Exchange Rate Volatility

Exchange rate volatility is a measure of the fluctuations in an exchange rate. It can be measured on an hourly, daily, or annual basis. Based on the assumption that changes in an exchange rate follow a normal distribution, volatility provides an idea of how much the exchange rate can change within a given period. Volatility of an exchange rate, just like that of other financial assets, is usually calculated from the standard deviation of movements of exchange rates.

Two measures of volatility are commonly employed in financial calculations. Historical volatility is calculated from the past values of an exchange rate. Given a series of past daily exchange rates, we can calculate the standard deviation of the daily price changes and then the annual volatility of the exchange rate. Suppose the US$/€ exchange rate was observed to have the following daily closing prices over a 10-day period: 1.562, 1.5745, 1.5615, 1.575, 1.5665, 1.5615, 1.5722, 1.5734, 1.5601, 1.5623. Standard deviation of daily price changes turns out to be 0.006774, and given that there are about 252 trading days in a year, annual volatility turns out to be 0.10754 or about 10.8 percent (volatility = standard deviation ∗ root of number of observations). This implies that, should the historical patterns continue, chances are (about 67 percent) that the exchange rate within the next year will be between 1.5623 + 10.8 percent and 1.5623 − 10.8 percent, that is, it will be somewhere between $1.73/€ and $1.39/€ at the end of one year. Historical volatility provides a good assessment of possible future changes when the financial markets and economies have not gone through structural changes.

Implied volatility is a forward-looking measure of volatility and is calculated from the market participants' estimates of what is likely to happen in the future. More precisely, implied volatility is estimated from the quoted price of a currency option when the values of all other determinants of the price of an option are known. The basis for this calculation is the Black-Scholes option pricing model, according to which the price of an option is determined by the following: the current price of the asset (the exchange rate or a stock or a commodity), the strike price at which the option can be exercised, the remaining time for the maturity of the option, the risk-free interest rate, and the volatility of the asset (or the exchange rate.)

When the market participants are able to quote the price of a foreign currency option, it can be assumed that they are using their estimate of the volatility (the implied volatility) to arrive at the price. Since all the other elements that determine an option price are easily observed, current market price of an option on a currency allows the calculation of the implied volatility. These calculations are fairly complex and require at least an advanced calculator. Many institutions provide software that can calculate the volatility when all other parameters are known.

Exchange rate volatility, like the volatility of any other financial asset, changes in response to information. Currency traders are sensitive to information that might influence the value of one currency in terms of another. The most important information is that about the macroeconomic performance of the economies behind the two currencies. Changes in the levels of uncertainty about the future of either economy will cause traders to become restless and less willing to hold a particular currency. Uncertainty about the future is the most important reason for the change in the volatility in the currency markets.

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