Volatility of default--free noncallable bond
= (bond duration)vV/D, (4)
The following section will discuss how the value (and yield) of a callable bond differs from a noncallable bond
. Using a well-known option pricing model, the final section will provide actual computations of how many more basis points a callable issuer should expect to pay over a noncallable issuer.
While 2.1 bp might seem exceedingly small, it is understandable when one considers that in a frictionless environment, calls are strictly endogenous and only occur when the credit spread for an equivalent noncallable bond
narrows to less than the make-whole premium.
This translates to an upper bound in the market value of the underlying noncallable bond
, which would limit the benefit of increased volatility.
On the day of the announcement (Day 0), callable bond returns fall 0.18% more than noncallable bond
We show the yields to maturity of a nine percent, ten-year, noncallable bond
when |Delta~ = 0.4 in Exhibit 7.
In a different vein, Yawitz and Anderson  and Marshall and Yawitz  considered the net tax benefit associated with the call premium paid when the bond is called.(1) Since the call premium is taxed as a capital gain to investor, but is deductible as an ordinary income expense to the firm, they concluded that the expected tax benefit for a callable bond will be higher than for an otherwise identical but noncallable bond
. Recently, however, Brick and Wallingford  have argued that the call premium tax asymmetry may produce even greater tax benefits for noncallable debt repurchased at market prices because there will be an expanded set of profitable call opportunities.
are like a ground lease that cannot be cancelled by the payor.
We designate a dummy for callable municipal bonds as these bonds tend to have higher yields than comparable noncallable bonds
. Bank qualified bonds are issues that qualify for preferential tax treatment by banks.
A par swap (with beginning value of zero) can be replicated by a portfolio of noncallable bonds
with the same par value and maturity as the swap.
Fourth, this duration measure was then adjusted for call features using a matrix provided by Goldman Sachs for adjusting the durations of noncallable bonds
to reflect call provisions.
(Before that date, the straight line method could be used.) For noncallable bonds
, the premium is amortized over the bond's life.