Question #35
Reading: Reading 30 Pricing and Valuation of Forward Commitments
PDF File: Reading 30 Pricing and Valuation of Forward Commitments.pdf
Page: 15
Status: Unattempted
Part of Context Group: Q35-36
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Question
For this question only, assume that the forward price of the FRA was 2.9%. Which of the following is the closest to the value accrued on the FRA from Brodeur's perspective one month after initiation of the contract?
Answer Choices:
A. +€2,300
B. +€2,200
C. –€2,265
Explanation
The value of a FRA before expiry can be calculated by comparing the fixed rate on the
original FRA to the fixed rate on a new FRA covering the same borrowing and lending
period.
Step 1: Identify the correct MRR rates.
After 1 month has passed there is now 1 month until the original FRAs expiry and 4
months to the end of the borrowing and lending period. So we will require 30 day and 120
day MRR (i.e., (1 × 4) FRA price)
Step 2: Unannualize rates.
MRR30 day = 1.8% ×
= 0.15%
MRR120 day = 2.8% ×
= 0.9333%
Step 3: Compute the fixed rate (forward price) on a new FRA with the same expiry as the
original FRA.
Forward rate = ((1 + long rate) / (1 + short rate) – 1)(360 / 90) = 3.1286%
Step 4: Compute the gain/(loss) on FRA at the end of the borrowing/lending period.
Gain to long = (new fixed rate – original fixed rate)(days / 360)(notional)
= (0.0313 – 0.029)(90 / 360)(4m) = 2,300
Step 5: Discount the gain/(loss) from the end of borrowing and lending to the valuation
date (120 days).