Discrete stochastic arbitrage models for pricing options on short and long term yields: Tests of the Ho and Lee and the Black, Derman and Toy models.

Abstract

The Chicago Board of Options Exchange introduced the short-term and the long-term options on interest rates in June, 1989. This paper develops versions of the Ho and Lee and the Black, Derman and Toy models, two of the most popular arbitrage based discrete stochastic term structure models, and conducts joint tests of the models and the option markets. Both parametric and non-parametric tests are employed. The data consist of the prices of these options and the term structure of interest rates from June, 1989 to June, 1992. The prices of the short and long-term interest options have been obtained from the Wall Street Journals for the period. The term structure of interest rates has been obtained as the prices of treasury bills and the seven, ten and thirty year treasury strips. It is found that the version of Black, Derman and Toy model used in the study is superior to the Ho and Lee model. The Black, Derman and Toy explains the option prices to some extent as seen from the significant R-square values but it does tend to underprice both the short and long-term options slightly. However, since the tests are joint tests of the model and the short and long-term interest rate option markets, it may be that though the model is pricing the options correctly, the markets are not efficient. This may be especially true in view of the fact that the trading in these options has been, at times, quite thin. The Ho and Lee model fails to significantly explain both the short and long-term option prices. The call prices are found to be reasonably close to the actual prices whereas the put prices are grossly over priced. As indicated by the theoretical concepts the unstable and sensitive nature of δ and the tendency for the interest rates at the extreme nodes to assume unrealistic values causes this problem.