Question

On the 15th of May 2012 you enter a Forward Rate Agreement (FRA) to borrow on the 15th of September 2012 $1’000’000 for 7 months at a fixed annualized interest rate of 5% (for a FRA with a contract length of 7 months the compounding frequency is 12 7 -times c.p.a.). What is the value of the FRA for you as a borrower on the 15th 3 of August 2012 if (on the 15th of August) the 1-month spot rate is 3% (semi-annual compounded) and the 8-month spot rate is 5% (monthly compounded)?

Answer 1

On 15th August  

1 month spot rate = 3% semiannually compounded or (1+0.03/2)^(1/6)-1 =0.002484517 for one month

8 month spot rate = 5% monthly compounded or (1+0.05/12)^8-1 =0.033823517 for 8 months

So,

Forward rate for the period from 15th Sep 2012 for 7 months = (1+0.033823517)/(1+0.002484517)-1 =0.031261331

Contracted borrowing rate = 1.05^(7/12)-1 =0.02886981

So, Value of FRA after 7 months from 15th Sep, 2012 (or 8 months from 15th August,2012)

=$1000000*(0.031261331- 0.02886981) = $2391.52

So, Value of FRA as a borrower on 15th Aug = 2391.52/1.033823517 = $2313.28

So, the value of FRA as a borrower on 15th Aug is $2313.28