Interest Rate Floor

An interest rate floor is the mirror image of a cap.

The workbook defines it as a series of interest rate put options in which the buyer receives a payment at the end of each period when the underlying interest rate is below the strike rate.

Who wants that? Anyone whose income falls when rates fall. Chapter 1 of the workbook describes the same protection embedded in a floating rate bond: the bond may provide for a floor beyond which the interest rate will not fall, in order to protect the interest of the investors, who would otherwise earn less every time the benchmark drops. A floor tops that income back up to the strike, period by period, in exchange for a premium paid upfront.

It is a put because the buyer gains when the rate falls. Once again, that is the reverse of a put on a bond, which gains when the price falls — that is, when rates rise.

The structure. A floor has the same components as a cap: an underlying floating rate, a strike rate, a notional principal, a series of periods — each covered by one put, sometimes called a floorlet — and a premium.

How each period pays. Applying the workbook's definition with the period fraction used in its FRA examples:

Floorlet pay-off = Notional × max(Strike rate − Underlying rate, 0) × (Months in period ÷ 12)

Where it sits. Floors are OTC interest rate options. The workbook's table of exchange traded versus OTC interest rate options places caps, floors, collars and reverse collars in the OTC column, with custom terms, negotiated prices, lower liquidity and counterparty exposure. The Black (1976) model is named as the valuation approach for caps and floors.

How floors combine. A floor is rarely the end of the story, because its premium can be used to pay for something else:

In both, the workbook specifies the same interest rate, the same maturity and the same notional principal on both legs.

For each period i:
  Floorlet pay-off_i = N × max(K − r_i, 0) × (m ÷ 12)

Floor pay-off       = Σ floorlet pay-offs
Net benefit         = Floor pay-off − Premium paid

Illustrative numbers. The premium is assumed.

A lender holds Rs 25 crore of loans earning a floating rate reset quarterly. To protect its income it buys a one-year floor at a strike of 6 percent for a premium of Rs 6,00,000.

The floor paid Rs 8,12,500 against a premium of Rs 6,00,000 — a net Rs 2,12,500. In quarters 2 and 3 the lender's loan income fell, and the floor refilled it up to the 6 percent line.

Note quarter 4. A rate equal to the strike is not below it, so nothing is paid — exactly as a put at the money is worth nothing at expiry.

If rates had risen all year, the floor would have paid nothing, the Rs 6,00,000 premium would be lost, and the lender would simply have enjoyed higher loan income.

Chapter 2 (Interest Rate Derivatives), section 2.2.3, defines the floor in the same list as the cap, collar and reverse collar. Chapter 4 (Exchange Traded Interest Rate Options) links caps and floors to the Black (1976) model and lists them among OTC interest rate options in its comparison table. Expect a matching question between the four structures and their definitions, and "series of put options" as the key phrase.

• A floor is a series of puts on the interest rate. A cap is a series of calls.
• It pays when the rate is below the strike. At the strike, nothing.
• Floor buyers are protecting income or asset returns from falling rates; cap buyers are protecting against rising borrowing costs.
• In a collar the floor is sold; in a reverse collar the floor is bought. Candidates routinely swap the two.
• Both legs of a collar share the same rate, maturity and notional.
• Floors are OTC, valued in the workbook with the Black (1976) model.
• A put on a rate gains when rates fall — the opposite of a put on a bond price.