FRM exam 2005

[sarita]

Kindly see the below question:

ABC in entered a forwad rate agreement ro recieve a rate of 3.75% with continuous compounding on a principal of 1million between the end of year 1 and 2. the zero rate are 3.25% and 3.50% for one and two years. What is the value of the FRA when the deal is just entered.

Solution: forward rate : 2*3.50-1*3.25=3.75% so 1000000(3.75-3.75)expo-3.5*2 = zero.

My question is: are we not supposed to use discrete rate for FRA? so whould we not convert the forward rate calculated (3.75%) from continuous to discret? by expo 3.75%-1??? i hope this answer is wrong.. cuz, i have in a few places that FRA rate must be converted to discrete.. kindly advice.

best,
s

 

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Kindly see the below question:

ABC in entered a forwad rate agreement ro recieve a rate of 3.75% with continuous compounding on a principal of 1million between the end of year 1 and 2. the zero rate are 3.25% and 3.50% for one and two years. What is the value of the FRA when the deal is just entered.

Solution: forward rate : 2*3.50-1*3.25=3.75% so 1000000(3.75-3.75)expo-3.5*2 = zero.

My question is: are we not supposed to use discrete rate for FRA? so whould we not convert the forward rate calculated (3.75%) from continuous to discret? by expo 3.75%-1??? i hope this answer is wrong.. cuz, i have in a few places that FRA rate must be converted to discrete.. kindly advice.

best,
s​

Saray,

The solution provided is definitely wrong, however the answer will be zero and they got extremely lucky.

1) As you rightly said, one needs to convert the cash flow to an annual rate from continuous compounding.
2) However, the beauty (which can definitely save a lot of time) with this problem is ABC is receiving fixed 3.75% (continuously compounded) and paying the floating rate which is also 3.75% cont. comp. (Voila!!) So the two cash flows are exactly equal and cancel each other. Hence, a value of zero. One does not even need to calculate the discrete rates.
3) However, more formally, the correct soln will look like
1,000,000((e^3.75%-1)-(e^3.75%-1))xdiscount = 1,000,000(3.82%-3.82%)xdiscount

Hope this explains.

Regards,
Alan