Interest Rate Cap

A borrower paying a floating rate has one fear: that the rate goes up. An interest rate cap puts a ceiling on that fear.

The workbook defines it as a series of interest rate call options (called caplets) in which the buyer receives a payment at the end of each period when the underlying interest rate is above a rate agreed in advance (the strike rate).

Read that as insurance renewed every period. Each caplet covers one interest period. If the benchmark ends up above the strike, that caplet pays the difference; if not, it expires worthless and the buyer has lost only his share of the premium. The borrower still pays the floating rate to his lender — the cap simply hands back whatever part of it exceeds the strike.

It is a call because the buyer profits when the rate rises. That is the opposite of a call on a bond, which profits when the price rises and therefore when rates fall.

Two places the idea appears. Chapter 1 describes caps embedded in floating rate bonds: an FRB issuer may cap its interest payment obligation if rates rise. Chapter 2 describes the stand-alone derivative. Caps are OTC products. In the workbook's comparison of exchange traded and OTC interest rate options, the OTC column lists European interest rate options including caps, floors, collars and reverse collars, along with swaptions and structured products. Exchange traded interest rate options in India are standardised premium-style European calls and puts on bonds — not caps.

What defines one. An underlying floating rate, a strike rate, a notional principal, a series of periods (and so a series of caplets), and a premium paid by the buyer. The notional, as with a swap or FRA, is never exchanged; it only sizes the payments.

How each caplet pays. Applying the definition period by period — and the same period-fraction convention the workbook uses for FRAs — a caplet pays:

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

How it is valued. The workbook names the Black (1976) model — which substitutes the discounted futures or forward price for the spot price in Black–Scholes — and lists interest rate caps and floors among its primary applications, together with options on futures, bond options and swaptions.

The OTC trade-off. Like all OTC interest rate options, a cap can be custom designed in size, dates and terms, but it is priced through negotiation, is less liquid, and carries counterparty risk that an exchange-traded option removes.

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

Cap pay-off      = Σ caplet pay-offs
Net benefit      = Cap pay-off − Premium paid

  N = notional principal   r_i = underlying rate for period i
  K = strike (cap) rate    m   = months in the period

Illustrative numbers. The premium is assumed.

A manufacturer has borrowed Rs 50 crore at a floating rate reset quarterly. It buys a one-year cap at a strike of 7 percent on the same benchmark and notional — four quarterly caplets — for an upfront premium of Rs 15,00,000.

Net of the premium the cap returned Rs 2,50,000. More usefully, in quarters 2 and 3 the company's borrowing cost above 7 percent was paid back to it: whatever the benchmark did, it never paid more than 7 percent plus the premium.

Had rates stayed below 7 percent all year, every caplet would have expired worthless and the company would be out Rs 15,00,000 — the price of the ceiling, paid whether or not the ceiling was needed.

Chapter 2 (Interest Rate Derivatives), section 2.2.3 on options, defines the interest rate cap alongside the floor, collar and reverse collar. Chapter 4 (Exchange Traded Interest Rate Options) names the Black (1976) model as the one used for caps and floors, and its comparison of exchange traded and OTC interest rate options lists caps among OTC products. Expect definition questions — caplets are calls, floors are puts — and the distinction between these OTC structures and exchange traded bond options.

• A cap is a series of calls on the interest rate, not a single option and not a put.
• A call on a rate profits when rates rise; a call on a bond profits when rates fall. Keep the underlying straight.
• The buyer receives a payment only when the rate is above the strike, at the end of the period.
• Caps, floors and collars are OTC products in the workbook, not exchange traded interest rate options.
• The notional principal is not exchanged. It only sizes each caplet's payment.
• The Black (1976) model, not plain Black–Scholes on spot, is the model the workbook associates with caps and floors.
• The premium is paid whether or not any caplet pays.