CFA Level I Exam · Forward Commitment and Contingent Claim Features and Instruments

Interest Rate Caps, Floors, Swaptions and Convertible Bonds

Updated 7 October 2026 · Fact-checked

A cap is a series of interest rate calls that pays when a reference rate exceeds the strike. A floor is a series of puts that pays when the rate falls below it. A swaption is an option to enter a swap. Embedded options (call, put, conversion) change a bond's value and risk.

Understand Other Contingent Claims: Caps, Floors, Swaptions and Convertibles

A contingent claim gives one side a right, not an obligation. The buyer pays a premium up front. The seller takes the premium and accepts the risk. Caps, floors and swaptions are interest rate options. Callable, putable and convertible features are options built into bonds.

An interest rate cap is a series of interest rate call options, called caplets, on a reference rate such as SOFR or Euribor. Each caplet pays if the rate at its reset date is above the strike. A borrower with a floating-rate loan buys a cap to set a ceiling on the interest cost. An interest rate floor is a series of interest rate put options, called floorlets. Each floorlet pays if the rate is below the strike. A lender or floating-rate investor buys a floor to protect income. Combining a long cap and a short floor is a collar. The premium received on the floor cuts the cost of the cap.

A swaption is an option on a swap. A payer swaption gives the right to pay fixed and receive floating at a set fixed rate. It gains when swap rates rise. A receiver swaption gives the right to receive fixed and pay floating. It gains when swap rates fall. The exercise rate is the fixed rate of the underlying swap. Think of a payer swaption as a call on the swap rate and a receiver swaption as a put on the swap rate.

Embedded options sit inside a bond. A callable bond lets the issuer buy the bond back at a set price. The issuer holds the option, so the bond is worth less than an otherwise identical option-free bond: callable price = option-free price − call option value. A putable bond lets the investor sell the bond back at a set price. The investor holds the option, so the bond is worth more: putable price = option-free price + put option value. A convertible bond lets the investor exchange the bond for a fixed number of the issuer's shares. The investor holds a call option on the stock, so the bond is worth more than a straight bond: convertible price = straight bond value + conversion option value. Investors accept a lower coupon for that option.

The same logic applies to asset-backed securities. Borrowers in a mortgage pool can prepay, which is a call option held by the borrower. That is why mortgage-backed securities show prepayment risk and negative convexity when rates fall.

Key formulas to remember

Caplet payoff (per period): Notional × max(0, reference rate − cap strike) × (days ÷ 360 or period fraction); The rate is set at the start of the period (in advance) and the payoff is made at the end (in arrears). This is the usual convention for caps and floors.
Floorlet payoff (per period): Notional × max(0, floor strike − reference rate) × period fraction; Gains when rates fall below the strike.
Collar: Long cap + short floor (borrower); long floor + short cap (lender); Premium on the short option offsets the cost of the long option.
Payer swaption: Right to pay fixed, receive floating at the exercise rate; Gains when market swap fixed rate rises above the exercise rate.
Receiver swaption: Right to receive fixed, pay floating at the exercise rate; Gains when market swap fixed rate falls below the exercise rate.
Callable bond value: Callable = option-free bond value − call option value; Issuer owns the call.
Putable bond value: Putable = option-free bond value + put option value; Investor owns the put.
Convertible bond value: Convertible = straight bond value + conversion option value; Conversion value = share price × conversion ratio. Value is at least the higher of straight value and conversion value.

How to solve Other Contingent Claims: Caps, Floors, Swaptions and Convertibles questions

Use this order for any question on interest rate options or embedded options.

1Identify who holds the option: buyer of the cap, floor or swaption, or the issuer or investor in the bond.
2Name the underlying: a floating reference rate, a swap fixed rate, a bond price or a stock price.
3Decide the direction: a cap, payer swaption or conversion option is a call; a floor, receiver swaption or put feature is a put.
4For payoff questions, compare the reference rate with the strike for each reset date and compute max(0, difference) × notional × period fraction.
5For bond value questions, start from the option-free value, then subtract options held by the issuer and add options held by the investor.
6Check who gains when rates move: the buyer's loss is limited to the premium; the seller's loss can be large. A short cap or short call has unlimited loss. A short floor's loss is limited but can be large. It is about strike × notional × period fraction per floorlet if the rate falls to zero, and a little more if rates go slightly negative, as has happened in Europe and Japan.
7Eliminate options that reverse the direction or the holder, then pick the remaining one.

Quickest way: Holder and direction check

When to use it: Use for conceptual three-option MCQs on who benefits, how a feature changes price, or which instrument fits a hedge.

Ask: does the borrower fear rates rising? Cap or payer swaption. Fear of rates falling? Floor or receiver swaption.
Ask: who owns the embedded option? Issuer's option lowers the bond price and raises the yield. Investor's option raises the price and lowers the yield.
For payoffs, check only whether the option is in the money. If not, the payoff is zero.
Cross out any answer that gives the option buyer a loss larger than the premium. The seller's loss can be large. It is unlimited for a short cap or short call. For a short floor, the loss is limited: at most about strike × notional × period fraction if the rate falls to zero. Rates can go slightly negative, so the loss can be a little larger than that.

Common mistakes in Other Contingent Claims: Caps, Floors, Swaptions and Convertibles

Treating a cap as a single option rather than a series of caplets.
The word cap sounds like one contract on one date.
Fix: Remember a cap covers many reset dates and pays separately on each where the rate exceeds the strike.
Mixing up payer and receiver swaptions.
Students focus on the word swaption rather than the fixed leg.
Fix: Payer pays fixed, so it gains when rates rise. Receiver receives fixed, so it gains when rates fall.
Adding the call option value to a callable bond.
Options usually have positive value, so students add them.
Fix: The issuer holds the call, so subtract it from the option-free price.
Forgetting the period fraction in the caplet payoff.
Rates are quoted annually but reset periods are shorter.
Fix: Multiply by days ÷ 360 or the stated fraction, such as 0.25 for quarterly.
Assuming a convertible is always worth its conversion value.
Students ignore the straight bond floor.
Fix: Value is at least the greater of conversion value and straight bond value, and normally trades above that floor because of the option's time value.

Worked examples

Example 1

A borrower holds a one-year floating-rate loan on €50,000,000, reset quarterly, and owns a cap with strike 3.00%. At one reset the reference rate is 3.60% for a 90-day period (use 90 ÷ 360). What is the caplet payoff for that period?

Show the solution

The rate 3.60% is above the strike 3.00%, so the caplet is in the money.
Rate difference = 3.60% − 3.00% = 0.60% = 0.0060.
Period fraction = 90 ÷ 360 = 0.25.
Payoff = €50,000,000 × 0.0060 × 0.25 = €75,000.

Answer: €75,000, paid at the end of the period.

Example 2

A convertible bond has a straight bond value of $940 and a conversion option valued at $85. The conversion ratio is 20 and the share price is $44. What is the bond's theoretical value and the conversion value?

Show the solution

Convertible value = straight bond value + conversion option value = 940 + 85 = $1,025.
Conversion value = share price × conversion ratio = 44 × 20 = $880.
Conversion value $880 is below the straight value $940, so the bond trades mainly on its bond features, with the option adding $85.
Check against the floor: $1,025 is above the straight value of $940 and above the conversion value of $880, so it is consistent with the value being at least the higher of the two.

Answer: Theoretical value is $1,025 and conversion value is $880. The $1,025 exceeds both the straight value ($940) and the conversion value ($880), as the floor requires.

Exam tips

Questions often ask who benefits from a rate move. Decide the holder and direction first.
Callable and putable bond questions test the sign of the option value, so check whether you add or subtract.
Expect conceptual wording on collars: a borrower's collar is a long cap and a short floor.
For a caplet payoff, compute the difference first. If it is negative, the answer is zero, so eliminate any negative option.

Practice questions from Forward Commitment and Contingent Claim Features and Instruments

Other Contingent Claims: Caps, Floors, Swaptions and Convertibles in other exams

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

Other Contingent Claims: Caps, Floors, Swaptions and Convertibles: frequently asked questions

What is the difference between an interest rate cap and a floor?

A cap is a series of calls on a rate and pays when the rate is above the strike. A floor is a series of puts and pays when the rate is below the strike. Borrowers with floating debt buy caps; floating-rate lenders buy floors.

What is a swaption?

A swaption is an option to enter an interest rate swap at a set fixed rate. A payer swaption gives the right to pay fixed and receive floating. A receiver swaption gives the right to receive fixed and pay floating.

Why is a convertible bond a contingent claim?

The investor has the right, not the obligation, to exchange the bond for shares. That right is a call option on the issuer's stock embedded in the bond. It adds value, so the coupon is usually lower than on a straight bond.

Does a callable bond have a higher or lower price than an option-free bond?

Lower, because the issuer owns the call and can redeem the bond when rates fall. Investors demand a higher yield to compensate. The price equals the option-free price minus the call option value.