The one-month (31-day) GC repo rate for French government bonds is quoted to you at 3.75-80%. As collateral, you are offered EUR25 million nominal of the 5.5% OAT April 2006, which is worth EUR 28,137,500. If you impose an initial margin of 1%, the Repurchase Price is:
A) EUR 27,947,276.43
B) EUR 27,946,077.08
C) EUR 27,950,071.43
D) EUR 27,948,871.97

Question

Quizplus · Accepted Answer

To calculate the repurchase price, we need to use the formula:

Repurchase Price = Market Value of Securities - Margin + Interest

Market Value of Securities = EUR 28,137,500
Margin = 1% of Market Value of Securities = EUR 281,375

To calculate the interest, we need to convert the annual GC repo rate into a rate for 31 days:

GC Repo rate for 31 days = (3.75 + 3.80) / 2 / 100 * 31 / 365 = 0.000973

Therefore, the interest = Market Value of Securities * GC Repo rate for 31 days = EUR 28,137,500 * 0.000973 = EUR 27,495.08

Now, we can calculate the repurchase price:

Repurchase Price = EUR 28,137,500 - EUR 281,375 + EUR 27,495.08 = EUR 27,948,871.97

The One-Month (31-Day) GC Repo Rate for French Government Bonds