# Exchange Rate Volatility Essay

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.

Changes in the proportions of hedgers versus speculators  can also change the volatility of a currency. Central banks can also influence the volatility of their currencies  with their announcements of their intentions to either intervene or otherwise in the markets for their  currencies.  While it is commonly  believed that  central  banks  can  influence  the  value of their currency at most in the short run, they can certainly cause a change in the volatility. It is market belief that the volatility of the dollar/euro  rate increased in early June of 2008 when the Federal Reserve Bank chairman, Ben Bernanke, expressed  his opinion  that  the falling dollar influenced  the U.S. inflation rate. Participants took the comment  to mean that the Federal Reserve was going to intervene in the markets to support the dollar even though  Mr. Bernanke had been strictly noncommittal on that specific point.

Bibliography:

1. Bauwens, D. Rime, and  G.  Sucarrat, “Exchange Rate Volatility and the Mixture of Distribution Hypothesis,” Empirical Economics (v.30/4, 2006);
2. BravoOrtega and J. di Giovanni, “Remoteness and Real Exchange Rate Volatility,” IMF Staff Papers (v.53, 2006);
3. Cady and J. Gonzalez-Garcia, “Exchange Rate Volatility and Reserves Transparency,” IMF Staff (v.54/4, 2007);
4. David A. Dubofsky and Thomas W. Miller Jr., Derivatives: Valuation and Risk Management  (Oxford University Press, 2003);
5. Emmanuel Farhi  and  Xavier Gabaix,  Rare Disasters and  Exchange Rates (National Bureau of Economic Research, 2008);
6. Frank J. Fabozzi and Franco Modigliani, Capital Markets: Institutions and Instruments (Pearson Prentice Hall, 2009);
7. Mathias Hoffmann and Peter Tillmann, Integration of Financial Markets and National Price Levels: The Role of Exchange Rate Volatility  (Dt. Bundesbank,  Press and  Public Relations Division, 2008);
8. Brian Kettell, What Drives Currency Markets (Prentice Hall, 2000).

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