Volatility Smiles
Volatility Smiles
Volatility Smiles
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Empirical Results‣ We have just shown that the smile used by traders for foreigncurrency options implies that they consider that thelognormal distribution understates the probability of extrememovements in exchange rates, but is this accurate?‣ A study of 12 different exchange rates over a 10-year periodwas conducted.‣ The first step was to calculate the standard deviation of dailypercentage change in each exchange rate. Then to note howoften the actual percentage of change exceeded one standarddeviation, two, three…etc. The final step was to calculatehow often this would have happened if the percentagechanges had been normally distributed. The lognormalmodel implies that percentage changes are almost exactlynormally distributed over a one day time period.‣ The table provides evidence to support the existence of heavytails and the volatility smile used by traders.4