Bond and option pricing models: Theory and econometric tests

The first paper proposes an efficient generalized method of moment (GMM) estimation method for nonlinear continuous-time stochastic processes such as the Constant Elasticity of Variance (CEV) process. With a new set of optimal instruments, the first paper achieves the most efficient GMM estimators that have minimal asymptotic variance. Simulation results based on the exact sampling method shows that the proposed efficient GMM achieves significant efficiency gains and increased power of the test over the standard GMM estimation used in previous studies. Thus the first paper provides a better econometric framework in which the specifications of the short-term interest rate can be tested.; The second paper empirically analyzes continuous time models of the spot interest rates, especially the class of CEV models. Specifically, the second paper applies the efficient GMM to actual data of short-term interest rates. Empirical results in the second paper show that the square-root process cannot be rejected, while a class of lognormal diffusions are clearly rejected. The major implication of the second paper is that the previous studies reject the Cox, Ingersoll and Ross (1985b) model because of their inefficient estimation methods. These results are also robust to different specifications. Empirical results in the second paper show that the generalized gamma distribution, which is an exact marginal distribution of the nonlinear-drift CEV process, fits the data well.; The third paper empirically analyzes the martingale restriction imposed by no arbitrage condition in option pricing models. In order to circumvent a specific assumption on the risk-neutral probability density, the third paper develops a method which approximates the risk-neutral probability density based on the Laguerre orthogonal polynomial series. The new method has advantages over previous methods because it is shown to have no bias against the martingale restriction and to have much smaller approximation errors. Empirical results show that the magnitude of deviations from the martingale restriction is much smaller than that in Longstaff (1995), and the martingale restriction cannot be rejected with the statistic based on pricing errors. Results are robust when the pricing relationship between futures contracts and options is utilized.