Knowledge that Transforms

Using option and stock transaction data for the period 1978–1979, three issues were investigated: first, the conformance of observed prices to various boundary conditions; second, the evolution of the market over time, as the volume of trading and the number of listed options increased; and third, to test the efficiency of the market. It was found that violations did occur. Using a trading rule based on the signal of observed violations, the results suggest that even after transaction costs the market was inefficient over the sample period.

Rational restrictions are derived for the values of American options on futures contracts. For these options, the optimal policy, in general, involves premature exercise. A model is developed for valuing options on futures contracts in a constant interest rate setting. Despite the fact that premature exercise may be optimal, the value of this American feature appears to be small and a European formula due to Black serves as a useful approximation. Finally, a model is developed to value these options in a world with stochastic interest rates. It is shown that the pricing errors caused by ignoring the location of the interest rate (relative to its long-run mean) range from −5% to 7%, when the current rate is ±200 basis points from its long-run value. The role of interest rate expectations is, therefore, crucial to the valuation. Optimal exercise policies are found from numerical methods for both models.

Vasicek and Fong 11 developed exponential spline functions as models of the interest rate term structure and claim such models are superior to polynomial spline models. It is found empirically that i) exponential spline term structure estimates are no more stable than estimates from a polynomial spline model, ii) data transformations implicit in the exponential spline model frequently condition the data so that it is difficult to obtain approximations in which one can place confidence, and iii) the asymptotic properties of the exponential spline model frequently are unrealistic. Estimation with exponential splines is no more convenient than estimation with polynomial splines and gives substantially identical estimates of the interest rate term structure as well.

Financial economists have long favored the use of a wind‐up measure of the firm's pension liabilities. Yet the pension liabilities of the firm also represent the pension wealth of its workers. It is reasonable to presume that workers and shareholders have a common view of the pension contract. If the wind‐up measure depicts the true pension liabilities of the firm, then the wage concession granted by its workers must reflect the fact that the firm may choose to terminate the plan at any time. Data on the wage‐service characteristics of the membership of a sample of final earnings plans in Canada suggest, contrary to the implications of the wind‐up measure, that workers' wages do not internalize accruing pension benefits on a year‐to‐year basis. Instead, the data suggest that pension plans may be a vehicle through which a significant portion of the total compensation of individual employees is deferred until their later work years, and that the wind‐up measure may well understate the pension liabilities of an on‐going firm.