Cap / floor / collar — concept
About this app
A rate cap is not a single instrument but a series of caplets — one bar per period. A floor bounds from below, a collar = buy cap + sell floor (free via the zero-cost snap). The forward staircase in the corridor shows which caplets bite. Debunks “a cap is one instrument with one price”.
Caps, floors and collars
A cap limits a floating borrowing rate from above. It is a series of caplets, one per interest period; each caplet is a call on that period’s forward rate and is usually priced with Black-76. A floor limits the rate from below and consists of floorlets, which are puts. A collar combines a bought cap with a sold floor, so the floor premium pays for the cap. In a zero-cost collar the two premiums cancel out.
What you see
For a given maturity with semi-annual periods, the app draws one bar per caplet or floorlet. The bars differ in height because each period has its own forward rate and time to fixing; the first period, whose rate is already set today, is left out. The forward-rate steps and the strike sit in the same chart. The panel lists the cap price as the sum of caplets, the floor price, the net collar cost, the number of caplets and the most expensive caplet.
Things to try
Lower the cap strike K below the forward steps and watch the caplets become more expensive. Increase the volatility σ and the maturity T. Switch to collar and press “Set zero-cost”: the floor strike moves until the net cost is zero. Steepen the curve with the slope s and see which periods fall inside the corridor between floor and cap.
Frequently asked questions
- What is an interest rate cap?
- An interest rate cap is an agreement that limits a floating rate from above. If the reference rate in a period exceeds the cap strike, the seller pays the difference on the notional. Borrowers buy caps as insurance against rising rates.
- What is a caplet?
- A caplet is the building block of a cap for a single interest period: a call on that period’s forward rate. A cap’s price is the sum of its caplet prices, each usually valued with the Black-76 model.
- What is a zero-cost collar?
- A collar combines a bought cap with a sold floor so that the rate stays within a corridor. In a zero-cost collar the floor strike is chosen so that the floor premium exactly covers the cap premium. The borrower pays nothing upfront but gives up any benefit from rates below the floor strike.
- What can I adjust in the app?
- You choose cap, floor or collar and set the strike, volatility, maturity, short rate and curve slope. In collar mode, “Set zero-cost” moves the floor strike to a net cost of zero.
Subject: Financial derivatives
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