See also post on why a bond’s callable provision is a risk.
P260 of CFA textbook on Eq and FI has a concise explanation.
– Suppose A issues a riskless non-callable bond, for a $109 price.
– Suppose B issues a callable bond, with identical features otherwise, for $106.8 price. The $2.2 price difference is the value of the embedded call option (to the issuer).
If issuer A uses $2.2 of the sales proceeds to buy a call option (to receive the coupons), then A’s position would match B’s. When rates drop to a certain level, the B issuer would call the bond, ending her obligation to pay those high coupons. A would continue to pay coupons, but his call option would produce a cash flow matching the coupon obligations.
Notice the callable bond is cheaper because the issuer holds a call option — to be exercised if low-interest happens.
Also notice — as expected IR volatility (implied vol) rises, the embedded option is worth more and the price spread between the A vs B bonds will widen.
In fact, since A price isn’t sensitive to vol, B price must drop — intuitive?
The B issuer is (believed to be) more likely to call the bond and refinance at a lower coupon, whereas the A bond will continue to pay the super-high coupon until maturity. So bond A is more valuable to an investor.