Why Callable Bonds Yield More: Embedded Call Options and Convexity

Summary

The document explains why a callable bond generally has a higher yield to maturity than a comparable noncallable bond. Its price can be viewed as the value of the noncallable bond minus the value of the issuer’s embedded call option. Since that option has positive value, the callable bond is worth less, which corresponds to a higher yield at the observed price.

The answer connects the option’s value to the forward curve and swaption volatility, with exercise likelihood reflected in no-arbitrage pricing. It also reframes the investor’s exposure: the holder retains risk-free-rate and credit exposure while being short the call option, including its volatility and convexity effects. This explains why comparing only expected duration with a shorter noncallable bond can miss a key source of return. The discussion is conceptual and does not provide a numerical valuation example or claim that yield alone fully describes the callable bond’s risks.

Key ideas

• A callable bond can be valued as a noncallable bond less the issuer’s call option value.
• The embedded option reduces the callable bond’s price and raises its yield to maturity.
• The option value depends on the forward curve and relevant swaption volatility.
• Callable bondholders are short the issuer’s option and bear associated volatility and convexity exposure.
• Duration alone does not capture the option risk that distinguishes callable bonds from shorter noncallable bonds.

Tags

# Why do a callable bond always have higher yields?


# Why do a callable bond always have higher yields?












In an american callable bond there is an expectation for the issuer to prepay its debt prior to maturity. I understand that this reduces it's value and therefore, higher yield.

But another way to think about it is that investing in a callable bond should yield the same as a non-callable bond with lower duration (due to the lower expected duration in a callable) bond. This second approach will have a lower yield in a positive slope curve envirement. What is wrong with this approach?

## Answer by Kch (score 4)

https://quant.stackexchange.com/a/61325



- A callable bond has a price that consists of the noncallable bond less the premium (n.b. option premium, not bond premium!) paid by the borrower for the option to call in the bonds. Options have a nonzero value, so the NC bond price less the option premium gives a bond price for the callable bond that is cheaper, thus the higher yield (YTM here). The option price is a product of the forward curve and prevailing swaption volatilities and, following no arbitrage, the price of the option would accurately reflect the current market conditions and probability such an option would be exercised.

- Because of #2, the callable bond buyer is long risk free and credit, and short option vol. His increased return comes from the convexity he sells off. Duration is less important here than understanding the effect the option has on convexity of the position.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.