Option Pricing Model with Time-Varying Volatility

Abstract

The paper extends the option pricing model of Merlon (1973) with lime-varying volatility of the underlying security. We develop the theoretical option model. Time-varying volatility is constructed by fitting a lime-polynomial to implied volatility values where the order of the polynomial is approximated by the number of options considered. We then predict the option price one day forward and compare the results with the standard Black and Scholcs model. When applied to PT-SE 100 index European options the new model was found to be more accurate titan the Black and Scholcs. Key words: Omion. Time-Varying. Volatility, Black and Scholcs.