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[pt] Este trabalho procura confirmar a hipótese de o modelo de apreçamento de opções GARCH reduzir alguns dos já amplamente estudados vieses do modelo de Black & Scholes, utilizando opções de compra da Telebras no período julho de 1995 a junho de 2000. Para isso, comparam-se os preços encontrados por intermédio do modelo GARCH com os do modelo de Black & Scholes, cotejando-os com os preços de mercado. Os resultados indicaram que o modelo GARCH foi capaz de diminuir alguns dos vieses, principalmente para opções fora- do-dinheiro com curto tempo para o vencimento. Desta forma, o modelo GARCH se mostrou uma alternativa eficaz ao modelo de Black e Scholes, sobretudo para opções com pouca liquidez, nas quais não é possível a utilização da volatilidade implícita da equação de Black e Scholes. / [en] This study attempts to confirm the hypothesis that the GARCH option pricing model reduces some of the well- documented biases associated with the Black & Scholes model, using Telebras calls in the period of July 1995 to June 2000. For this purpose, the prices obtained by the GARCH model are compared with the ones obtained by the Black and Scholes model, and both of them are checked with the market prices. The results of this research indicate that the GARCH model is able to lessen some biases, specially for out-of-the-money options with short maturity. Thus, the GARCH model is an efficient alternative to the Black and Scholes model, mainly for options with low liquidity, in which it is not possible to use the implicit volatility of the Black and Scholes equation.

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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.

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