Why is an interest rate floor equivalent to a portfolio of put options on interest rates?

This is a concept that trips up many candidates because we typically think of puts as being on assets with prices, not on interest rates. The key insight is understanding the relationship between interest rates and bond prices.

What Is an Interest Rate Floor?

An interest rate floor is a contract that pays the holder whenever the reference rate (e.g., SOFR) falls below a specified floor rate. It protects floating-rate lenders (or investors in FRNs) against declining rates.

A floor consists of a series of individual floorlets, each covering one reset period.

Each Floorlet = Put Option on the Reference Rate

A floorlet pays: max(0, Floor Rate - Reference Rate) x Notional x Day Count Fraction

This has exactly the same structure as a put option payoff: max(0, K - S)

• K = Floor Rate
• S = Reference Rate

When the reference rate falls below the floor rate, the floorlet pays the difference — just like a put pays when the asset price falls below the strike.

Example — Sandoval Capital FRN Protection

Sandoval Capital holds a $20M floating rate note paying SOFR + 1.50%, reset quarterly. They buy a 2-year floor at 3.00% to guarantee minimum income.

The floor consists of 8 floorlets (one per quarter over 2 years).

Quarter 3 scenario: SOFR = 2.40%

Floorlet payout = max(0, 3.00% - 2.40%) x $20M x (90/360)

= 0.60% x $20M x 0.25

= $30,000

Sandoval's FRN pays: (2.40% + 1.50%) x $20M x 0.25 = $19,500

Floor payout: $30,000

Effective income: $19,500 + $30,000 = $49,500

This equals what they'd earn if SOFR were 3.00%: (3.00% + 1.50%) x $20M x 0.25 = $22,500 per quarter... Wait, let me recalculate properly.

Actually: The floor guarantees minimum coupon based on the floor rate:

• Effective minimum rate = max(SOFR, Floor Rate) + Spread = max(2.40%, 3.00%) + 1.50% = 4.50%
• Income at 4.50% = $20M x 4.50%/4 = $22,500/quarter

Symmetry with Caps:

Why Floorlets = Puts on FRAs or Calls on Bond Prices:

There's a duality: since bond prices and interest rates move inversely, a put on rates is equivalent to a call on bond prices. Each floorlet can also be viewed as a call option on a zero-coupon bond with face value at the payment date. This is how they're actually priced using the BSM framework — you can't directly apply BSM to interest rates, but you can apply it to bond prices.

Exam Tip: CFA Level II may ask you to identify the equivalent option structure for caps and floors. Remember: caps = calls on rates = puts on bonds; floors = puts on rates = calls on bonds.

Explore interest rate derivatives in our CFA Level II course.