Hull: Options, Futures, and Other Derivatives, Ninth Edition Chapter 9: OIS Discounting, Credit Issues, and Funding Costs Multiple Choice Test Bank: Questions with Answers 1. Prior to the credit crisis that started in 2007 which of the following was used by derivatives traders for the discount rate when derivatives were valued A. The Treasury rate B. The LIBOR rate C. The repo rate D. The overnight indexed swap rate Answer: B Derivatives markets used LIBOR as the discount rate pre-crisis. 2. Since the credit crisis that started in 2007 which of the following have derivatives traders used as the risk-free discount rate for collateralized transactions A. The Treasury rate B. The LIBOR rate C. The repo rate D. The overnight indexed swap rate Answer: D Derivatives markets have used the OIS rate as the discount rate for collateralized transactions since the crisis. 3. Which A. B. C.
of the following is true OIS rates are less than the corresponding LIBOR/swap rates OIS rates are greater than corresponding LIBOR/swap rates OIS rates are sometimes greater and sometimes less than LIBOR/swap rates D. OIS rates are equivalent to one-day LIBOR rates Answer: A
OIS rates are less than LIBOR /swap rates when both have the same maturity.
4. Which of the following describes a 3-month overnight indexed swap (OIS)? A. A fixed rate is exchanged for the overnight rate every day for three months B. LIBOR is exchanged for the overnight rate every day for three months C. The arithmetic average of overnight rates is exchanged for a fixed rate at the end of three months
D. The geometric average of overnight rates is exchanged for a fixed rate at the end of three months Answer: D The OIS rate is the rate exchanged for the geometric average of overnight rates. In the U.S. the overnight rate is the fed funds rate 5. Suppose that OIS rates for all maturities are 2.5% and swap rates for all maturities are 3%. Which of the following is true? A. Forward LIBOR rates are greater when OIS discounting is used than when LIBOR discounting is used B. Forward LIBOR rates are less when OIS discounting is used than when LIBOR discounting is used C. Forward LIBOR rates are the same for both OIS discounting and LIBOR discounting D. Either A or B can be true Answer: C When the yield curves are flat, all forward LIBOR rates are 3% regardless of whether OIS or LIBOR discounting is used. This is because, when all forward LIBOR rates equal 3%, all exchanges on all swaps are worth zero regardless of the discount rate used. 6. CVA stands for A. Collateral value adjustment B. Credit value adjustment C. Credit value agreement D. Collateral value agreement Answer: B CVA stands for credit value adjustment 7. In a fully collateralized transaction which of the following leads to a pricing adjustment A. The rate paid on cash collateral is the fed funds rate B. The rate paid on cash collateral is greater than the fed funds rate C. The rate paid on cash collateral is less than the fed funds rate D. Both B and C Answer: D If the rate paid on cash collateral is different from the fed funds rate then an adjustment is necessary. The OIS rate is linked to the fed funds rate and is the rate used for discounting fully collateralized transactions. 8. When A. B. C.
a bank’s borrowing rate goes up, which of the following is true DVA increases so that the bank’s profit goes down DVA increases so that the bank’s profit goes up DVA declines so that the bank’s profit goes down
D. DVA declines so that the bank’s profit goes up Answer: B The bank is considered more likely to default. Its DVA therefore increases and this increases its profit because it is then considered more likely that it will default and not have to meet derivatives obligations. 9. In October 2008 the three-month LIBOR-OIS spread rose to A. 231 basis points B. 364 basis points C. 450 basis points D. 520 basis points Answer: B In October 2008 the three-month LIBOR-OIS spread rose to 364 basis point, a record. 10.As a bank`s borrowing rate increases, which of the following is true if a bank calculates FVA A. FVA increases B. FVA declines C. FVA stays the same D. FVA may increase or decline. Answer: A FVA is the funding value adjustment. As borrowing costs increase it costs the bank more to fund its operations and FVA increases. (In theory, as explained in the text, funding value adjustments should not be made but in practice they are often made.)
11.Which of the following is true A. CVA and DVA can be calculated deal by deal B. CVA and DVA must both be calculated for the whole portfolio a bank has with a counterparty C. CVA can be calculated deal by deal but DVA must be calculated for a portfolio D. DVA can be calculated deal by deal but CVA must be calculated for a portfolio Answer: B Because of netting, all derivatives in a portfolio are considered to be a single derivative in the event of a default. CVA which measures the cost of a counterparty default and DVA which measures the benefit of the bank defaulting must therefore be calculated on a portfolio basis.
12.Which of the following is true when a bank uses OIS discounting for valuing a LIBOR-for-fixed swap A. The LIBOR/swap zero curve is calculated before the OIS zero curve B. The OIS zero curve is calculated before the LIBOR/swap zero curve C. The swap is valued using OIS forward rates and OIS discounting D. The forward rates are calculated from the bank’s borrowing costs Answer: B First the OIS zero curve is calculated. LIBOR forward rates are then calculated so that all swaps when entered into at mid-market swap rates have zero value 13.It is assumed that a company can default after one year or after two years. The probability of default at each time is 1.5%. The present value of the expected loss to a bank on a derivatives portfolio if the company defaults after one year is estimated to be $1 million. The present value of the expected loss if it defaults after two years is estimated to be $2 million. Which of the following is the bank’s CVA ? A. $3,000,000 B. $300,000 C. $450,000 D. $150,000 Answer: C The present value of the expected loss is 0.015×$1,000,000 + 0.015×$2,000,000 or $450,000. This is the CVA. 14.Accountants like to value a derivatives portfolio at A. The bid price B. The offer price C. The exit price D. Original cost less depreciation Answer: C Accountants like to value a derivatives position at the exit price. This is the price at which the bank could trade out of the position or enter into an offsetting transaction. 15.In the A. B. C. D.
U.S., which of the following is true about Treasury instruments Their income is not subject to tax at the state level Their income is not subject to tax at the federal level Both A and B are true They are not subject to capital gains tax at the federal level
Answer: A Income from Treasury instruments is not subject to tax at the state level. This is one of the reasons why the yield on Treasuries is lower than the yield on other instruments that have very little credit risk.
16.Suppose that OIS rates of all maturities are 6% per annum, continuously compounded. The one-year LIBOR rate is 6.4%, annually compounded and the two-year swap rate for a swap where payments are exchanged annually is 6.8%, annually compounded. Which of the following is closest to the LIBOR forward rate for the second year when LIBOR discounting is used and the rate is expressed with annual compounding A. 7.199% B. 7.221% C. 7.223% D. 7.225% Answer: C When LIBOR discounting is used, the OIS rates are irrelevant. The two year LIBOR/swap zero rate, R, is given by
6.8 106.8 100 1.064 (1 R ) 2 so that R=6.8137%. We can calculate the forward rate from the one- and twoyear zero rates as 1.0681372/1.064−1 or 7.223%
17.Suppose that OIS rates of all maturities are 6% per annum, continuously compounded. The one-year LIBOR rate is 6.4%, annually compounded and the two-year swap rate for a swap where payments are exchanged annually is 6.8%, annually compounded. Which of the following is closest to the LIBOR forward rate for the second year when OIS discounting is used and the rate is expressed with annual compounding? A. 7.199% B. 7.221% C. 7.223% D. 7.225% Answer: D In the two-year swap the forward rate corresponding to the first exchange is the one-year zero rate or 6.4%. This means that, when a fixed rate is paid the value of that exchange per $100 of principal is $100×(0.064-0.068)e −0.06×1 =-$0.3767. If F is the forward rate for the second year we must have (F-0.068)e-0.06×2 =0.3767 so that F=0.07225. 18.Which of the following involves most credit risk A. Exchange trading B. OTC trading with a central clearing party being used C. OTC trading with bilateral clearing and collateral being posted D. OTC trading with bilateral clearing and no collateral being posted
Answer: D In the case of both exchange trading and trading using a CCP initial margin and variation margin have to be posted so that the risk of a loss because of a default is low. Bilateral clearing usually involves more credit risk than exchange/CCP trading and credit risk is greater when there is no collateral agreement. 19.A bank has three uncollateralized transactions with a counterparty worth + $10 million, −$20 million and +$25 million. A netting agreement is in place. What is the maximum loss if the counterparty defaults today. A. $15 million B. $35 million C. $20 million D. Zero Answer: A The netting agreement means that the three transactions are considered to be a single transaction. The net value of the transactions to the bank is 10−20+25 or $15 million. This is the maximum amount that could be lost if the counterparty defaults today. 20.Since the 2008 credit crisis A. LIBOR has replaced OIS swaps B. OIS has replaced LIBOR swaps C. LIBOR has replaced OIS D. OIS has replaced LIBOR
as the discount rate for non-collateralized as the discount rate for non-collateralized as the discount rate for collateralized swaps as the discount rate for collateralized swaps
Answer: D OIS has replaced LIBOR as the discount rate for collateralized derivatives.
