Estimating the term structure of volatility and fixed income derivative pricing

Estimating the parameters of the instantaneous spot interest rate process is ofcrucial importance for pricing fixed income derivative securities. This paper presentsan estimation for the parameters of the Gaussian interest rate model for pricing fixedincome derivatives based on the term structure of volatility. We estimate the termstructure of volatility for US treasury rates for the period 1983 - 1995, based on ahistory of yield curves. We estimate both conditional and first differences term structuresof volatility and subsequently estimate the implied parameters of the Gaussianmodel with non-linear least squares estimation. Results for bond options illustratethe effects of differing parameters in pricing.