13.15.1 Estimating Term Structure Parameters

Many discussions of the use of term structure models in risk management overlook the difficulties of estimating the parameters for such models. Market participants have become used to the idea of estimating parameters from observable market data through the popularity of the Black-Scholes option pricing model and the accepted market practice of estimating volatility for use in the model from market option prices.

“Implied volatility” is the value of volatility in the Black-Scholes model that makes the theoretical price equal to the observable market price.

Treasury Services Corporation (since acquired by Oracle in September of 1997) and Kamakura Corporation made an in-depth analysis of this parameter estimation problem. The analysis was based on the data set that includes 2,320 days of Canadian Government Bond data provided by a major Canadian financial institution. The data spanned the period January 2, 1987, to March 6, 1996. In the last section, American swaption data provided by one of the leading New York derivatives dealers is used.

Estimating procedures for term structure models have not progressed as rapidly as the theory of the term structure itself, and leading-edge practice is progressing rapidly. There is a hierarchy of approaches of varying quality to determine the appropriate parameters.