The Information Content of Implied Stochastic Volatility from Currency Options

Abstract

This paper investigates the predictability of implied variances extracted frorn currency options. Under the assumption that the options market is informationally efficient and that options are priced according to the models of Black-Scholes (1973), Hull-White (1987) and Heston (1993), implied variances are estimated from transaction prices of currency options traded on the Philadelphia Stock Exchange (PHLX). If implied variances are efficient, variance forecasts from time-series models should have no predictive power for subsequently realized market variances. The empirical evidence on testing the implied volatility hypothesis is mixed. Latane and Rendleman (1976) and Chiras and Manaster (1978) find evidence favourable to the hypothesis: the weighted implied standard deviation explains more of the cross-sectional variation in the future standard deviations of individual security returns than do historical volatilities. Day and Lewis (1992) find that the implied volatilities from the S & P 100 index options contain incremental information for the GARCH models. Canina and Figlewski (1993) find evidence against the hypothesis: the implied volatilities from S & P 100 index options have less predictive power for subsequently realized volatility than simple historical volatilities. Lamoureux and Lastrapes (1993) make the first attempt to introduce the stochastic volatility option model into the study of implied volatility. Their tests on individual stock options reject the orthogonality restriction that the forecast from time-series models should not have predictive power in addition to implied volatility. These findings, based on stock index and individual stock options, are inconsistent with the hypothesis that implied volatility is the optimal predictor of future volatility. This contradiction motivates the present paper, which explores the performance of implied volatility in the foreign exchange market. The paper seeks to extend existing research by (a) reducing measurement errors, (b) adopting stochastic volatility option pricing models, and (c) improving the techniques of statistical inference.