CFA Level II Exam · Valuation and Analysis of Bonds with Embedded Options

Embedded Options in Bonds: Types and Features

Updated 7 October 2026 · Fact-checked

An embedded option is a right written into a bond's terms. A call option favours the issuer and lowers bond value. A put option favours the bondholder and raises it. A convertible adds an equity option for the holder. Caps hurt floating-rate holders, floors help them. Value = straight bond ± option value.

Understand Embedded Options in Bonds: Types and Features

A straight bond (option-free bond) pays fixed coupons and returns principal at maturity. Neither side can change the terms. An embedded option is a right written into the bond that lets one party change the cash flows under set conditions. You value the whole bond as a package of the straight bond and the option.

The key question is always: who owns the option? The owner pays for it through the bond's terms. If the issuer owns it, the bond is worth less to the investor. If the investor owns it, the bond is worth more.

Callable bond: the issuer can redeem the bond before maturity at a set call price, usually when rates fall and it can refinance more cheaply. The investor is short the call. Value of callable = value of straight bond − value of call option. It must offer a higher yield than a comparable straight bond. Calls come in types: American (anytime after the first call date), European (one date only), Bermudan (specified dates), plus a call protection or lockout period.

Putable bond: the bondholder can sell the bond back to the issuer at a set put price, usually when rates rise or credit quality falls. The investor is long the put. Value of putable = value of straight bond + value of put option. It offers a lower yield than a comparable straight bond.

Convertible bond: the holder can exchange the bond for a fixed number of the issuer's shares, set by the conversion ratio. The holder owns a call option on the stock. Value of convertible = value of straight bond + value of call option on the stock. It usually has a lower coupon than a straight bond. Many convertibles are also callable and sometimes putable, so several options can sit in one bond.

Capped and floored floating-rate bonds: a floating-rate note pays a reference rate plus a spread. A cap sets a maximum coupon rate. It protects the issuer, so the investor is short a cap. Value of capped FRN = value of FRN − value of cap. A floor sets a minimum coupon rate. It protects the investor, so the investor is long a floor. Value of floored FRN = value of FRN + value of floor. A bond with both is a collar.

Option value also depends on volatility, and you must use the right type of volatility. For calls, puts, caps and floors, the relevant measure is interest rate volatility. Higher interest rate volatility raises the value of each of these options, whoever owns it. So it lowers the value of a callable bond and a capped FRN, and raises the value of a putable bond and a floored FRN.

For the conversion option in a convertible bond, the relevant measure is share price volatility. Higher share price volatility raises the value of the conversion option and so the value of the convertible.

Key formulas to remember

Callable bond value: V(callable) = V(straight) − V(call option); The call belongs to the issuer, so it is subtracted. Callable value is never above the straight bond value.
Putable bond value: V(putable) = V(straight) + V(put option); The put belongs to the investor, so it is added. Putable value is never below the straight bond value.
Convertible bond value: V(convertible) = V(straight) + V(call option on issuer's stock); The holder owns the equity call. Valuation of the straight bond uses the yield for a comparable non-convertible bond.
Capped FRN value: V(capped FRN) = V(FRN) − V(cap); The cap benefits the issuer and limits coupons when the reference rate rises.
Floored FRN value: V(floored FRN) = V(FRN) + V(floor); The floor benefits the investor and guarantees a minimum coupon when the reference rate falls.
Value of the option (implied): V(call) = V(straight) − V(callable); V(put) = V(putable) − V(straight); Use these to back out the option value from two bond prices.
Conversion value: Conversion value = market price per share × conversion ratio; The value of the shares received if the holder converts now.
Volatility effect: Higher interest rate volatility → higher value of calls, puts, caps and floors. Higher share price volatility → higher value of the conversion option.; Higher interest rate volatility lowers a callable bond and a capped FRN, and raises a putable bond and a floored FRN. Higher share price volatility raises a convertible bond. Do not mix the two types of volatility.

How to solve Embedded Options in Bonds: Types and Features questions

Use this routine for any question on embedded options. It forces you to find the option owner first, which fixes the direction of every answer.

1Identify the bond type from the vignette: callable, putable, convertible, capped, floored, or a combination.
2Decide who owns each option: issuer (call, cap) or investor (put, floor, conversion).
3Write the value relationship: add the option if the investor owns it, subtract it if the issuer owns it.
4Pick out the numbers you need from the exhibits: straight bond value, option-bond price, conversion ratio, share price.
5Compute the required item, such as the option value or conversion value, using the relationship in step 3.
6Check direction with a sanity test: callable ≤ straight, putable ≥ straight, capped FRN ≤ FRN, floored FRN ≥ FRN.
7If the question changes rates or volatility, reason through how the option value moves, then apply it to the bond value.

Quickest way: Owner-sign shortcut

When to use it: Use this for qualitative questions asking how a feature or a change in rates, volatility or share price affects value, yield or call/put likelihood.

Ask: who holds the option? Issuer-held means minus sign. Investor-held means plus sign.
Ask what makes the option more valuable: lower rates for a call, higher rates for a put, higher share price for conversion, higher interest rate volatility for a call, put, cap or floor, and higher share price volatility for the conversion option.
If the option gains value, then the bond value moves in the direction of the sign. Issuer-held: bond falls. Investor-held: bond rises.
Yield works opposite to value: investor-held option means a lower required yield, issuer-held means a higher required yield.
Eliminate any answer choice that breaks callable ≤ straight or putable ≥ straight.

Common mistakes in Embedded Options in Bonds: Types and Features

Adding the call option value to a callable bond's price.
Students remember that options have positive value and forget who owns them.
Fix: The issuer owns the call. The investor is short it, so subtract it. Always ask who owns the option first.
Saying a putable bond has a higher yield than a comparable straight bond.
Confusing the bond with the risk it protects against.
Fix: The put is a benefit to the investor, so the investor accepts a lower yield. Callable bonds have higher yields. Putable and convertible bonds have lower yields.
Thinking higher volatility lowers the value of all bonds with options.
Linking volatility with risk and a lower price.
Fix: Volatility raises the option's value. Higher interest rate volatility lowers a callable bond (investor is short the call) and raises a putable bond (investor is long the put). Higher share price volatility raises a convertible bond (investor is long the conversion option).
Treating a cap as a benefit to the bondholder.
Cap sounds like protection, as in a rate cap on a borrower.
Fix: On a floating-rate bond, the cap limits the coupon the investor receives. It helps the issuer. The floor helps the investor.
Valuing the straight part of a convertible using the convertible's own yield.
Using the lower yield implied by the convertible price.
Fix: Discount the straight bond cash flows at the yield of a comparable non-convertible bond from the same issuer. The conversion option is valued separately.
Calling a call option exercised whenever rates are below the coupon without checking call price and call dates.
Ignoring the structure of the option.
Fix: Check the call type, first call date, and call price. A call is attractive to the issuer when refinancing saves more than the call price premium and the bond is callable.

Worked examples

Example 1

A vignette gives these values for bonds from the same issuer with the same coupon and maturity: straight bond ₹1,02,000 per ₹1,00,000 face, callable bond ₹98,500, putable bond ₹1,04,300. Questions: (1) What is the value of the embedded call? (2) What is the value of the embedded put? (3) Which bond has the lowest yield-to-maturity?

Show the solution

Call value: the issuer owns the call, so V(call) = V(straight) − V(callable) = 1,02,000 − 98,500 = ₹3,500.
Put value: the investor owns the put, so V(put) = V(putable) − V(straight) = 1,04,300 − 1,02,000 = ₹2,300.
Yield: the three bonds have the same coupon and maturity, so the highest price gives the lowest yield-to-maturity. Putable at ₹1,04,300 is the highest price, so it has the lowest yield-to-maturity. This matches the rule that investor-held options reduce yield. The callable bond at ₹98,500 has the lowest price, so it has the highest yield-to-maturity.
Yield-to-maturity is calculated on the stated cash flows to maturity. It ignores the call (and the put), so for the callable bond it overstates the yield an investor is likely to earn if the issuer calls the bond. Do not treat the yields-to-maturity of bonds with options as a like-for-like comparison. Use yield-to-worst or option-adjusted spread (OAS) instead.

Answer: Call value ₹3,500; put value ₹2,300; the putable bond has the lowest yield-to-maturity because it has the highest price for the same coupon and maturity. The callable bond's yield-to-maturity assumes no call and overstates its likely yield, so compare bonds with options using yield-to-worst or OAS.

Example 2

A convertible bond has face value of ₹1,00,000 and a conversion ratio of 40 shares. The share price is ₹2,200. The straight bond value (using the yield of a comparable non-convertible bond) is ₹86,000. The convertible trades at ₹1,02,000. Questions: (1) What is the conversion value? (2) What is the implied value of the option? (3) If share price volatility rises, what happens to the convertible value, all else equal?

Show the solution

Conversion value = share price × conversion ratio = 2,200 × 40 = ₹88,000. This is the value of the shares if the holder converts now. It is not the option value.
Implied option value = convertible price − straight bond value = 1,02,000 − 86,000 = ₹16,000.
Check: the minimum value of a convertible is the greater of its conversion value and its straight value. Here that is the greater of ₹88,000 and ₹86,000, which is ₹88,000. The price of ₹1,02,000 is above this floor, so it is consistent. The ₹16,000 option value is the intrinsic value of the conversion option, 88,000 − 86,000 = ₹2,000, plus time value of ₹14,000.
The holder owns a call on the stock. Higher share price volatility raises the call value. The straight bond value is unchanged because only equity volatility changes, so the convertible value rises.

Answer: Conversion value ₹88,000; implied option value ₹16,000 (₹2,000 intrinsic value plus ₹14,000 time value); the convertible value rises.

Exam tips

Start every question by writing who owns the option. The sign of the whole answer follows from that.
Memorise the direction checks: callable ≤ straight, putable ≥ straight. Use them to remove wrong options fast.
Read the vignette for call dates, call price and the issuer's refinancing view. Questions often hinge on whether calling is likely in a falling-rate scenario.
For convertibles, note which yield was used for the straight bond. Questions test whether you separate straight value from option value.
There is no penalty for wrong answers, so answer every question, even when you are short of time.

Embedded Options in Bonds: Types and Features 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 IEmbedded Options and Contingency Provisions

Embedded Options in Bonds: Types and Features: frequently asked questions

What is the difference between a callable and a putable bond?

A callable bond gives the issuer the right to redeem early, so it lowers the bond's value and requires a higher yield. A putable bond gives the investor the right to sell back to the issuer, so it raises value and allows a lower yield. The option owner is the key difference.

How do embedded options affect bond value?

Options owned by the investor, such as puts, floors and conversion rights, add to bond value. Options owned by the issuer, such as calls and caps, subtract from it. Higher interest rate volatility raises the value of the option itself.

Why do convertible bonds have lower coupons?

The holder owns a call option on the issuer's shares, which has value. The investor pays for it by accepting a lower coupon or yield than a straight bond would give.

Do caps and floors apply only to floating-rate bonds?

In this topic they apply to floating-rate bonds. A cap limits the coupon rate and benefits the issuer. A floor sets a minimum coupon and benefits the investor.