Empirical testing of alternative options models on Nairobi Securities Exchange

Abstract

This study presents a new pricing approach and examines the volatility index by using GARCH-type approximation relation on a security in a local capital market. The originality of this approach is to model the local volatility of the securities to obtain accurate approximations with tight estimates of the error terms. This approach can also be used in the case of pricing options with stochastic convenience yields. The model is applied to Nairobi Securities Exchange (NSE) All Share Index Stock data. From the real market data, the realized volatility is empirically analysed by measuring the deviations of pricing errors. Because of its analytical tractability, the implied parameters are estimated from minimizing the weighted sum of squared errors between the market data. The study combines the computational knowledge and option pricing theory, to investigate, design and implement a new option pricing approach, by empirically testing the alternative GARCH pricing model, which can process the observed volatilities or market returns to price the equities. The approach could help researchers to test the accuracy of the pricing model or their input volatility, and also can help investor to compare the market with the estimated price to discover the best investment moment. The discussion, methodology and testing are focused on the issues of computational finance. The findings in this study have evidenced that positive correlation between stock index returns and volatility has two implications. When the stock index return is high, volatility tends to be high. Conversely, when the stock index return is low, volatility tends to be low. The approach of this study can be used to adjust volatility index levels by measuring deviations of pricing errors of future share prices before expiration of each trading period