Volatility, interest rates and call option prices: A theoretical and empirical analysis
In the valuation of any derivative security, a major unknown is the volatility of the underlying security's rate of return. Most option pricing models have generally assumed that volatility depended on time and the price of the underlying security only. These models totally ignored the impact of leverage. Since leverage has been shown to have an impact on asset returns risk, it is incorporated as a variable in the determination of call option prices. The Black-Scholes model is shown to be a special case of the derived call option pricing model.^ The estimation of volatility is of paramount importance. In the literature, various techniques have been used. These range from the use of historical prices to autoregressive conditional heteroscedasticity. In this dissertation, these techniques are reviewed and the Glosten-Jagannathan-Runkle (GJR) approach is used in modelling conditional volatility. It is shown that the risk-free rate of return and financial leverage contain very valuable information about the future course of volatility, based on the limited number of securities studied. Another significant finding is the fact that persistence in variance is related to the size of a firm and that the level of persistence using daily data is very low.^ The degree of over-pricing by the derived call option pricing model was found to be an increasing function of financial leverage for the two securities studied. Interest rate bias was found to be very minimal and there was a zero bias for the time to maturity of a call option.^ Finally, it was also found that it was impossible to generate above-normal rates of return using the derived model. This is an indication that the market for call options is efficient. ^
Erivona, Charles E, "Volatility, interest rates and call option prices: A theoretical and empirical analysis" (1995). ETD Collection for Fordham University. AAI9530027.