Date of Award

1-1-1999

Degree Type

Thesis

Degree Name

Master of Business

Faculty

Faculty of Business and Public Management

First Advisor

Dave Allen

Abstract

The use of the term structure of interest rates to price options is relatively new in the literature. It describes the relationship between interest rates and the maturities of bonds. The first model that described the interest rate process was the Vasicek (1977) model. There have been many studies on the formulation of theoretical pricing models. Yet limited empirical research has been done in the area of actually testing the models. In this thesis we report the results of a set of tests of the models indicated below. This paper involves analysis of the pricing errors of the Black model ( 1976), Asay model (1982), Extended-Vasicek model (1990) and Heath-Jarrow-Morton model (HJM) ( 1992) as applied to call options on 90-day Bank Accepted Bill (BAB) futures. Monthly yield curves are generated from cash, futures, swap and interest rate cap data. A number of different methods of analysis are used. These include the use of inferential statistics, non-parametric sign tests and Ordinary Least Square Regressions. The Wilcoxon non-parametric sign test assists the interpretation of whether the pricing errors are from the same distribution. Ordinary Least Square Regressions are used to assess the significance of factors affecting pricing errors. In addition, data are plotted against different variables in order to show any systematic patterns in how pricing errors are affected by the changes in the chosen variables. Monthly options data on BAB futures in the year 1996 suggest that the term structure models have significantly lower pricing errors than the Black and the Asay model. The Heath-Jarrow-Morton model (1992) is overall the better model to use. For the term structure models, pricing errors show a decreasing trend as moneyness increases. The Extended-Vasicek model and the HJM model have significantly lower errors for deep-in the-money and out-of-the-money options. Higher mean absolute errors are observed for at-the-money options for both term structure models. The HJM model overprices at-the money options but underprices in and out-of-the-money options while the Extended Vasicek model underprices deep-in-the-money options but overprices options of other categories. The mean and absolute errors for both the Black model and the Asay model rise as time to maturity and volatility increases. The two models overprice in, at and out-of-the money options and the mean pricing error is lowest for in-the-money options. The results suggest that the factor time to maturity is significant at the 0.05 level to the -mean pricing error for all four models. Moneyness is the only insignificant factor when the Asay model is used. It is also negatively correlated to mean pricing error for the Black model, the Asay model, the Extended-Vasicek model and the HJM model. The R-square for the Extended-Vasicek model was found to be the lowest. Overall, the HJM model gives the lowest pricing error when pricing options on 90-Day Bank Accepted Bill Futures.

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