Optimal Coupon Schedules for Municipal Bonds

When an underwriting syndicate submits a bid for a new issue of municipal bonds, one of the important decisions that it must make involves the scheduling of interest coupons to be placed on the bonds. Given the bid specifications stated by the issuing municipality and some prior decisions of the underwriters, it is shown that the determination of the optimal coupon schedule can be expressed as a linear programming problem. Since this LP problem has a special structure, a simple computational algorithm requiring less computation than the simplex method is derived. This paper goes beyond previous contributions to the literature in three important ways. First, simple formulas for obtaining the dual evaluators are developed; the marginal effect of shifts in the yield curve is also presented. Second, it is shown that in the non-integer year case both the conclusions of previous writers and the conventional heuristics of the market may be erroneous, whereas the general solution techniques developed in this paper remain valid. Finally, a direct analogy between the coupon schedule problem and the microeconomic theory of the firm is used in obtaining the special computational algorithm for this LP problem.