Diffusion functions in term-structure models are measures of uncertainty about future price movements and are directly related to the risk associated with holding financial securities. Correct specification of diffusion functions is crucial in pricing options and other derivative securities. In contrast to the standard parametric two-factor models, we propose a non-parametric two-factor term-structure model that imposes no restrictions on the functional forms of the diffusion functions. Hence, this model allows for maximum flexibility when fitting diffusion functions into data. A non-parametric procedure is developed for estimating the diffusion functions, based on the discretely sampled observations. The convergence properties and the asymptotic distributions of the proposed non-parametric estimators of the diffusion functions with multivariate dimensions are also obtained. Based on U.S. data, the non-parametric prices of the bonds and bond options are computed and compared with those calculated under an alternative parametric model. The empirical results show that the non-parametric model generates significantly different prices for the derivative securities.
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Paper provided by Bank of Canada in its series Working Papers with number
99-19.
Find related papers by JEL classification: C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Semiparametric and Nonparametric Methods C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
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