Perhaps the best way to understand the impact of including a call option on a municipal bond is to look at the value of a callable bond as if it were the value of a noncallable bond minus the value of the embedded call.
where CB is the value of a callable bond, NCB is the value of a noncallable bond, and OVB is the option value of the embedded call.
The greater the value of the call option, the greater the difference in value between callable and noncallable bonds and the greater the spread between callable and noncallable bonds.
We consider two types of bonds: 1) a bond with a make-whole call provision and 2) an option-free or noncallable bond.
With a noncallable bond, if a situation arises where the firm must retire the bond early, the firm will normally attempt a bond tender offer.
If such an event arrives, the firm with a noncallable bond tenders for its bond at the risk-free rate plus a tender spread z (V, r, T - t) that depends on the credit quality of the bond subject to the tender.
To control for term effects and market movements not associated with the call,(5) we selected a matched-control sample of independent noncallable bonds with a maturity date on or immediately following the call date.
The coupon range for noncallable bonds is slightly larger than that of callable bonds, although the standard deviation is substantially smaller.
Numerical Solutions to the Valuation Equation for Noncallable Bonds
The parameter values chosen are the same as those for noncallable bonds.
Initially, suppose that the firm issues a two-period default-free noncallable bond.
is determined in Equation (9) as the coupon payment which would make the marginal investor of the previous section indifferent between purchasing a callable or a noncallable bond at time 0.
For example, several BABs were structured as noncallable bonds
with a single term or bullet maturity, rather than the serial maturity structure traditionally used in tax-exempt bonds.
Our tests are based on a sample of 958 bonds issued during 1987-1991, when issuance of noncallable bonds was quite common.
Of the three, only the Kish and Livingston study has a sufficient number of noncallable bonds to estimate a zero/one equation on the inclusion of a call option, although they are forced to overweight the sample of noncallable bonds.