The Relationship Between Implied And Realized Volatility In The Danish Option And Equity Markets

In this paper we examine the information content of options on the Danish KFX share index. These options are traded very infrequently and with a low volume. We consider the relationship between the volatility implied in an option's price and the subsequently realized volatility. Recently, Christensen and Prabhala (1998) find that implied volatility in at-the-money one month OEX call options on the Samp;P100 index is an unbiased and efficient forecast of ex-post realized index volatility after the 1987 stock market crash. Gwilym and Buckle (1999) study the UK FTSE100 index and find that although historical volatility estimates have greater accuracy, implied volatility contains more information, based on regression tests, in particular when very short maturities are avoided. In this paper we investigate whether the UK and US markets are special, and whether the infrequent trading and low volume in the KFX case lead to bias and inefficiency in the implied volatility forecast. We examine one month at-the-money KFX calls and similar puts, and we introduce an implied volatility measure that combines information from both call and put prices. We find that implied volatility indeed contains information about realized index return volatility. In fact, implied volatility remains significant even in the multiple regression where historical volatility is included, it subsumes the information content of this, and the bias in the implied volatility forecast is insignificant. The results suggest that the finding in the OEX market may be extended to the much smaller KFX market.