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P2.T5.506. Risk-free rate versus LIBOR and the overnight indexed swap (OIS) rate

Nicole Seaman

Director of FRM Operations
Staff member
Learning outcomes: Explain the main considerations in choosing a risk-free rate for derivatives valuation. Describe the OIS rate and the LIBOR-OIS spread, and explain their uses.


506.1. With respect to the risk-free rate, LIBOR, and the overnight indexed swap (OIS) rate, consider the following five statements:
(Source: Hull, Options, Futures, and Other Derivatives, Pearson; 9 edition (January 25, 2014))

I. Among derivatives traders and market participants, the most common assumption for the risk-free rate is U.S. Treasury bills, notes and bonds.​
II. Following the credit crisis, banks have abandoned LIBOR as the risk-free rate for non-collateralized transactions​
III. An overnight indexed swap (OIS) is a swap where a fixed rate (i.e., the OIS rate) for a period (e.g., one month, three months) is exchanged for the geometric average of the overnight rates (e.g., Federal Funds rate in the U.S.) during the period​
IV. Three-month LIBOR rate is normally higher than the three-month OIS rate because there more risk in making a single three-month loan to a creditworthy bank than a series of overnight loans to creditworthy banks​
V. LIBOR is the rate of interest at which AA-rated banks borrow for periods up to 12 months from other banks.​

According to Hull, which of the above statements is (are) true?

a. None are true
b. I. and II. only are true
c. III., IV. and V. are true
d. All are true

506.2. Which of the following is the most accurate statement about the LIBOR-OIS spread?

a. Due to arbitrage opportunities in highly liquid markets, and given equivalent risk factors, the LIBOR-OIS spread should almost never deviate much from zero
b. The three-month LIBOR-OIS is a measure of stress in financial markets because it tends to increase when banks become reluctant to lend to each other
c. The three-month LIBOR-OIS has generally been discarded as a measure of stress because it barely reacted (i.e., it neither narrowed nor widened) during the Global Financial Crisis (GFC)
d. The natural state of the 3-month LIBOR-OIS spread is negative due to the expectation that the 3-month OIS rate should be higher than the 3-month LIBOR rate

506.3. Suppose that the 1-year LIBOR rate is 2.0% and the 2-year LIBOR-for-fixed swap rate with annual payments is 3.0%. The OIS zero curve has been calculated and the OIS rates are 100 basis points: the 1-year OIS zero rate is 1.0% and the 2-year OIS zero rate is 2.0%. Both LIBOR and OIS rates are annually compounded. If a bank uses OIS rates for discounting, which is nearest to the implied forward LIBOR rate for the one-year period beginning in one year?

a. 3.030%
b. 3.040%
c. 4.030%
d. 4.040%

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