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Embedded Options

A call gives the issuer the right to repay early; a put gives the holder the right to demand repayment. Each is an option, and someone pays for it.

MadStockAlerts Research · Updated August 29, 2026

What to take away

  • A callable bond is a bullet bond with a short call option sold by the holder.
  • Issuers call when rates fall, which is when the holder least wants repayment.
  • The holder is compensated with a higher yield for that risk.
  • A puttable bond reverses the arrangement, and yields less as a result.
  • Yield to worst is the conventional way to quote a bond with a call.

MAD Academy Training Video · 0:46

Somebody Else Holds an Option

An embedded call lets the issuer repay early, which caps your upside exactly when falling rates would have paid you.

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What a call does

A call provision lets the issuer repay the bond before maturity, at stated dates and prices set in the indenture. Issuers exercise it when they can refinance more cheaply, which is when rates have fallen or their credit has improved.

For the holder, that is exactly the wrong time to be repaid. The bond that would otherwise have appreciated as rates fell is instead redeemed at a fixed price, and the proceeds must be reinvested at the new lower rates.

This is negative convexity: the price appreciation is capped as rates fall and the depreciation is not capped as they rise. The holder has sold an option, and the higher yield is the premium received for it.

The upside is capped and the downside is not
The upside is capped and the downside is not80100120140Capped at the call price, whateverrates do+2%+1%0-1%-2%-3%Change in yieldsBond price

Scroll the chart sideways to see all of it.

  • Non-callable
  • Callable
Negative convexity, drawn. The issuer calls when rates fall, which is exactly when the bond would otherwise have appreciated. The higher yield is the premium for having sold that option.

How a callable bond is quoted

MeasureWhat it assumes
Yield to maturityThe bond runs to its stated maturity
Yield to callThe bond is called at the next call date
Yield to worstThe lowest across every possible call date and maturity

Yield to worst is the conventional quote precisely because the issuer holds the option and will exercise it in whichever way suits the issuer. Quoting the yield to maturity on a bond likely to be called overstates what a holder will actually receive.

A bond trading well above par with a near-term call date is very likely to be called at that date. Buying it at a premium and receiving par shortly afterwards produces a materially lower return than the yield to maturity implied.

Puts, and the other direction

A puttable bond gives the holder the right to require repayment on stated dates. It is the mirror of a call: the holder owns the option, and the yield is correspondingly lower.

  • A holder exercises when rates have risen, since the proceeds can be reinvested at a better rate.
  • The put therefore caps the downside on the bond's price, which is positive convexity for the holder.
  • Puts are less common than calls in corporate issuance.
  • A change-of-control put, which is triggered by an acquisition rather than by rates, is a different and common provision.

The last item is worth noting for anyone following a company through a takeover. A change-of-control put can require an acquirer to repay debt it might have preferred to leave in place, which is a real cost of the transaction and is disclosed in the indenture.

Where the effect is largest

Callable structures are pervasive in some markets and rare in others, and the concentration is worth knowing.

MarketPrevalence of calls
US TreasuriesEssentially none in current issuance
Investment-grade corporatesCommon, often with a make-whole provision
High-yield corporatesNearly universal, with a defined non-call period
Municipal bondsVery common on longer maturities
Agency mortgage securitiesEffectively callable, through prepayment by homeowners

The last row is the largest example of negative convexity in any market. Homeowners refinance when rates fall, which shortens the security's life at exactly the moment a holder would want it extended, and the effect drives a substantial part of that market's behaviour.

Make-whole calls

Not every call provision is exercisable at par. A make-whole call requires the issuer to pay a price computed from the present value of the remaining payments, discounted at a government yield plus a stated spread.

make-whole price = present value of remaining coupons and principal, discounted at the reference yield + a stated spread

  • the spread is set in the indenture and is typically small
  • the price rises as rates fall, which removes most of the issuer's incentive to call

The effect is to make early repayment expensive rather than to prohibit it. Make-whole provisions are common in investment-grade issuance and are usually exercised only in a transaction, such as an acquisition, rather than to refinance opportunistically.

For a holder, a make-whole call is a much weaker form of negative convexity than a par call. It is one of the terms that separates otherwise similar bonds and it is stated in the indenture rather than in any summary.

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