# Interest Rate and Currency Swaps

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 Interest Rate and Currency Swaps Eiteman et al., Chapter 14 Winter 2004 Bond Basics Consider the following: Zero-Coupon Zero-Coupon One-Year 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 zero-coupon bond yields also give us implied forward zero-coupon 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 zero-coupon 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 over-the-counter 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 zero-coupon 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 zero-coupon bond maturing at time t and selling short 1 + r 0 (t,t + s) zero-coupon 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 zero-coupon 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 time-t 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 91-day period starting 120 days from now is then P(0, 120) P(0,211) 1 = = 1.8%. So the cost of times a zero-coupon bond maturing in 211 days is the same as a zero-coupon 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 3-month eurodollar futures as an example. The yield of a futures contract is calculated from the settlement price. If the settlement price of the 3-month eurodollar future maturing in March 2005 is 95.68, the annual yield over the 3-month period ending in March 2005 is expected to be = 4.32%, for a 3-month 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 floating-rate 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 fixed-rate 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 floating-rate 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 fixed-rate 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) Zero-coupon 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 3-year 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 three-year 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 two-year rate is 5.5% and the Sfr two-year 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 pre-specified notional principal at a pre-specified strike rate. 52

### FIN 472 Fixed-Income Securities Forward Rates

FIN 472 Fixed-Income Securities Forward Rates Professor Robert B.H. Hauswald Kogod School of Business, AU Interest-Rate Forwards Review of yield curve analysis Forwards yet another use of yield curve forward

### 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

### Lecture 09: Multi-period Model Fixed Income, Futures, Swaps

Lecture 09: Multi-period Model Fixed Income, Futures, Swaps Prof. Markus K. Brunnermeier Slide 09-1 Overview 1. Bond basics 2. Duration 3. Term structure of the real interest rate 4. Forwards and futures

### FIN 472 Fixed-Income Securities Forward Rates

FIN 472 Fixed-Income Securities Forward Rates Professor Robert B.H. Hauswald Kogod School of Business, AU Interest-Rate Forwards Review of yield curve analysis Forwards yet another use of yield curve forward

### Forward 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

### Manual 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

### Introduction 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 (Texas-Austin) and Donald

### VALUATION OF PLAIN VANILLA INTEREST RATES SWAPS

Graduate School of Business Administration University of Virginia VALUATION OF PLAIN VANILLA INTEREST RATES SWAPS Interest-rate swaps have grown tremendously over the last 10 years. With this development,

### Hedging 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

### We 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.

### Finance 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

### Lecture 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

### International Bond and Money Markets. Quiz Questions. True-False Questions

Chapter 9 International Bond and Money Markets Quiz Questions True-False Questions 1. The abolition of the Interest Equalization Tax, Regulation M, the cold war, and the US and UK foreign exchange controls

### CFA 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

### Learning Curve Interest Rate Futures Contracts Moorad Choudhry

Learning Curve Interest Rate Futures Contracts Moorad Choudhry YieldCurve.com 2004 Page 1 The market in short-term interest rate derivatives is a large and liquid one, and the instruments involved are

### CHAPTER 14 INTEREST RATE AND CURRENCY SWAPS SUGGESTED ANSWERS AND SOLUTIONS TO END-OF-CHAPTER QUESTIONS AND PROBLEMS

CHAPTER 14 INTEREST RATE AND CURRENCY SWAPS SUGGESTED ANSWERS AND SOLUTIONS TO END-OF-CHAPTER QUESTIONS AND PROBLEMS QUESTIONS 1. Describe the difference between a swap broker and a swap dealer. Answer:

### 550.444 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

### Eurodollar 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

### A) 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.

DERIVATIVES Presented by Sade Odunaiya Partner, Risk Management Alliance Consulting DERIVATIVES Introduction Forward Rate Agreements FRA Swaps Futures Options Summary INTRODUCTION Financial Market Participants

### Advanced 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

### INTEREST 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:

### The Pricing and Hedging of Interest-Rate Derivatives: Theory and Practice

The Pricing and Hedging of Interest-Rate Derivatives: Theory and Practice Ser-Huang Poon 1, Richard C. Stapleton 2 and Marti G. Subrahmanyam 3 April 28, 2005 1 Manchester Business School 2 Manchester Business

### 19. 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 bid-ask

### CHAPTER 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

### Callable 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 pre-agreed value prior to the final original maturity

### CHAPTER 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

### Hot 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 Libor-Dependent Financial Instruments The Scandal 2 Spot Interest Rates Bond Market The yield on a bond

Equity-index-linked 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. 3-month LIBOR) and the

### Coupon Bonds and Zeroes

Coupon Bonds and Zeroes Concepts and Buzzwords Coupon bonds Zero-coupon bonds Bond replication No-arbitrage price relationships Zero rates Zeroes STRIPS Dedication Implied zeroes Semi-annual compounding

### David 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

### 2 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.

### International 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

### Bond 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

### This 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

### Assumptions: 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,

### FIXED-INCOME SECURITIES. Chapter 11. Forwards and Futures

FIXED-INCOME 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

### Fixed 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,

### Managing 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

### Mid-Term Exam Practice Set and Solutions.

FIN-469 Investments Analysis Professor Michel A. Robe Mid-Term Exam Practice Set and Solutions. What to do with this practice set? To help students prepare for the mid-term exam, two practice sets with

### INTEREST 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...

### SOCIETY 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 1-30 are from the prior version of this document. They have been edited to conform

### FIXED-INCOME SECURITIES. Chapter 10. Swaps

FIXED-INCOME 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

### CHAPTER 7 FUTURES AND OPTIONS ON FOREIGN EXCHANGE SUGGESTED ANSWERS AND SOLUTIONS TO END-OF-CHAPTER QUESTIONS AND PROBLEMS

CHAPTER 7 FUTURES AND OPTIONS ON FOREIGN EXCHANGE SUGGESTED ANSWERS AND SOLUTIONS TO END-OF-CHAPTER QUESTIONS AND PROBLEMS QUESTIONS 1. Explain the basic differences between the operation of a currency

### Caps, Floors, and Collars

Caps, Floors, and Collars Concepts and Buzzwords Caps Capped Floaters Inverse Floaters with % Floor Floors Floaters with Floors Collars Floaters with Collars Strike rate, settlement frequency, index, notional

### CHAPTER 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

### The 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 different-term assets. The term structure under certainty Forward rates Theories

### Financial-Institutions 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)

### Currency and Interest Rate Swaps

MWF 3:15-4:30 Gates B01 Final Exam MS&E 247S Fri Aug 15 2008 12:15PM-3:15PM Gates B01 Or Saturday Aug 16 2008 12:15PM-3:15PM Gates B01 Remote SCPD participants will also take the exam on Friday, 8/15 Please

### Fixed-Income Securities. Assignment

FIN 472 Professor Robert B.H. Hauswald Fixed-Income Securities Kogod School of Business, AU Assignment Please be reminded that you are expected to use contemporary computer software to solve the following

### Bond 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

### Practice set #4 and solutions

FIN-465 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

### Chapter 16 OVER-THE-COUNTER 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 OVER-THE-COUNTER

### What 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

### CHAPTER 11 CURRENCY AND INTEREST RATE FUTURES

Answers to end-of-chapter exercises ARBITRAGE IN THE CURRENCY FUTURES MARKET 1. Consider the following: Spot Rate: \$ 0.65/DM German 1-yr interest rate: 9% US 1-yr interest rate: 5% CHAPTER 11 CURRENCY

### Notes for Lecture 3 (February 14)

INTEREST RATES: The analysis of interest rates over time is complicated because rates are different for different maturities. Interest rate for borrowing money for the next 5 years is ambiguous, because

### 8. 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

### Fina4500 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

### Pricing Forwards and Swaps

Chapter 7 Pricing Forwards and Swaps 7. Forwards Throughout this chapter, we will repeatedly use the following property of no-arbitrage: P 0 (αx T +βy T ) = αp 0 (x T )+βp 0 (y T ). Here, P 0 (w T ) is

### Learning 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,

### American 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

### Chapter 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

### Forward 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

### Introduction 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

### MULTIPLE 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

### Chapter 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

### Money 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

### Interest 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

### FIN 684 Fixed-Income Analysis From Repos to Monetary Policy. Funding Positions

FIN 684 Fixed-Income Analysis From Repos to Monetary Policy Professor Robert B.H. Hauswald Kogod School of Business, AU Funding Positions Short-term funding: repos and money markets funding trading positions

### Forwards and Futures

Prof. Alex Shapiro Lecture Notes 16 Forwards and Futures I. Readings and Suggested Practice Problems II. Forward Contracts III. Futures Contracts IV. Forward-Spot Parity V. Stock Index Forward-Spot Parity

### CHAPTER 15: THE TERM STRUCTURE OF INTEREST RATES

CHAPTER 15: THE TERM STRUCTURE OF INTEREST RATES 1. Expectations hypothesis. The yields on long-term bonds are geometric averages of present and expected future short rates. An upward sloping curve is

### The Irony In The Derivatives Discounting

The Irony In The Derivatives Discounting Marc Henrard Head of Quantitative Research, Banking Department, Bank for International Settlements, CH-4002 Basel (Switzerland), e-mail: Marc.Henrard@bis.org Abstract

### Chapter 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

### A 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

### Introduction 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

### Fundamentals 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

### SYLLABUS The ACI Dealing Certificate (Prometric Code: 3I0-008)

SYLLABUS The ACI Dealing Certificate (Prometric Code: 3I0-008) Examination delivered in ENGLISH and GERMAN The ACI Dealing Certificate is a foundation programme that allows candidates to acquire a working

### Name 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

Review for Exam 1 Instructions: Please read carefully The exam will have 21 multiple choice questions and 5 work problems. Questions in the multiple choice section will be either concept or calculation

### Analysis 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

### ANALYSIS 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

### Bonds 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.

### CHAPTER 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,

### Chapter 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 10-year 7% coupon Treasury bond that pays interest annually. a. You have been told that the yield to maturity

### Interest 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

### INTEREST 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

### CHAPTER 20. Financial Options. Chapter Synopsis

CHAPTER 20 Financial Options Chapter Synopsis 20.1 Option Basics A financial option gives its owner the right, but not the obligation, to buy or sell a financial asset at a fixed price on or until a specified

### CHAPTER 12 INTERNATIONAL BOND MARKETS SUGGESTED ANSWERS AND SOLUTIONS TO END-OF-CHAPTER QUESTIONS AND PROBLEMS

CHAPTER 12 INTERNATIONAL BOND MARKETS SUGGESTED ANSWERS AND SOLUTIONS TO END-OF-CHAPTER QUESTIONS AND PROBLEMS QUESTIONS 1. Describe the differences between foreign bonds and Eurobonds. Also discuss why

### Financial-Institutions Management. Solutions 1. 6. A financial institution has the following market value balance sheet structure:

FIN 683 Professor Robert Hauswald Financial-Institutions Management Kogod School of Business, AU Solutions 1 Chapter 7: Bank Risks - Interest Rate Risks 6. A financial institution has the following market

### Fixed Income: Practice Problems with Solutions

Fixed Income: Practice Problems with Solutions Directions: Unless otherwise stated, assume semi-annual payment on bonds.. A 6.0 percent bond matures in exactly 8 years and has a par value of 000 dollars.

### Interest 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

### Treasury 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, marking-to-market, convergence

### Determination of Forward and Futures Prices

Determination of Forward and Futures Prices Options, Futures, and Other Derivatives, 8th Edition, Copyright John C. Hull 2012 Short selling A popular trading (arbitrage) strategy is the shortselling or

### Understanding Cross Currency Swaps. A Guide for Microfinance Practitioners

Understanding Cross Currency Swaps A Guide for Microfinance Practitioners Cross Currency Swaps Use: A Currency Swap is the best way to fully hedge a loan transaction as the terms can be structured to exactly

### LOCKING IN TREASURY RATES WITH TREASURY LOCKS

LOCKING IN TREASURY RATES WITH TREASURY LOCKS Interest-rate sensitive financial decisions often involve a waiting period before they can be implemen-ted. This delay exposes institutions to the risk that

### Derivatives Interest Rate Futures. Professor André Farber Solvay Brussels School of Economics and Management Université Libre de Bruxelles

Derivatives Interest Rate Futures Professor André Farber Solvay Brussels School of Economics and Management Université Libre de Bruxelles Interest Rate Derivatives Forward rate agreement (FRA): OTC contract

### C(t) (1 + y) 4. t=1. For the 4 year bond considered above, assume that the price today is 900\$. The yield to maturity will then be the y that solves

Economics 7344, Spring 2013 Bent E. Sørensen INTEREST RATE THEORY We will cover fixed income securities. The major categories of long-term fixed income securities are federal government bonds, corporate

### FNCE 301, Financial Management H Guy Williams, 2006

REVIEW We ve used the DCF method to find present value. We also know shortcut methods to solve these problems such as perpetuity present value = C/r. These tools allow us to value any cash flow including