Question

1. A forward rate agreement (FRA) specifies the contract interest rate at 8% on a principal of $5 million for a 6-month period starting in 5 years. Given the 5-year zero rate is 10% and 5.5-year zero rate, 11%, please estimate the price of FRA.
2. Theoretically, once a trader enters into a FRA, the interest locked at the forward rate. Do you agree? Please prove your answer.

Answer 1

Actual forward rate for those six month= (1.11)^5.5/1.10^5 - 1

= 1.1023-1

= 10.23%

Now if we have not entered into a contract we have to pay 10.23% effectively and because of the contract we have to just pay 8% saving of 2.23% per annum.

Total savings = Amount*rate*Months/12

= 5000000*2.23%*6/12

= 55750

This is the value of FRA after 5.5 years

Present value = 55750/1.11^5.5

= 31402.81

Yes the statement is true unlike in the option contract owner have the right and obligation both to objet the contract and onece you enter into a contract you lockdown the future Interest rate from now as we have seen in above question if we did not enter in to a FRA we would have to pay the 11% but due to FRA we had saving in interest rate it is an simplest form on Interest rate derivatives.