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

Knowledge of the term structure (or yield curve) is undeniably important. It enables the price of a stream of cash flows to be determined. It is a key element for pricing certain types of derivative instruments. It is useful in the formation of economic policy. It can be used to calibrate the parameters of the stochastic process governing interest rates. Notwithstanding its importance, there are some difficulties in estimating the term structure of interest rates that prevails in the economy. This paper suggests a new way -- the application of a philosophy with origins in the derivative market that has gained popularity there. We show how the spirit of that philosophy can be applied to the estimation of the term structure. There is a relatively new trend in the finance literature. Rather than assume the risk-neutral distribution of stock prices, the distribution is imputed from prices available in the market. The object is to uncover a density function under which the expected discounted values of future payoffs from a set of equity options on an asset are equal to the option prices observed in the market. That is, the data are allowed to "speak for themselves". This paper follows the trend. Here though, we are interested in the estimation of the term structure rather than in the estimation of the density function for derivative securities. It is the norm used in the estimation that is imputed from the available data. We make use of information often discarded. We conclude that the resultant term structure estimation is superior in the particular case on which we focus: it is capable of making the puzzle of negative option prices in bonds disappear. Alternatively viewed, we demonstrate that the puzzle never really existed.