Interest Rate and Currency Swaps


 Jocelin Sutton
 4 years ago
 Views:
Transcription
1 Interest Rate and Currency Swaps Eiteman et al., Chapter 14 Winter 2004 Bond Basics Consider the following: ZeroCoupon ZeroCoupon OneYear Implied Maturity Bond Yield Bond Price Forward Rate t r 0 (0,t) P (0,t) r 0 (t 1,t) 1 Year 6.00% % 2 Years 6.50% % 3 Years 7.00% % Note: the above forward rates are forward interest rates. 2
2 Bond Basics For each time to maturity t, bond prices are obtained as follows: P(0,t) = 1 ( 1 + r0 (0,t) ) t. 3 Bond Basics That is, P(0, 1) = 1 (1+r 0 (0,1)) 1 = = P(0, 2) = 1 (1+r 0 (0,2)) 2 = 1 (1.065) 2 = P(0, 3) = 1 (1+r 0 (0,3)) 3 = 1 (1.070) 3 =
3 Bond Basics For each time t 1 and t 2, the implied forward interest rate r(t 1,t 2 ) is such that (1 + r 0 (0,t 1 )) t 1 (1 + r 0 (t 1,t 2 )) t 2 t 1 = (1 + r 0 (0,t 2 )) t 2. This gives (1 + r 0 (t 1,t 2 )) t 2 t 1 = (1 + r 0(0,t 2 )) t 2 (1 + r 0 (0,t 1 )) t 1. 5 Bond Basics In the above table, we have r 0 (1,2) = (1 + r 0(0,2)) 2 (1 + r 0 (0,1)) 1 1 = (1.065)2 (1.060) 1 1 = % r 0 (2,3) = (1 + r 0(0,3)) 3 (1 + r 0 (0,2)) 2 1 = (1.070)3 (1.065) 2 1 = % 6
4 Bond Basics Note that (1 + r 0 (t 1,t 2 )) t 2 t 1 = (1 + r 0(0,t 2 )) t 2 (1 + r 0 (0,t 1 )) t 1 = P(0,t 1) P(0,t 2 ). 7 Bond Basics Combinations of actual zerocoupon bond yields also give us implied forward zerocoupon bond prices: P(t 1,t 2 ) = 1 (1 + r 0 (t 1,t 2 )) t = (1 + r 0(0,t 1 )) t1 2 t 1 (1 + r 0 (0,t 2 )) t 2 = P(0,t 2) P(0,t 1 ). 8
5 Bond Basics The implied forward zerocoupon bond prices in the present example are P(1,2) = P(0,2) P(0,1) = = P(2,3) = P(0,3) P(0,2) = = Forward Rate Agreements Consider the problem of a borrower who wishes to hedge against increases in the cost of borrowing. Suppose a firm expects to borrow $100m for 91 days, beginning 120 days from today, in June. The loan will be repaid in September. Suppose the effective quarterly interest rate at that time can either be 1.5% or 2%, implying a borrowing cost of $1.5m or $2m, a difference of $500,
6 Forward Rate Agreements To hedge against this uncertainty, the firm could enter into a forward rate agreement (FRA). A FRA is an overthecounter contract that guarantees a borrowing or lending rate on a given notional amount. FRAs can be settled either at the initiation or maturity (in arrears) of the borrowing or lending transaction. 11 Forward Rate Agreements FRAs are forward contracts based on the interest rate and do not entail the actual lending of money. The borrower who enters a FRA is paid if a reference rate is above the FRA rate, and pays if the rate is below the FRA rate. 12
7 Forward Rate Agreements FRA Settlement in Arrears Let r FRA denote the FRA rate and let r q denote the prevailing quarterly rate at the time the loan was contracted. The payment to a borrower who would have previously entered into a FRA is then ( rq r FRA ) notional principal if the FRA is settled when the loan matures. 13 Forward Rate Agreements FRA Settlement in Arrears Suppose that, in the previous example, r FRA = 1.8%. Then the firm would receive ( rq ) $100m at the end of the loan period, which means ( ) $100m = $0.3m if r q = 1.5% ( ) $100m = + $0.2m if r q = 2.0%. 14
8 Forward Rate Agreements FRA Settlement at the Time of Borrowing In this case the payment made by one of the two parties to the other is simply the amount that would have been paid at the loan maturity discounted over the loan period. In the present example, the loan period is one quarter and thus the payment to the borrower would be r q r FRA 1 + r q notional principal. 15 Forward Rate Agreements FRA Settlement at the Time of Borrowing For the firm in our example, this gives $100m = $0.296m if r q = 1.5% $100m = + $0.196m if r q = 2.0%. 16
9 Forward Rate Agreements Synthetic FRAs Note that a future lending or borrowing rate can be locked in by trading zerocoupon bonds. Suppose for example that money will be borrowed at time t and the loan will be repaid at time t + s. The borrower wants to lock in r(t,t + s) in advance. How can this be done? 17 Forward Rate Agreements Synthetic FRAs Recall that (1 + r 0 (t,t + s)) s = P(0,t) P(0,t + s), where the subscript 0 is used to emphasize the fact that this rate is determined at time 0. 18
10 Forward Rate Agreements Synthetic FRAs Take s as the reference period. That is, s could be a quarter and thus r 0 (t,t + s) a quarterly rate. Then 1 + r 0 (t,t + s) = P(0,t) P(0,t + s). 19 Forward Rate Agreements Synthetic FRAs Consider a portfolio buying 1 zerocoupon bond maturing at time t and selling short 1 + r 0 (t,t + s) zerocoupon bonds maturing at time t + s. The payoff of this portfolio is (1 + r 0 (t,t + s))p(0,t + s) P(0,t) = 0 today, +1 at time t, (1 + r 0 (t,t + s)) at time t + s. 20
11 Forward Rate Agreements Synthetic FRAs The above payoff is the same as the payoff to a borrower entering a FRA to be settled in arrears with r FRA = r 0 (t,t + s). 21 Forward Rate Agreements Synthetic FRAs If the zerocoupon bond maturing at time t + s is repaid at time t, payoffs are (1 + r 0 (t,t + s))p(0,t + s) P(0,t) = 0 today, 1 (1+r 0(t,t+s)) (1+r t (t,t+s)) = r t(t,t+s) r 0 (t,t+s) 1+r t (t,t+s) at time t, which is the payoff to a borrower entering a FRA to be settled at the beginning of the loan period with r FRA = r 0 (t,t + s). 22
12 Forward Rate Agreements Synthetic FRAs In the previous slide, r t (t,t + s) denotes the interest from time t to time t + s as determined at time t. It is the timet spot interest rate. 23 Forward Rate Agreements Synthetic FRAs Continuing the example of the firm willing to borrow $100m, suppose P(0, 211) = and P(0, 120) = The implied of forward rate for the 91day period starting 120 days from now is then P(0, 120) P(0,211) 1 = = 1.8%. So the cost of times a zerocoupon bond maturing in 211 days is the same as a zerocoupon bond maturing in 120 days. 24
13 Eurodollars Futures The Eurodollar futures contract is one of the most widely used interest rate futures contract. Take the 3month eurodollar futures as an example. The yield of a futures contract is calculated from the settlement price. If the settlement price of the 3month eurodollar future maturing in March 2005 is 95.68, the annual yield over the 3month period ending in March 2005 is expected to be = 4.32%, for a 3month rate of 1.08%. 25 Eurodollars Futures Eurodollar futures can be used to hedge against interest risk as follows: Borrower: Sell Eurodollar futures. If interest rates go up, futures prices will decrease and the gains from the futures trades will compensate for the increased borrowing costs. Lender: Buy Eurodollar futures. 26
14 Interest Rate Swaps Suppose firm XYZ borrows at the London Interbank Offered Rate (LIBOR), which is a variable rate, but would prefer paying a fixed rate. The loan contract is for 3 periods and the actual and expected rates are as in the table used before. XYZ could enter into a swap agreement with a swap dealer wherein XYZ would pay ( LIBOR) notional principal to the swap dealer each period, % being the swap rate. 27 Interest Rate Swaps XYZ having to pay the LIBOR times the notional principal to whomever it borrowed the money each period, its net payoff is then % times the notional principal. Where does the rate % come from? 28
15 Interest Rate Swaps Let R denote the fixed rate of interest agreed upon in the swap agreement and let r t denote the variable LIBOR at time t. The payoff to the swap dealer per unit of the notional principal is then each period. R r t 29 Interest Rate Swaps The swap dealer could eliminate his own interest rate risk by entering into FRAs, in which case is net payoff each period would be R r t + r t r 0 (t 1,t) = R r 0 (t 1,t). 30
16 Interest Rate Swaps The loan being over three periods, the swap rate R must be such that R r 0 (0,1) 1+r 0 (0,1) + R r 0(1,2) + R r 0(2,3) (1+r 0 (0,2)) 2 (1+r 0 (0,3)) 3 which gives R = %. = R R (1.065) 2 + R (1.070) 3 = 0, 31 Interest Rate Swaps More generally, letting T denote the number periods covered by the swap agreement, R must be such that which gives T P(0,t)(R r 0 (t 1,t)) = 0, t=1 R = T t=1 P(0,t)r 0(t 1,t) T t=1 P(0,t). 32
17 Interest Rate Swaps Since r 0 (t 1,t) = P(0,t 1) P(0,t) 1, we can write R = T t=1 (P(0,t 1) P(0,t)) t=1 T P(0,t) = 1 P(0,T ) t=1 T P(0,t). 33 Interest Rate Swaps Swaps are contractual agreements to exchange a series of cash flows. If the agreement is for one party to swap its fixed interest rate payments for the floating interest rate payments of another, it is termed an interest rate swap. If the agreement is to swap currencies of debt service obligations, it is termed currency swap. A single swap may combine elements of both interest rate and currency swaps. 34
18 Interest Rate Swaps A borrower with floatingrate debt who believes that interest rates are about to increase may enter into a swap agreement to pay fixed/receive floating. Similarly, a borrower with fixedrate debt who believes that interest rates are about to fall may enter a swap agreement to pay floating/receive fixed. 35 Currency Swaps All swaps being derived from the yield curve in each major currency, the fixed to floatingrate interest rate swap in each currency allows to swap across currencies. The motivation for a currency swap is to replace cash flows scheduled in an undesired currency with flows in a desired currency. Look at Exhibit
19 Currency Swaps Swapping floating dollars into fixedrate Swiss francs, say, would proceed as follows: 1. First determine the rate at which the floating dollar payments can be exchanged for fixed dollar payments; 2. Find the fixed rate in Swiss francs corresponding to the fixed rate in dollars. 37 Currency Swaps How are currency swap rates determined? Let P(0,t) Zerocoupon bond price maturing at time t, S 0 Spot rate at time 0 (dollars/desired currency), F 0 (t) Forward exchange rate at time t as of time 0 (dollars/desired currency), N Notional principal in dollars, R Fixed rate in desired currency, R Fixed rate in dollars. 38
20 Currency Swaps Without a swap agreement, the present value of the borrower s payments is PV = T P(0,t)RN + P(0,T )N. t=1 Note that if the bonds are sold at par, PV = N. 39 Currency Swaps In the desired currency, the notional principal is N/S 0 and the interest payment is R N/S 0 per period. The present value of the (hedged) desired currency payments is PV = T P(0,t)F 0 (t)r N/S 0 + P(0,T )F 0 (T )N/S 0. t=1 In equilibrium, we must have PV = PV. 40
21 Currency Swaps Example 1 Take, for example, a 3year U.S. dollar bond with N = $100 and R = 6.95%. Let the spot and forward rates $/ be S 0 = , F 0 (1) = , F 0 (2) = and F 0 (3) = The annual yields are as before, i.e. P(0, 1) = , P(0, 2) = and P(0,3) = What rate would be paid if the debt payments were all made in euros? 41 Currency Swaps Example 1 First note that at the rate 6.95% the firm s bonds are sold at par and thus PV = N. So we need to find R such that PV = T P(0,t)F 0 (t)r N/S 0 + P(0,T )F 0 (T )N/S 0 = N. t=1 42
22 Currency Swaps Example 1 This gives R = 1 P(0,T )F 0(T )/S 0 T t=1 P(0,t)F 0(t)/S Currency Swaps Example 1 In the present example, we need R = = 6.43% for the swap agreement to have a zero net present value. 44
23 Currency Swaps Example 2 The problem is much simpler if we assume the exchange rate constant over the loan period (i.e. F 0 (t) = S 0 for all t) and the annual yield to be the same over any subperiod (r 0 (0,t) = r, say, for all t). Consider then the case of a US$ debt issue sold at par with coupon rate 5.56% and face value $10,000,000. What would be the equivalent Sfr rate? 45 Currency Swaps Example 2 If the current spot rate is Sfr1.5000/$, the rate R would be such that ,000,000 = Sfr15,000,000 would also be sold at par. If the annual yield in Switzerland is 2.01%, then R will be 2.01%. 46
24 Unwinding Swaps One of the partners to a swap may wish to terminate the agreement before it matures. If the present value of the contract is not zero at the time it is terminated, one partner will have to pay a termination fee to compensate the other. 47 Unwinding Swaps Take the example of a threeyear pay Swiss francs/receive US$ currency swap on a notional principal of $10m at 5.56% arranged when the spot rate is Sfr1.5000/$. The equivalent Sfr loan is Sfr15,000,000 at 2.01%. 48
25 Unwinding Swaps If the exchange rate falls to Sfr after the first year, when the US twoyear rate is 5.5% and the Sfr twoyear rate is 2%, then the present value of the Sfr payments is 301, ,301, = Sfr15,002,912 = $10,240,896 and the present value of the US$ payments is 556, ,556, = $10,011, Unwinding Swaps If the borrowing firm wishes to terminate the swap agreement, it will have to pay to the swap dealer. 10,240,896 10,011,078 = $229,818 50
26 Interest Rate Caps and Floors Interest Rate Cap: Option limiting the maximum interest rate to be paid over a given period. Interest Rate Floor: Option limiting the minimum interest rate to be received over a given period. 51 Swaptions A swaption is an option to enter into a swap agreement on a prespecified notional principal at a prespecified strike rate. 52
Bond Options, Caps and the Black Model
Bond Options, Caps and the Black Model Black formula Recall the Black formula for pricing options on futures: C(F, K, σ, r, T, r) = Fe rt N(d 1 ) Ke rt N(d 2 ) where d 1 = 1 [ σ ln( F T K ) + 1 ] 2 σ2
More informationLecture 09: Multiperiod Model Fixed Income, Futures, Swaps
Lecture 09: Multiperiod Model Fixed Income, Futures, Swaps Prof. Markus K. Brunnermeier Slide 091 Overview 1. Bond basics 2. Duration 3. Term structure of the real interest rate 4. Forwards and futures
More informationFIN 472 FixedIncome Securities Forward Rates
FIN 472 FixedIncome Securities Forward Rates Professor Robert B.H. Hauswald Kogod School of Business, AU InterestRate Forwards Review of yield curve analysis Forwards yet another use of yield curve forward
More informationManual for SOA Exam FM/CAS Exam 2.
Manual for SOA Exam FM/CAS Exam 2. Chapter 7. Derivatives markets. c 2009. Miguel A. Arcones. All rights reserved. Extract from: Arcones Manual for the SOA Exam FM/CAS Exam 2, Financial Mathematics. Fall
More informationForward Contracts and Forward Rates
Forward Contracts and Forward Rates Outline and Readings Outline Forward Contracts Forward Prices Forward Rates Information in Forward Rates Reading Veronesi, Chapters 5 and 7 Tuckman, Chapters 2 and 16
More informationIntroduction to swaps
Introduction to swaps Steven C. Mann M.J. Neeley School of Business Texas Christian University incorporating ideas from Teaching interest rate and currency swaps" by Keith C. Brown (TexasAustin) and Donald
More informationHedging with Futures and Options: Supplementary Material. Global Financial Management
Hedging with Futures and Options: Supplementary Material Global Financial Management Fuqua School of Business Duke University 1 Hedging Stock Market Risk: S&P500 Futures Contract A futures contract on
More informationVALUATION OF PLAIN VANILLA INTEREST RATES SWAPS
Graduate School of Business Administration University of Virginia VALUATION OF PLAIN VANILLA INTEREST RATES SWAPS Interestrate swaps have grown tremendously over the last 10 years. With this development,
More informationLecture 12. Options Strategies
Lecture 12. Options Strategies Introduction to Options Strategies Options, Futures, Derivatives 10/15/07 back to start 1 Solutions Problem 6:23: Assume that a bank can borrow or lend money at the same
More informationCHAPTER 14 INTEREST RATE AND CURRENCY SWAPS SUGGESTED ANSWERS AND SOLUTIONS TO ENDOFCHAPTER QUESTIONS AND PROBLEMS
CHAPTER 14 INTEREST RATE AND CURRENCY SWAPS SUGGESTED ANSWERS AND SOLUTIONS TO ENDOFCHAPTER QUESTIONS AND PROBLEMS QUESTIONS 1. Describe the difference between a swap broker and a swap dealer. Answer:
More informationLearning Curve Interest Rate Futures Contracts Moorad Choudhry
Learning Curve Interest Rate Futures Contracts Moorad Choudhry YieldCurve.com 2004 Page 1 The market in shortterm interest rate derivatives is a large and liquid one, and the instruments involved are
More informationWe first solve for the present value of the cost per two barrels: (1.065) 2 = 41.033 (1.07) 3 = 55.341. x = 20.9519
Chapter 8 Swaps Question 8.1. We first solve for the present value of the cost per two barrels: $22 1.06 + $23 (1.065) 2 = 41.033. We then obtain the swap price per barrel by solving: which was to be shown.
More informationInternational Bond and Money Markets. Quiz Questions. TrueFalse Questions
Chapter 9 International Bond and Money Markets Quiz Questions TrueFalse Questions 1. The abolition of the Interest Equalization Tax, Regulation M, the cold war, and the US and UK foreign exchange controls
More information550.444 Introduction to Financial Derivatives
550.444 Introduction to Financial Derivatives Week of October 7, 2013 Interest Rate Futures Where we are Last week: Forward & Futures Prices/Value (Chapter 5, OFOD) This week: Interest Rate Futures (Chapter
More informationCFA Level 2 Derivatives  I
CFA Level 2 Derivatives  I EduPristine www.edupristine.com Agenda Forwards Markets and Contracts Future Markets and Contracts Option Markets and Contracts 1 Forwards Markets and Contracts 2 Pricing and
More informationEurodollar Futures, and Forwards
5 Eurodollar Futures, and Forwards In this chapter we will learn about Eurodollar Deposits Eurodollar Futures Contracts, Hedging strategies using ED Futures, Forward Rate Agreements, Pricing FRAs. Hedging
More informationThe Pricing and Hedging of InterestRate Derivatives: Theory and Practice
The Pricing and Hedging of InterestRate Derivatives: Theory and Practice SerHuang Poon 1, Richard C. Stapleton 2 and Marti G. Subrahmanyam 3 April 28, 2005 1 Manchester Business School 2 Manchester Business
More informationFinance 350: Problem Set 6 Alternative Solutions
Finance 350: Problem Set 6 Alternative Solutions Note: Where appropriate, the final answer for each problem is given in bold italics for those not interested in the discussion of the solution. I. Formulas
More informationINTEREST RATE SWAPS September 1999
INTEREST RATE SWAPS September 1999 INTEREST RATE SWAPS Definition: Transfer of interest rate streams without transferring underlying debt. 2 FIXED FOR FLOATING SWAP Some Definitions Notational Principal:
More informationA) 1.8% B) 1.9% C) 2.0% D) 2.1% E) 2.2%
1 Exam FM Questions Practice Exam 1 1. Consider the following yield curve: Year Spot Rate 1 5.5% 2 5.0% 3 5.0% 4 4.5% 5 4.0% Find the four year forward rate. A) 1.8% B) 1.9% C) 2.0% D) 2.1% E) 2.2% 2.
More informationDERIVATIVES Presented by Sade Odunaiya Partner, Risk Management Alliance Consulting DERIVATIVES Introduction Forward Rate Agreements FRA Swaps Futures Options Summary INTRODUCTION Financial Market Participants
More informationAdvanced forms of currency swaps
Advanced forms of currency swaps Basis swaps Basis swaps involve swapping one floating index rate for another. Banks may need to use basis swaps to arrange a currency swap for the customers. Example A
More informationCHAPTER 13 CURRENCY AND INTEREST RATE SWAPS
CHAPTER 13 CURRENCY AND INTEREST RATE SWAPS Chapter Overview This chapter is about currency and interest rate swaps. It begins by describing the origins of the swap market and the role played by capital
More informationCHAPTER 9 SUGGESTED ANSWERS TO CHAPTER 9 QUESTIONS
INSTRUCTOR S MANUAL MULTINATIONAL FINANCIAL MANAGEMENT, 9 TH ED. CHAPTER 9 SUGGESTED ANSWERS TO CHAPTER 9 QUESTIONS 1. What is an interest rate swap? What is the difference between a basis swap and a coupon
More informationHot Topics in Financial Markets Lecture 1: The Libor Scandal
Hot Topics in Financial Markets Lecture 1: The Libor Scandal Spot and Forward Interest Rates Libor LiborDependent Financial Instruments The Scandal 2 Spot Interest Rates Bond Market The yield on a bond
More informationEquityindexlinked swaps
Equityindexlinked swaps Equivalent to portfolios of forward contracts calling for the exchange of cash flows based on two different investment rates: a variable debt rate (e.g. 3month LIBOR) and the
More informationInternational Swaps and Derivatives Association, Inc. Disclosure Annex for Interest Rate Transactions
International Swaps and Derivatives Association, Inc. Disclosure Annex for Interest Rate Transactions This Annex supplements and should be read in conjunction with the General Disclosure Statement. NOTHING
More information19. Interest Rate Swaps
19. Interest Rate Swaps Reading: Stigum 19 on Swaps. See also Hull who builds from the idea (mentioned in Stigum) that swaps are like a portfolio of forward contracts. Daily Financial Times includes bidask
More informationBond Valuation. Capital Budgeting and Corporate Objectives
Bond Valuation Capital Budgeting and Corporate Objectives Professor Ron Kaniel Simon School of Business University of Rochester 1 Bond Valuation An Overview Introduction to bonds and bond markets» What
More informationCoupon Bonds and Zeroes
Coupon Bonds and Zeroes Concepts and Buzzwords Coupon bonds Zerocoupon bonds Bond replication Noarbitrage price relationships Zero rates Zeroes STRIPS Dedication Implied zeroes Semiannual compounding
More informationCallable Bonds  Structure
1.1 Callable bonds A callable bond is a fixed rate bond where the issuer has the right but not the obligation to repay the face value of the security at a preagreed value prior to the final original maturity
More information2 Stock Price. Figure S1.1 Profit from long position in Problem 1.13
Problem 1.11. A cattle farmer expects to have 12, pounds of live cattle to sell in three months. The livecattle futures contract on the Chicago Mercantile Exchange is for the delivery of 4, pounds of cattle.
More informationFixed Income Portfolio Management. Interest rate sensitivity, duration, and convexity
Fixed Income ortfolio Management Interest rate sensitivity, duration, and convexity assive bond portfolio management Active bond portfolio management Interest rate swaps 1 Interest rate sensitivity, duration,
More informationFIXEDINCOME SECURITIES. Chapter 10. Swaps
FIXEDINCOME SECURITIES Chapter 10 Swaps Outline Terminology Convention Quotation Uses of Swaps Pricing of Swaps Non Plain Vanilla Swaps Terminology Definition Agreement between two parties They exchange
More informationThis act of setting a price today for a transaction in the future, hedging. hedge currency exposure, short long long hedge short hedge Hedgers
Section 7.3 and Section 4.5 Oct. 7, 2002 William Pugh 7.3 Example of a forward contract: In May, a crude oil producer gets together with a refiner to agree on a price for crude oil. This price is for crude
More informationFIXEDINCOME SECURITIES. Chapter 11. Forwards and Futures
FIXEDINCOME SECURITIES Chapter 11 Forwards and Futures Outline Futures and Forwards Types of Contracts Trading Mechanics Trading Strategies Futures Pricing Uses of Futures Futures and Forwards Forward
More informationDavid Bob Case Scenario
David Bob Case Scenario David Bob, CFA, is a derivatives analyst at Capital Inc. Capital Inc. deals mainly in arbitrage positions along with leveraged positions. David is following the options prices and
More informationFinancialInstitutions Management. Solutions 4. 8. The following are the foreign currency positions of an FI, expressed in the foreign currency.
Solutions 4 Chapter 14: oreign Exchange Risk 8. The following are the foreign currency positions of an I, expressed in the foreign currency. Currency Assets Liabilities X Bought X Sold Swiss franc (S)
More informationSOCIETY OF ACTUARIES FINANCIAL MATHEMATICS. EXAM FM SAMPLE QUESTIONS Financial Economics
SOCIETY OF ACTUARIES EXAM FM FINANCIAL MATHEMATICS EXAM FM SAMPLE QUESTIONS Financial Economics June 2014 changes Questions 130 are from the prior version of this document. They have been edited to conform
More informationAssumptions: No transaction cost, same rate for borrowing/lending, no default/counterparty risk
Derivatives Why? Allow easier methods to short sell a stock without a broker lending it. Facilitates hedging easily Allows the ability to take long/short position on less available commodities (Rice, Cotton,
More informationThe Term Structure of Interest Rates CHAPTER 13
The Term Structure of Interest Rates CHAPTER 13 Chapter Summary Objective: To explore the pattern of interest rates for differentterm assets. The term structure under certainty Forward rates Theories
More informationBond Valuation. FINANCE 350 Global Financial Management. Professor Alon Brav Fuqua School of Business Duke University. Bond Valuation: An Overview
Bond Valuation FINANCE 350 Global Financial Management Professor Alon Brav Fuqua School of Business Duke University 1 Bond Valuation: An Overview Bond Markets What are they? How big? How important? Valuation
More informationFixedIncome Securities. Assignment
FIN 472 Professor Robert B.H. Hauswald FixedIncome Securities Kogod School of Business, AU Assignment Please be reminded that you are expected to use contemporary computer software to solve the following
More informationManaging Interest Rate Exposure
Managing Interest Rate Exposure Global Markets Contents Products to manage Interest Rate Exposure...1 Interest Rate Swap Product Overview...2 Interest Rate Cap Product Overview...8 Interest Rate Collar
More informationThe Irony In The Derivatives Discounting
The Irony In The Derivatives Discounting Marc Henrard Head of Quantitative Research, Banking Department, Bank for International Settlements, CH4002 Basel (Switzerland), email: Marc.Henrard@bis.org Abstract
More informationCurrency and Interest Rate Swaps
MWF 3:154:30 Gates B01 Final Exam MS&E 247S Fri Aug 15 2008 12:15PM3:15PM Gates B01 Or Saturday Aug 16 2008 12:15PM3:15PM Gates B01 Remote SCPD participants will also take the exam on Friday, 8/15 Please
More informationINTEREST RATE SWAP (IRS)
INTEREST RATE SWAP (IRS) 1. Interest Rate Swap (IRS)... 4 1.1 Terminology... 4 1.2 Application... 11 1.3 EONIA Swap... 19 1.4 Pricing and Mark to Market Revaluation of IRS... 22 2. Cross Currency Swap...
More informationA Teaching Note on Pricing and Valuing Interest Rate Swaps Using LIBOR and OIS Discounting
A Teaching Note on Pricing and Valuing Interest Rate Swaps Using LIBOR and OIS Discounting June 202 Donald J. Smith Associate Professor of Finance Boston University School of Management 595 Commonwealth
More informationPricing Forwards and Swaps
Chapter 7 Pricing Forwards and Swaps 7. Forwards Throughout this chapter, we will repeatedly use the following property of noarbitrage: P 0 (αx T +βy T ) = αp 0 (x T )+βp 0 (y T ). Here, P 0 (w T ) is
More informationCHAPTER 11 CURRENCY AND INTEREST RATE FUTURES
Answers to endofchapter exercises ARBITRAGE IN THE CURRENCY FUTURES MARKET 1. Consider the following: Spot Rate: $ 0.65/DM German 1yr interest rate: 9% US 1yr interest rate: 5% CHAPTER 11 CURRENCY
More informationCHAPTER 15: THE TERM STRUCTURE OF INTEREST RATES
CHAPTER 15: THE TERM STRUCTURE OF INTEREST RATES 1. Expectations hypothesis. The yields on longterm bonds are geometric averages of present and expected future short rates. An upward sloping curve is
More informationCHAPTER 7 FUTURES AND OPTIONS ON FOREIGN EXCHANGE SUGGESTED ANSWERS AND SOLUTIONS TO ENDOFCHAPTER QUESTIONS AND PROBLEMS
CHAPTER 7 FUTURES AND OPTIONS ON FOREIGN EXCHANGE SUGGESTED ANSWERS AND SOLUTIONS TO ENDOFCHAPTER QUESTIONS AND PROBLEMS QUESTIONS 1. Explain the basic differences between the operation of a currency
More informationInterest Rate Swaps. Key Concepts and Buzzwords. Readings Tuckman, Chapter 18. Swaps Swap Spreads Credit Risk of Swaps Uses of Swaps
Interest Rate Swaps Key Concepts and Buzzwords Swaps Swap Spreads Credit Risk of Swaps Uses of Swaps Readings Tuckman, Chapter 18. Counterparty, Notional amount, Plain vanilla swap, Swap rate Interest
More informationChapter 16 OVERTHECOUNTER INTEREST RATE DERIVATIVES
Page 238 The information in this chapter was last updated in 1993. Since the money market evolves very rapidly, recent developments may have superseded some of the content of this chapter. Chapter 16 OVERTHECOUNTER
More informationMidTerm Exam Practice Set and Solutions.
FIN469 Investments Analysis Professor Michel A. Robe MidTerm Exam Practice Set and Solutions. What to do with this practice set? To help students prepare for the midterm exam, two practice sets with
More informationThe Pricing and Valuation of Swaps 1
The Pricing and Valuation of Swaps 1 I. Introduction The size and continued growth of the global market for OTC derivative products such as swaps, forwards, and option contracts attests to their increasing
More informationWhat are Swaps? Spring 2014. Stephen Sapp
What are Swaps? Spring 2014 Stephen Sapp Basic Idea of Swaps I have signed up for the Wine of the Month Club and you have signed up for the Beer of the Month Club. As winter approaches, I would like to
More informationFIN 684 FixedIncome Analysis From Repos to Monetary Policy. Funding Positions
FIN 684 FixedIncome Analysis From Repos to Monetary Policy Professor Robert B.H. Hauswald Kogod School of Business, AU Funding Positions Shortterm funding: repos and money markets funding trading positions
More informationIntroduction to Options. Derivatives
Introduction to Options Econ 422: Investment, Capital & Finance University of Washington Summer 2010 August 18, 2010 Derivatives A derivative is a security whose payoff or value depends on (is derived
More informationChapter 8. Step 2: Find prices of the bonds today: n i PV FV PMT Result Coupon = 4% 29.5 5? 100 4 84.74 Zero coupon 29.5 5? 100 0 23.
Chapter 8 Bond Valuation with a Flat Term Structure 1. Suppose you want to know the price of a 10year 7% coupon Treasury bond that pays interest annually. a. You have been told that the yield to maturity
More informationCHAPTER 22: FUTURES MARKETS
CHAPTER 22: FUTURES MARKETS PROBLEM SETS 1. There is little hedging or speculative demand for cement futures, since cement prices are fairly stable and predictable. The trading activity necessary to support
More informationMoney Market and Debt Instruments
Prof. Alex Shapiro Lecture Notes 3 Money Market and Debt Instruments I. Readings and Suggested Practice Problems II. Bid and Ask III. Money Market IV. Long Term Credit Markets V. Additional Readings Buzz
More informationChapter 5  Determination of Forward and Futures Prices
Chapter 5  Determination of Forward and Futures Prices Investment assets vs. consumption assets Short selling Assumptions and notations Forward price for an investment asset that provides no income Forward
More informationAmerican Options and Callable Bonds
American Options and Callable Bonds American Options Valuing an American Call on a Coupon Bond Valuing a Callable Bond Concepts and Buzzwords Interest Rate Sensitivity of a Callable Bond exercise policy
More informationFixed Income: Practice Problems with Solutions
Fixed Income: Practice Problems with Solutions Directions: Unless otherwise stated, assume semiannual payment on bonds.. A 6.0 percent bond matures in exactly 8 years and has a par value of 000 dollars.
More information8. Eurodollars: Parallel Settlement
8. Eurodollars: Parallel Settlement Eurodollars are dollar balances held by banks or bank branches outside the country, which banks hold no reserves at the Fed and consequently have no direct access to
More informationInterest Rate Futures Pricing, Hedging, Trading Analysis and Applications
Interest Rate Futures Pricing, Hedging, Trading Analysis and Applications Vincent Chia Last Updated on 30 Nov 2010 vincent.chia@thomsonreuters.com Agenda 1. Financial Instruments 2. Pricing Methodology
More informationForward Price. The payoff of a forward contract at maturity is S T X. Forward contracts do not involve any initial cash flow.
Forward Price The payoff of a forward contract at maturity is S T X. Forward contracts do not involve any initial cash flow. The forward price is the delivery price which makes the forward contract zero
More informationFundamentals of Finance
Euribor rates, forward rates and swap rates University of Oulu  Department of Finance Fall 2015 What next Euribor rates, forward rates and swap rates In the following we consider Euribor spot rate, Euribor
More informationIntroduction to Derivative Instruments Part 1 Link n Learn
Introduction to Derivative Instruments Part 1 Link n Learn June 2014 Webinar Participants Elaine Canty Manager Financial Advisory Deloitte & Touche Ireland ecanty@deloitte.ie +353 1 417 2991 Christopher
More informationChapter 2 An Introduction to Forwards and Options
Chapter 2 An Introduction to Forwards and Options Question 2.1. The payoff diagram of the stock is just a graph of the stock price as a function of the stock price: In order to obtain the profit diagram
More informationCHAPTER 15: THE TERM STRUCTURE OF INTEREST RATES
Chapter  The Term Structure of Interest Rates CHAPTER : THE TERM STRUCTURE OF INTEREST RATES PROBLEM SETS.. In general, the forward rate can be viewed as the sum of the market s expectation of the future
More informationCHAPTER 15: THE TERM STRUCTURE OF INTEREST RATES
CHAPTER : THE TERM STRUCTURE OF INTEREST RATES CHAPTER : THE TERM STRUCTURE OF INTEREST RATES PROBLEM SETS.. In general, the forward rate can be viewed as the sum of the market s expectation of the future
More informationAnalysis of Deterministic Cash Flows and the Term Structure of Interest Rates
Analysis of Deterministic Cash Flows and the Term Structure of Interest Rates Cash Flow Financial transactions and investment opportunities are described by cash flows they generate. Cash flow: payment
More informationPractice set #4 and solutions
FIN465 Derivatives (3 credits) Professor Michel Robe Practice set #4 and solutions To help students with the material, seven practice sets with solutions will be handed out. They will not be graded: the
More informationLearning Curve Forward Rate Agreements Anuk Teasdale
Learning Curve Forward Rate Agreements Anuk Teasdale YieldCurve.com 2004 Page 1 In this article we review the forward rate agreement. Money market derivatives are priced on the basis of the forward rate,
More informationFinancialInstitutions Management. Solutions 1. 6. A financial institution has the following market value balance sheet structure:
FIN 683 Professor Robert Hauswald FinancialInstitutions Management Kogod School of Business, AU Solutions 1 Chapter 7: Bank Risks  Interest Rate Risks 6. A financial institution has the following market
More informationCHAPTER 12 INTERNATIONAL BOND MARKETS SUGGESTED ANSWERS AND SOLUTIONS TO ENDOFCHAPTER QUESTIONS AND PROBLEMS
CHAPTER 12 INTERNATIONAL BOND MARKETS SUGGESTED ANSWERS AND SOLUTIONS TO ENDOFCHAPTER QUESTIONS AND PROBLEMS QUESTIONS 1. Describe the differences between foreign bonds and Eurobonds. Also discuss why
More informationThe PricewaterhouseCoopers Credit Derivatives Primer
The PricewaterhouseCoopers Credit Derivatives Primer Financial Advisory Services John D. Finnerty Table of Contents What are Credit Derivatives?...................................3 A Definition............................................4
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
ECON 4110: Sample Exam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) Economists define risk as A) the difference between the return on common
More informationSYLLABUS The ACI Dealing Certificate (Prometric Code: 3I0008)
SYLLABUS The ACI Dealing Certificate (Prometric Code: 3I0008) Examination delivered in ENGLISH and GERMAN The ACI Dealing Certificate is a foundation programme that allows candidates to acquire a working
More informationChapter 15 OPTIONS ON MONEY MARKET FUTURES
Page 218 The information in this chapter was last updated in 1993. Since the money market evolves very rapidly, recent developments may have superseded some of the content of this chapter. Chapter 15 OPTIONS
More informationChapter 16: Financial Risk Management
Chapter 16: Financial Risk Management Introduction Overview of Financial Risk Management in Treasury Interest Rate Risk Foreign Exchange (FX) Risk Commodity Price Risk Managing Financial Risk The Benefits
More informationName Graph Description Payoff Profit Comments. commodity at some point in the future at a prespecified. commodity at some point
Name Graph Description Payoff Profit Comments Long Commitment to purchase commodity at some point in the future at a prespecified price S T  F S T F No premium Asset price contingency: Always Maximum
More informationExotic options [April 4]
Exotic options [April 4] We ve looked at European and American Calls and Puts European options with general payoff functions From a theoretical point of view. This could be carried further, to more Exotic
More informationINTEREST RATES AND FX MODELS
INTEREST RATES AND FX MODELS 4. Convexity and CMS Andrew Lesniewski Courant Institute of Mathematical Sciences New York University New York February 20, 2013 2 Interest Rates & FX Models Contents 1 Introduction
More informationBonds and Yield to Maturity
Bonds and Yield to Maturity Bonds A bond is a debt instrument requiring the issuer to repay to the lender/investor the amount borrowed (par or face value) plus interest over a specified period of time.
More informationANALYSIS OF FIXED INCOME SECURITIES
ANALYSIS OF FIXED INCOME SECURITIES Valuation of Fixed Income Securities Page 1 VALUATION Valuation is the process of determining the fair value of a financial asset. The fair value of an asset is its
More informationFina4500 Spring 2015 Extra Practice Problems Instructions
Extra Practice Problems Instructions: The problems are similar to the ones on your previous problem sets. All interest rates and rates of inflation given in the problems are annualized (i.e., stated as
More informationCaput Derivatives: October 30, 2003
Caput Derivatives: October 30, 2003 Exam + Answers Total time: 2 hours and 30 minutes. Note 1: You are allowed to use books, course notes, and a calculator. Question 1. [20 points] Consider an investor
More informationYIELD CURVE GENERATION
1 YIELD CURVE GENERATION Dr Philip Symes Agenda 2 I. INTRODUCTION II. YIELD CURVES III. TYPES OF YIELD CURVES IV. USES OF YIELD CURVES V. YIELD TO MATURITY VI. BOND PRICING & VALUATION Introduction 3 A
More informationLOCKING IN TREASURY RATES WITH TREASURY LOCKS
LOCKING IN TREASURY RATES WITH TREASURY LOCKS Interestrate sensitive financial decisions often involve a waiting period before they can be implemented. This delay exposes institutions to the risk that
More informationGuidance Note Capital Requirements Directive Market Risk
Guidance Note Capital Requirements Directive Issued : 18 December 2007 Revised: 13 March 2013 V3 Please be advised that this Guidance Note is dated and does not take into account any changes arising from
More informationForwards and Futures
Prof. Alex Shapiro Lecture Notes 16 Forwards and Futures I. Readings and Suggested Practice Problems II. Forward Contracts III. Futures Contracts IV. ForwardSpot Parity V. Stock Index ForwardSpot Parity
More informationInterest Rate Futures. Chapter 6
Interest Rate Futures Chapter 6 1 Day Count Convention The day count convention defines: The period of time to which the interest rate applies. The period of time used to calculate accrued interest (relevant
More informationPractice Questions for Midterm II
Finance 333 Investments Practice Questions for Midterm II Winter 2004 Professor Yan 1. The market portfolio has a beta of a. 0. *b. 1. c. 1. d. 0.5. By definition, the beta of the market portfolio is
More informationBond valuation and bond yields
RELEVANT TO ACCA QUALIFICATION PAPER P4 AND PERFORMANCE OBJECTIVES 15 AND 16 Bond valuation and bond yields Bonds and their variants such as loan notes, debentures and loan stock, are IOUs issued by governments
More informationCHAPTER 22: FUTURES MARKETS
CHAPTER 22: FUTURES MARKETS 1. a. The closing price for the spot index was 1329.78. The dollar value of stocks is thus $250 1329.78 = $332,445. The closing futures price for the March contract was 1364.00,
More informationTreasury Bond Futures
Treasury Bond Futures Concepts and Buzzwords Basic Futures Contract Futures vs. Forward Delivery Options Reading Veronesi, Chapters 6 and 11 Tuckman, Chapter 14 Underlying asset, markingtomarket, convergence
More informationCHAPTER 10. CURRENCY SWAPS
CHAPTER 10. CURRENCY SWAPS The advent of swaps, as much as anything else, helped transform the world s segmented capital markets into a single, truly integrated, international capital market. John F. Marshall
More information