CFA Level I Exam · Fixed-Income Cash Flows and Types

Contingency Provisions: Embedded Options in Bonds Explained

Updated 7 October 2026 · Fact-checked

An embedded option is a right written into a bond's terms. A call option benefits the issuer, a put option benefits the bondholder, and a conversion option benefits the bondholder. The holder-friendly options raise the bond's price and lower its yield. The issuer-friendly call lowers the price and raises the yield.

Understand Contingency Provisions: Embedded Options

A plain bond pays coupons and returns principal. Many bonds add a contingency provision, a right that can be used only if a stated event or choice occurs. The right is an embedded option. It is part of the bond contract and cannot be detached and traded separately (unlike a warrant).

A callable bond gives the issuer the right to buy the bond back at a set call price on or after set dates. The issuer calls when rates fall, because it can refinance more cheaply. The investor bears this risk, so a callable bond has a higher yield than an otherwise identical option-free bond. Its price is lower: callable bond value = option-free bond value − call option value. Call features can be American (any time after the protection period), European (one date only) or Bermudan (specific dates). The call protection period is the time when the bond cannot be called.

A putable bond gives the investor the right to sell the bond back to the issuer at a set price, usually par. The investor puts when rates rise or credit worsens. The bond is worth more than an option-free bond: putable value = option-free value + put option value. It has a lower yield.

A convertible bond lets the holder exchange the bond for a set number of the issuer's shares. The conversion ratio is the number of shares received per bond. The conversion price = bond par value ÷ conversion ratio. Conversion value = share price × conversion ratio. The market conversion price = convertible bond price ÷ conversion ratio. The conversion premium = market conversion price − current share price, often shown as a percentage. The holder gets upside from the shares and downside protection from the bond. So the yield is lower than a straight bond. The issuer may add a call as well.

A warrant is a separate option, issued with a bond, to buy the issuer's shares at a set exercise price. It can usually be detached and traded on its own. When exercised, the issuer issues new shares and gets cash. A contingent convertible bond (CoCo) is a bond that converts to equity or is written down if a trigger event occurs, such as a bank's capital ratio falling below a threshold. CoCos are issued mainly by banks to build loss-absorbing capital. The conversion is forced and works against the bondholder, since it happens when the issuer is weak. So CoCos carry a higher yield than similar straight bonds.

Key formulas to remember

Callable bond value: Callable bond = Option-free bond − Call option; Issuer owns the call, so the investor's bond is worth less. Yield is higher.
Putable bond value: Putable bond = Option-free bond + Put option; Investor owns the put, so the bond is worth more. Yield is lower.
Convertible bond value (floor and option): Convertible bond = Straight bond value + Conversion option value; Price is at least the higher of the straight bond value and the conversion value.
Conversion price: Conversion price = Par value ÷ Conversion ratio; Share price at which par value equals conversion value.
Conversion value: Conversion value = Share price × Conversion ratio; What the bond is worth if converted now.
Market conversion price: Market conversion price = Convertible bond price ÷ Conversion ratio; Effective price paid per share if you buy the bond and convert.
Conversion premium: Conversion premium per share = Market conversion price − Current share price; premium % = that ÷ Current share price; Extra cost of buying shares through the bond versus buying shares directly.
Effect of interest rate changes on options: Rates fall: call more valuable to issuer; put less valuable to holder. Rates rise: put more valuable to holder; call less valuable to issuer; When rates fall, the issuer is more likely to call and the put is less likely to be exercised. When rates rise, the put is more likely to be exercised and the call is less likely to be exercised.

How to solve Contingency Provisions: Embedded Options questions

Use this routine for any embedded option question.

1Identify the option: call, put, conversion, warrant or CoCo trigger.
2Decide who holds the right. Call: issuer. Put: bondholder. Conversion: bondholder. Warrant: holder of the warrant. CoCo conversion: triggered by the issuer's condition, not chosen by the investor.
3Compare to an option-free bond. A holder-friendly option raises price and lowers yield. An issuer-friendly option lowers price and raises yield.
4Judge the interest rate or share price scenario. Falling rates favour calling. Rising rates favour putting. A rising share price favours conversion.
5For a convertible, compute the figures in order: conversion ratio, conversion value, market conversion price, then premium.
6Check that your answer matches the direction of benefit, then pick the option that fits.

Quickest way: Who holds the option?

When to use it: For conceptual questions on pricing, yield or benefit, where no calculation is needed.

Ask: whose right is it? That party benefits.
A bondholder-owned option (put, conversion) raises the bond's price because the investor pays for it. An issuer-owned option (call) lowers the price because the investor is compensated.
Yield moves opposite to price: callable bonds yield more, putable and convertible bonds yield less than a straight bond.
For convertibles, remember: conversion value = price × ratio, and market conversion price = bond price ÷ ratio.

Common mistakes in Contingency Provisions: Embedded Options

Saying a callable bond is worth more than an option-free bond.
Students think any option adds value.
Fix: Check who owns the option. The issuer owns the call, so the investor's bond is worth less.
Mixing up conversion price and market conversion price.
Both are called a price per share and the names look alike.
Fix: Conversion price uses par value ÷ ratio. Market conversion price uses the bond's market price ÷ ratio.
Calculating the premium against the wrong share price.
Students compare to conversion price instead of the current share price.
Fix: Premium = market conversion price − current share price. Divide by current share price for a percentage.
Treating a warrant as the same as a convertible bond.
Both can end up with shares.
Fix: A warrant is a separate option to buy shares and can be detached and traded. Exercising it brings cash to the issuer. A convertible bond is exchanged for shares and the debt disappears.
Thinking CoCo investors choose when to convert.
The word convertible suggests a holder option.
Fix: CoCo conversion or write-down is triggered by an event such as a capital shortfall. It is not the investor's choice, which is why it carries higher yield.
Saying a bank issues a CoCo mainly to lower its funding cost versus straight debt.
Students confuse the purpose of the instrument with its side effects.
Fix: The primary purpose is regulatory loss-absorbing capital. Investors take on the added risk of forced conversion or write-down, so they demand a higher yield than on similar straight bonds.

Worked examples

Example 1

A convertible bond has a par value of $1,000 and a conversion ratio of 20. It trades at $1,100. The share price is $48. What is the conversion premium per share? A) $2 B) $7 C) $12

Show the solution

Market conversion price = $1,100 ÷ 20 = $55.
Conversion premium per share = $55 − $48 = $7.
Check: conversion value is 20 × $48 = $960, below the bond price of $1,100, consistent with a premium.

Answer: B) $7 per share (about 14.6% of the share price).

Example 2

When market interest rates fall sharply, which is most likely? A) The holder of a putable bond becomes more likely to exercise the put. B) The issuer of a callable bond becomes more likely to call the bond. C) The issuer of a callable bond becomes obliged to call it at the next call date.

Show the solution

Falling rates mean the issuer can refinance at a lower coupon, so calling the bond becomes attractive. This supports B.
A put lets the investor sell at a fixed price, usually par. With rates down, the bond trades above par, so selling at par is unattractive. This rules out A.
A call is a right, not an obligation. The issuer is never forced to call, so C is wrong.

Answer: B)

Exam tips

For direction questions, decide who owns the option first. Then eliminate the two options that contradict it.
Callable bonds have higher yield, putable bonds have lower yield. Wrong options often reverse this.
Premium questions need two divisions and one subtraction. Do the market conversion price first.
Warrant questions test exercise: the issuer receives cash and issues new shares. Convertible conversion gives no new cash.
CoCo questions focus on trigger events, bank capital and the investor's loss risk.

Practice questions from Fixed-Income Cash Flows and Types

Contingency Provisions: Embedded Options in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

CFA Level IIEmbedded Options in Bonds: Types and Features

Contingency Provisions: Embedded Options: frequently asked questions

Callable vs putable bond: who benefits?

The issuer benefits from a callable bond because it can redeem early when rates fall. The investor benefits from a putable bond because it can sell back at the put price when rates rise. The investor is compensated for the call with a higher yield and pays for the put with a lower yield.

How do you find the conversion ratio and conversion premium?

The conversion ratio is given in the bond terms, or equals par value ÷ conversion price. The market conversion price is the bond price ÷ conversion ratio. The premium is that price minus the current share price.

What is a contingent convertible bond (CoCo)?

A CoCo is a bond that converts to equity or is written down if a trigger occurs, such as a bank's capital ratio falling below a set level. Banks issue them to build loss-absorbing capital. Investors take extra risk, so CoCos carry higher yields than similar straight bonds.

How is a warrant different from a convertible bond?

A warrant gives the right to buy shares at a set price and can usually be traded separately from the bond. A convertible bond is exchanged for shares and cannot be split. Exercising a warrant raises cash for the issuer.