Term Structure Estimation - An Implied Norm Approach: Negative Option Prices - A Puzzle or Just Noise?

Abstract

Knowledge of the term structure of interest rates is undeniably important. It enables the price of a stream of cash flows to be determined and is a key element for pricing certain types of derivative instruments including swaps and forward contracts. It is useful in the formation of economic policy. It is used to calibrate the parameters of the stochastic process assumed to govern the evolution of interest rates. Notwithstanding its importance, estimating the term structure of interest rates remains fraught with difficulty. It is usual to produce an estimate of the term structure that is known to result in arbitrage opportunities. This paper suggests a new way which results in a no-arbitrage estimate of the term structure. The origins of our method lie with the implied valuation philosophy that has its roots in the derivative market and has gained popularity there. We show how the spirit of that philosophy can be applied to the estimation of the term structure. The goal in this paper is to uncover the discount function implicit in the prices and cash flows of bonds, and to infer the implicit selection criterion employed. It is common practice to use only straight bonds to estimate the term structure and to throw out of the sample the bonds with embedded options, resulting in the loss of information and an estimate that is quite likely inaccurate. We will show that discarding this sort of information when estimating the term structure creates the illusion of a puzzle -- the illusion of arbitrage opportunities. This puzzle is apparently negatively valued options implicit in the government bonds of three countries. The approach used for term structure estimation in this paper allows the researcher to harness the information contained in government bonds with embedded options and results in an arbitrage-free estimate of the term structure.