Interest rate is a fundamental determinant of asset prices in financial markets. Many stochastic models have been developed by academic researchers in the continuous-time setting (see, e.g., Vasicek [10], Brennan and Schwartz [1 ], Cox, Ingersoll and Ross ). These models provide a rich framework for specifying the dynamic behaviour of interest rates. Based on an assumed stochastic interest rate model interest-rate contingent securities, such as bonds and bond options, can be evaluated as solutions to some partial differential equations. For certain models (such as the Vasicek and Cox-Ingersoll-Ross models) analytic solutions are available. Otherwise, numerical methods may be used to price the interest-rate contingent securities.
While much has been done on the pricing of securities conditional on an assumed interest rate model, little research has been focused on the estimation and selection of interest rate models. Recently, Chan, Karolyi, Longstaff and Sanders (CKLS hereafter) [ 2,3] compared empirically various interest rate models for Japan and U.S. under a general framework of a stochastic differential equation. Similar research has been extended to other countries by Tse . It was found that no single model can satisfactorily describe the stochastic structure of interest rates for all countries. In particular, the conditional volatility of interest rates may vary a lot across countries.
Empirical research on option pricing typically selects models rather arbitrarily. Little empirical comparison of the pricing of option based on different models is available. As the results of Tse show that parameter estimates may be quite sensitive to the restrictions imposed, it would be interesting to see how the adoption of different models may affect the valuation of options. The objective of this paper is to conduct a sensitivity analysis on the pricing of option with respect to different models.
The remainder of the paper is as follows. In Section 2 we outline the models to be compared. Section 3 discusses the methodology of option valuation. Empirical' results are summarized in Section 4 and concluding remarks are given in Section 5.