The meaning of implied volatility in pricing stock options traded in options markets

Ph.D. in the Faculty of Business Administration

When stock option implied volatilities are calculated using the Black and Scholes [73] model, even considering the adjustment for dividends proposed by Black [75], there are different figures for the same underlying assets with different exercise prices and/or different maturities. Such a phenomenon, which contradicts one of the main assumptions of the model thathere is only one "future·volatility" for the time to expiration, is often used in the literature as a source for an efficiency hypothesis test. The literature on implied volatility estimators has developed from using a siinple at-the­ money volatility to incorporatig all of the available market information. The uses of implied volatility estimators depend on the purpose of the studies analysed. While some estimators have been used for time series analysis (Latane and Rendleman'[76], Trippi [77], Chiras and Manaster [78], Be kers [81], Whaley [82], Day and Lewis [88]), others have been used in option pricing only(MacBeth and Mervine [79] or Finucane [89a]). Authors have suggested different implied volatility estimators to handle apparently contradicting information. These different theoretical estimators lead to significantly different empirical estimates. The analysis of the database of implied volatilities resulted in two particular pheomena:·a significant presence of outliers and a "smile" shape for implied volatilites. The outliers were excluded from the principal database and analysed as a separate case. The number of outliers seemed to increase as the tiine to maturity decreased (maturity effects) and the market index increased (market effects). Also, the ggregate number of outliers changed according to the moneyness degree (moneyness effect).There was no apparent relation between these variables and changes in the open interest of these outliers. The main part of the thesis studied the effectiveness of implied volatility estimators inforecasting future volatilities. Several historical, implied and future volatility estimators were calculated. Then they were compared and significant differences were found among them. Implied volatility estimators were divided into three groups based on their method of calculation. It was expected a priori that the group that takes into account the exercise price effect, in particular the Finucane [89a] and [89b] estimator, would have the lowest mean absolute errors. Is implied volatility a good predictor of future volatility? Since there are several methods for calculating implied volatility, each method is examined in attempting to answer this essential question. Future volatility seems to be related to both historical and implied volatility.Models that embody both historical and implied are successful in explaining future volatility. However, independence of the variables and autocorrelation are important weaknesses of such regression model . The Cochrane-Orcutt procedure was used to overcome the autocorrelation problem; however, the revised figures often result in conflicting conclusions. In particular, historical volatility seems to be more important than implied volatility in predicting / explaining future volatility, after correcting for autocorrelation. This conclusion depends on·the estimators used to calculate both historical and implied volatility. Also, forecasting errors using impiied volatilities seem to be related to tline to maturity. Implied volatility is empirically related to historical volatility (positively correlated), time to maturity (negatively correlated) and the underlying stock price returns (negatively correlated). Since different volatility estimators often lead to different conclusions regarding forecasting future volatility, some short period sample tests were devised to test for ·option market inefficiency. Although there are differences in the efficiency of using different implied volatility estimators for option market transactions, these differences were not large enough to dramatically change the general support of market efficiency after-introducing transaction costs. However, in some ·cases the Finucane [89a] and [89b] estimator shows.that positive·abnormal returns could be obtained even after considering transaction costs. In a final chapter, the effect of the "smile" in simple and sophisticate hedging strategies was examined. The results did not changafter introducing transaction costs. Simple delta hedging strategies seem to outperform more sophisticated strategies. Delta hedging strategies for at-the-money series result in the most effective outcome. But for more complex strategies, the best outcome is obtained by the simultaneous use of near-in and out­ of-the-money series.