A Linearization Approach In Modeling Quasi-Affine Coupon Rate Term Structures And Related Derivatives

For an affine model, we propose a “dynamic bootstrapping” method that would linearly relate coupon (or swap) rates to the term structure model's factors. Two techniques targeting different applications are considered, the standard linearization intended for equilibrium modeling or historical fine-tuning, and stochastic linearization (moment matching) for pricing interest rate derivatives. Analyzing theoretical accuracy of these techniques we conclude that it is sufficiently high and suitable for most applications they are intended for.Among other results, we prove that a two-factor Gaussian model with constant coefficients does a very decent work in modeling term structures of the U.S. Treasury rates and especially the swap rates. The daily factor increments for the period of 1995–2000 appear to be “moderately Gaussian” whereas the achieved accuracy of the term structure modeling as measured across maturities, ranges from 3 basis points (2-year to 30-year swaps) to 6 basis points (3-month to 10-year Treasuries). Although the fine-tuned model parameters do depend on chosen historical sub-interval, the two principal components reveal robustness in shape and size.Finally, we consider the role played by volatility term structure and inter-rate correlations in pricing financial derivatives contingent on coupon or swap rates.