Bond Valuation I – Present Value

What is a Zero-Coupon Bond?

A zero-coupon bond (or ZCB) is a discount bond (assuming positive time value of money) whose face value, or par value, is repaid in full at the time of maturity, with no coupon payments in between.

What is so Special about ZCB’s?

The great thing about ZCB’s is that if you collect together a whole bunch of them (a portfolio) with the right maturity dates (one ZCB for each payment date) then a vanilla bond (with coupon) can be replicated by this portfolio of ZCBs. If you do it right then you can enhance the formula for the present value of the vanilla bond with coupons because now you can discount each coupon at a different unique interest rate corresponding to the implied rate by the ZCB maturing on the date of the coupon payment. This contrasts with the previous way of doing it where we just assumed that each coupon is discounted at a constant interest rate i.

Pricing bonds this way has an additional strength: it uses market prices of ZCB’s to discount the future coupon payments. This way we know that our discounting rate is quite accurate. For example, if we priced a bond a different way and found that it differed from the method just mentioned then we are inherently implying that there is a ZCB out there in the market that has the wrong price and this introduces an arbitrage possibility. In this way, pricing a bond via replicating a portfolio of ZCBs is called the arbitrage-free pricing approach.

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Bond Valuation III