Kristensen, Dennis
(2004)
Semiparametric estimation of diffusion models with applications in finance.
PhD thesis, London School of Economics and Political Science.
Abstract
This thesis concerns semiparametric modelling and estimation of diffusion models, and the application of these in mathematical finance. Two general classes of semiparametric scalar diffusion models are proposed, and an estimator of the drift and the diffusion function based on discrete observations with a fixed time distance in between is defined. The asymptotic properties of the estimator is derived; in particular it is shown to be consistent and asymptotically normally. These semiparametric models can be applied to the pricing of financial derivatives. We assume that preliminary estimates of the drift and diffusion term are available, and give general conditions under which implied derivative prices calculated on the basis of the estimates will be consistent, and follow a normal distribution asymptotically. In particular, we verify these conditions for the proposed semiparametric estimator. The theoretical results are applied in an empirical study of a proxy of the Eurodollar short-term interest rate. We fit a semiparametric single-factor diffusion model to a data set of daily observations of the Eurodollar rate in the period 1973-1995. The resulting estimates of the drift and diffusion exhibit nonlinearities that standard parametric models cannot capture. We test the most flexible parametric single-factor model against the semiparametric alternative, and reject the model. Furthermore, it is demonstrated that the two competing models lead to significantly different bond prices.
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