Zero-Coupon Convertibles

Zero-coupon convertible bonds are well established in the market. When they are issued at a discount to par, they exhibit an implicit yield and trade essentially as coupon convertibles. Similarly, if they are issued at par but redeemed at a stated price above par, an implicit coupon is paid and so again these bonds trade in similar fashion to coupon convertibles. A zero-coupon bond issued at par and redeemed at par is a slightly different instrument for investors to consider. With these products, the buyer is making more of an equity play than with conventional convertibles, but with an element of capital protection retained. 

With par-priced zero-coupon convertibles, buyers often are taking a view on equity price volatility rather than equity price per se, and the value 

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The short end of the swap curve, out to three months, is based on the overnight, 1-month, 2-month, and 3-month deposit rates. The short-end deposit rates are inherently zero-coupon rates and need only be converted to the base currency swap rate compounding frequency and day count convention. The following equation is solved to compute the continuously compounded zero-swap rate (r ) ... 

We consider EURIBOR rates with maturities ranging from one day to one year. These rates, expressed on an actual/360 basis, are first converted into equivalent zero-coupon rates on an Actual/365 basis. Eor example, on 1 January 1999, the 1-month EURIBOR rate was equal to 2.5%. Using the Actual/365 basis, the equivalent zero-coupon rate (denoted by R(0,l/12)) is given by... 

Least-squared methods used to derive the current interbank curve are very similar to those used to derive the current nondefault Treasury curve. After converting market data into equivalent zero-coupon rates, the zero-coupon yield curve is derived using a two-stage process, first writing zero-coupon rates as a B-spline function, and then fitting them through an ordinary least-squared method. 

Analysts and researchers frequendy work with logarithms of yields and prices, or continuously compounded rates. One advantage of the logarithmic approach is that it converts the nonlinear relationship expressed in (3-2) into a linear one. The zero-coupon bond price equation in continuous time is... 

Synthetic convertible notes are securities with fixed coupons, typically set at a relatively low level, whose total return is linked to an external source, such as the level of an equity index or the price of a specific security. In one common structure, the note is redeemable above par if the reference index or security value exceeds a stated minimum. The notes thus give investors the opportunity to profit from the benchmarks performance while providing the safety net of redemption at par should this performance fall short. Another typical synthetic convertible structure is the zero-coupon note. These notes are issued at par and redeemable at par, or higher, if a specified equity index performs better than a stated level. 

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