Interest Rate Put Option

CFA Level I Derivatives
#1

Hello Everyone,

Please help me to understand below mentioned :

I am not able to understand Interest Put option.

Holder has the right to make do unknown interest payment and receive fixed interest payment.

Not able to understand this definition practically.

And how Long call + Short Put = FRA

Thanks

#2

Being long on an interest put option means you will receive payments if the reference rate falls below the strike price. It’s a protection against interest rate risk to the lender. Shorting an interest put option will force you to make payments (since you’re the counterparty of a put option “longer”) when the reference rate falls below the strike price. A call option is also known as a cap, and longing it will give you the right to receive payments if the interest rate rises above the strike price.

An FRA is a forward OTC contract, fixing the interest rate to which you will make/receive payments. If you’re long, you will receive payments when the reference rate is above the the rate agreed on ex-ante, and you will make payments when the rate is below the one agreed on ex-ante. It’s basically the same as having a Long interest rate Call and a Short interest rate Put

#3

Hi Gurifissu,

You explained it correctly but still not able to draw the picture of the prcoess in mind .

Example Let say there are two parties involved A and B

A - Lender

B- Borrower

Single period (3 Month )Loan amount= $ 1 Million rate of interest is floating based on LIBOR = 4%+LIBOR =5% Assumed LIBOR=1%

In this example A has a downside risk so he will buy interest put option strike price = 5% , Notional amount = 1 million expire after 3 month.

And B has upside risk so he will buy interest call option with above mentioned details.

Correct me if I am wrong in above scenario.

Now according you FRA instrument is meant for lenders only . so if A go for FRA then payoff will be like

= 1,000,000(LIBOR-5%) - 1,000,000(5%-LIBOR)

Thnaks

#4

First, to be clear, the combination of a long position in an interest rate call and a short position in an interest rate put (same expiration, same notional, same fixed rate, same floating rate, same loan period) is equivalent (but not identical) to a long position in an FRA.

Consider what happens with the option portfolio in the three possible scenarios at expiration:

  • If the floating rate is higher than the fixed rate, then
    • the call expires in the money and you get paid the difference between the floating rate and the fixed rate (on the notional amount, for the loan period), and
    • the put expires out of the money so you neither gain nor lose on it
  • If the fixed rate is higher than the floating rate, then
    • the call expires out of the money so you neither gain nor lose on it, and
    • the put expires in the money and you have to pay the difference between the floating rate and the fixed rate (on the notional amount, for the loan period)
  • If the floating rate and the fixed rate are equal, both options expire at the money, so you neither gain nor lose on them

Now consider what happens with the FRA in those same scenarios at expiration:

  • If the floating rate is higher than the fixed rate, then you get paid the difference between the floating rate and the fixed rate (on the notional amount, for the loan period), and
  • If the fixed rate is higher than the floating rate, then you have to pay the difference between the floating rate and the fixed rate (on the notional amount, for the loan period)
  • If the floating rate and the fixed rate are equal you pay nothing and you are paid nothing

As you can see, in all scenarios, the payoffs are the same.

(The reason that they’re not identical is that the payoffs for the option portfolio will occur at the end of the loan period, whereas the payoffs for the FRA will occur at the beginning of the loan period, the end-of-period payoffs being discounted to the beginning at the floating rate.)

3 Likes
#5

Thanks Magician :slight_smile:

#6

You’re quite welcome.