FRAs vs Interest Rate Options

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allalongthewatc

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Hello All,
For computing the payment to long, the curriculum says that the interest savings are discounted by a factor of (1/1+rf*90/360) where, rf = risk-free rate; However, I didn’t see such discounting for Interest rate options. Considering that both are paid in arrears, I am not sure why the two are different. Can someone please help me?
In other words, for FRAs, Interest = (Interest rate - base rate) 90/360 * Notional Amount;
And Actual payment = Interest/ (1+base rate *90/360).
However, for Interest Rate options, the book mentions that Interest = (Strike Rate - Exercise Rate) 90/360 * Notional Amount. No discounting is done.
Any thoughts?
Best regards
 
FRAs are not settled in arrears; the payoff is computed for settlement in arrears, then discounted and settled in advance.
A 4 × 7 FRA, for example, will have the payoff computed as of 210 days from today, but that will be discounted and settled 120 days from today.
 
S2000magician wrote:
FRAs are not settled in arrears; the payoff is computed for settlement in arrears, then discounted and settled in advance.
A 4 × 7 FRA, for example, will have the payoff computed as of 210 days from today, but that will be discounted and settled 120 days from today.
Click to expand...
Hello S2000magician,
I didn’t follow your reply. From what I have understood: for 4X7, the FRA contract will expire in 4*30= 120 days, and at expiration the underlying 90-day rate will be used. Moreover, the payment will not be made at expiration but 90 days after the contract expiration. Isn’t this payment in arrears by incurring debt? Hence, we will have to discount the payment by (1+underlying 90-day rate) because the payment will be made in future.
However, I am not sure why the risk-free rate is not used for discounting interest rate options, just as we do for FRAs above? Am I missing anything? Can you please help me?
Thank in advance.
 
FRAs are settled in advance, at the expiration of the FRA, not at the end of the loan period. We discount at the LIBOR spot rate applicable for the loan period; in the case of the 4 × 7 FRA, we discount at the 90-day LIBOR rate that exists on day 120.
Take a look at the article I wrote on FRAs: http://financialexamhelp123.com/fras/.
 
S2000magician wrote:
FRAs are settled in advance, at the expiration of the FRA, not at the end of the loan period. We discount at the LIBOR spot rate applicable for the loan period; in the case of the 4 × 7 FRA, we discount at the 90-day LIBOR rate that exists on day 120.
Take a look at the article I wrote on FRAs: http://financialexamhelp123.com/fras/.
Click to expand...
Thank you S2000magician for sending me an excellent article. FRA part is now clear. Can you please explain why for Interest Rate Options, Actual payment = Interest/ (1+base rate *90/360). As we do for FRA, why dont we discount using the reference rate in the denominator? 1+3.6%(912)
I read and re-read the curriculum, but I couldn’t find any explanation. I would appreciate your help.
Thanks in advance1+3.6%(912)
 
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