasing globalization of markets, including financial markets.

Competition among fund managers has led them to seek out opportunities across the world. For example, U.S. pension funds increased their foreign investment from about 6% in 1991 to 12% in 1993. Investing in foreign equities also provides greater diversification potential.

Greater investment in foreign assets brings with it exposure to not only the risks associated directly with the investment, but also exchange rate risk. In a study by a U.S. consulting firm, it was found that for a fund manager investing in foreign bonds and equity and measuring (or "booking") the profit in U.S. currency, exchange rate movements affected fixed income and equity assets very differently. Approximately 80% of the volatility of fixed income returns and approximately 30% of the volatility of equity returns was attributed to exchange rate fluctuations.

Currency markets can also be quite volatile. As an illustration, consider that during the European currency crisis in 1992, the implied volatility (i.e., the volatility calculated from option prices) for sterling/dollars and dmark/dollars jumped from the 11-12% range in August 1992 to levels in excess of 20% by October 1992. These volatilities then fell back sharply to near historical levels soon thereafter. Options are an important tool for managing currency risk. Currency options are traded on many exchanges, including the Philadelphia Stock Exchange.

In this chapter, in topic 10.3 we develop the Garman-Kolhagen (1983) model of currency options. This model extends the Black-Scholes model to currencies, and in particular, shows that currency options are similar to options on stocks that pay a continuous dividend yield. First we explain an important arbitrage relationship, called the Interest Rate Parity Relationship. This relationship, between exchange rates (spot and forward) and pure discount bonds (domestic and foreign), is important for understanding how the arbitrage free value of the option is determined.

Finally, in topic 10.4 titled Currency Options: Hedge Parameters, we present the hedge parameters from the currency option pricing model.

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