An empirical study of implied volatility in Australian index option markets

With the rapid development of option markets throughout the world, option pricing has become an important field in financial engineering. Among a variety of option pricing models, volatility of underlying asset is associated with risk and uncertainty, and hence is treated as one of the key factors affecting the price of an option. In particular, in the framework of the Black-Scholes option pricing model, volatility of the underlying stock is the only unobservable variable, and has attracted a large amount of attention of both academics and practitioners. This thesis is concerned with the implied volatility in the Australian index option market. Two interesting problems are examined.

First, the relation between implied volatility and subsequently realized volatility is investigated by using the S&P/ASX 200 (XJO) index options over a five-year period from April 2001 to March 2006. Unlike the S&P 100 index options in the US market, the XJO index options are traded infrequently, in low volumes, and with a long maturity cycle. This implies that the errors-in-variable problem for the measurement of implied volatility is more likely to exist. After accounting for this problem by the instrumental variable method, it is found that both call and put options implied volatilities are nearly unbiased and superior to historical volatility in forecasting future realized volatility.

Second, the volatility structure implied by the XJO index options is examined during the period from April 2001 to June 2005. The volatility structure with respect to moneyness and time to maturity are investigated for both call and put option price series. It is found that the volatility smile largely exists, with call (put) option implied volatilities decreasing monotonically as the call (put) goes deeper out of the money (in the money). This result is consistent with the welldocumented evidence of volatility smile on other index options since the stock market crash of 1987.

In summary, this thesis presents some important findings on the volatility inferred from the XJO index options traded on the ASX.