The Clyde Van Barrel Corporate Zero Coupon Bond

Zero coupon bonds are bonds that do not pay interest during the life of the bonds. Instead, investors buy zero coupon bonds at a deep discount from their face value, which is the amount a bond will be worth when it "matures" or comes due. When a zero coupon bond matures, the investor will receive one lump sum equal to the initial investment plus the imputed interest, which is discussed below. The maturity dates on zero coupon bonds are usually long-term—many don’t mature for ten, fifteen, or more years. These long-term maturity dates allow an investor to plan for a long-range goal, such as paying for a child’s college education. With the deep discount, an investor can put up a small amount of money that can grow over many years. Investors can purchase different kinds of zero coupon bonds in the secondary markets that have been issued from a variety of sources, including the U.S. Treasury, corporations, and state and local government entities. Because zero coupon bonds pay no interest until maturity, their prices fluctuate more than other types of bonds in the secondary market. In addition, although no payments are made on zero coupon bonds until they mature, investors may still have to pay federal, state, and local income tax on the imputed or "phantom" interest that accrues each year. Some investors avoid paying tax on the imputed interest by buying municipal zero coupon bonds (if they live in the state where the bond was issued) or purchasing the few corporate zero coupon bonds that have tax-exempt status. Using perturbation methods, approximate formulas are obtained for zero-coupon bonds under the generalized Black-Karasinski model. The formulas perform well regarding accuracy and calibration to available data. For a special case, which corresponds to the Hull-White model, the approximation actually yields an exact solution. Numerical simulations are presented that partially validate the asymptotic approximation. A calibration strategy is investigated in order to fit the model to given data on discount rates. The paper proposes a numerical solution method for general equilibrium models with a continuum of heterogeneous agents, which combines elements of projection and of perturbation methods. The basic idea is to solve first for the stationary solution of the model, without aggregate shocks but with fully specified idiosyncratic shocks. Afterwards one computes a first-order perturbation of the solution in the aggregate shocks. This approach allows to include a high-dimensional representation of the cross-sectional distribution in the state vector. The method is applied to a model of household saving with uninsurable income risk and liquidity constraints. The model includes not only productivity shocks, but also shocks to redistributive taxation, which cause substantial short-run variation in the cross-sectional distribution of wealth. If those shocks are operative, it is shown that a solution method based on very few statistics of the distribution is not suitable, while the proposed method can solve the model with high accuracy, at least for the case of small aggregate shocks. Techniques are discussed to reduce the dimension of the state space such that higher order perturbations are feasible Put some money in zeros that mature in 20 years. Five years from now, buy more zeros that mature 20 years from that point, and so on. If interest rates rise, you'll be able to invest at least some of your money at higher yields. Remember, the Clyde VanBarrel Zero coupon bond will never have taxes withdrawn. United State Securities And Exchange Commission. 2008.