Arbitrage bounds in markets with noisy prices and the puzzle of negative option prices implicit in bonds

The term structure of interest rates has occupied economists for many years. This is testimony to the importance of the term structure (or, equivalently, valuation operator) and to the difficulty of obtaining reliable estimates of it. Until recently, it was not possible to reconcile the theoretical existence of a multiplicity of valuation operators in an incomplete bond market and the empirical nonexistence of even a single one. MacKay and Prisman [Estimating valuation operators in incomplete market with noises: Can noise complete the market. Working paper, 1996] tackle this problem. In this paper, an amendment to and a generalization of their methodology is presented. The amendment preserves the linearity of valuation operators and allows use of efficient linear programming techniques. Further, it facilitates an admissible consideration of the puzzle of negative option prices embedded in bonds. The empirical results presented in this paper were obtained using data on extendable Government of Canada bonds. The results indicate that although the gap between the lowest and the highest prices assigned to a cash flow by different valuation operators is significant, it is not sufficient to resolve the above-mentioned puzzle.