Essays on currency options and volatility

Tse-Shih Wang

doi:10.17918/00007603

The implied volatility is defined as the volatility obtained by inverting the option pricing model given the price of the option observed in the market. We can use the implied volatility to represent the volatility of the underlying assets if option pricing models are correct and options markets are efficient. Unfortunately, empirical findings are contradictory to this statement. First, implied volatilities seem to be a biased estimator for future volatility. Second, implied volatilities show term structure effects: the implied volatilities of options with the same underlying assets but different maturities are different. Finally, implied volatilities exhibit U-shaped "smile" in moneyness. As a result, it is necessary to investigate the characteristics of the implied volatilities implicit in option prices further to yield important clues for the improvement of existing option pricing models or for the justification of efficient market hypothesis. This dissertation is composed of several parts. First, we test if the information set contained in the historical data provides additional information for future volatilities given the implied volatilities. To yield more robust results, we use the vector autoregressive models to test the Granger causality relationship. The results show that neither implied volatilities nor the historical data contain the complete information for future volatilities. Second, it is well documented that exchange rates follow ARCH/GARCH processes, which is inconsistent with the assumption of the traditional option pricing models. To test the common information set contained in the currency options and underlying currencies, we test if there exists common autoregressive features between implied volatilities and the volatilities of the underlying exchange rates. The results of common ARCH feature tests are mixed for different currencies. Third, we find that implied volatilities do have such ARCH/GARCH effects. However, the sizes of the mean-reverting coefficients are biased downward and are not constant over maturities. Finally, we find that the implied binomial tree approach, which incorporates the smile effect and the term structure effect, yields unsatisfactory results in predicting future volatilities.

Essays on currency options and volatility

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Essays on currency options and volatility

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