12. ABC, Inc., entered a forward rate agreement (FRA) to receive a rate of 3.75% with continuous compounding on a principal of USD 1 million between the end of year 1 and the end of year 2. Assume the following zero rates with continuous compounding:

What is the value of the FRA when the deal is just entered?

A. USD 35,629

B. USD 34,965

C. USD 664

D. USD 0

Correct answer is Dfficeffice" />

The value of an FRA is:

       L * (Rk ? Rf) * (T2 ? T1) * e?R2T2

Where

       L: principal

       Rf: Market quoted forward rate between T2 and T1

       Rk: FRA interest rate to be earned between T2 and T1

       Ri: Actual zero rates observed when deal is entered

The continuous compounding forward rate between year 1 and year 2 is then:

       ln(e 0.035 * 2 / e 0.0325 * 1) = 0.0375

The value of the FRA is then

       V = $1,000,000 * (0.0375 ? 0.0375) * (2 ? 1) * e ?0.035 * 2 = $0

Only answer D is correct.

Reference: John Hull, Options, Futures, and Other Derivatives, 5th ed. (ffice:smarttags" />New York:

Prentice Hall, 2003), Chapter 5.

Type of Question: Market Risk