# Interest Rate Options

## Inhaltsverzeichnis

### Merke

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Compare and contrast interest Rate Options with forward rate agreements (FRAs).

## Interest Rate Options and FRAs

For interest rate options, the exercise price is an interest rate, and payoffs depend on a reference rate such as LIBOR.

The combination of a long interest rate call option plus a short interest rate put option has the same payoff as an FRA.

Long interest rate call + short interest rate put = FRA

 Interest Rate Option FRA Payoff is made After the option expiration At settlement

### Beispiel

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Example:

A long interest rate call and a short interest rate put is an equivalent position to:

A. a long position in a forward rate agreement.

B. a pay-fixed interest rate swap.

C. a short position in a forward rate agreement.

The answer is A. A long call and short put on interest rates is equivalent to a long position in a forward rate agreement. Both gain when forward rates increase and decline in value when interest rates decrease.

### Merke

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{*LOSnr26*}

Define interest rate caps, floors, and collars.

## Interest Rate Caps, Floors and Collars

A caplet is a European call option on interest rates. An interest rate cap is a combination of caplets, with each caplet having the same strike rate (cap rate).

A floorlet is a European put option on interest rates. An interest rate floor is a combination of floorlets, with each floorlet having the same strike rate (floor rate).

An interest rate collar is a combination of a long (short) cap and a short (long) floor on the same underlying rate with the same expiring dates.

Floating-rate loan borrowers can long a cap and short a floor to hedge the risk of interest rates.

The value of a cap or a floor is just the sum of the values of the individual caplets or floorlets.

Caps and floors pay in arrears.

### Beispiel

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Example:

An investor who bought a floating-rate security and wishes to establish a minimum periodic cash flow on his investment could:

B. sell an interest-rate floor.

C. sell an interest-rate cap.

The buyer of a floor will receive a payment when the floating rate is below the floor rate, effectively establishing a minimum rate on the floating rate security.

### Beispiel

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Example:

Buying an interest-rate cap and selling an interest-rate floor is equivalent to:

A. buying a series of interest-rate puts and selling a series of interest rate calls.

B. buying a series of interest-rate calls and selling a series of interest-rate puts.

C. buying a series of interest-rate puts and calls.

A cap is equivalent to a series of (long) interest-rate calls and selling a floor is equivalent to selling a series of interest-rate puts.