# VALUATION OF PLAIN VANILLA INTEREST RATES SWAPS

Save this PDF as:

Size: px
Start display at page:

## Transcription

2 -2- net cost of the debt to the firm ends up equaling the fixed rate to the swap partner (the third party) plus 75 basis points. The objective of this note is to show how an interest-rate swap should be valued, i.e., how the fixed-rate portion of the deal should be determined. The Problem The problem of pricing a standard interest-rate swap can be addressed at a number of different levels, depending on the level of accuracy required. Accuracy in this case means how accurately you account for potential differences in the timing of the cash flows to each party. In a real transaction involving \$500 million or more, the interest cost or payment received for just one day makes a difference. This note avoids this issue by assuming that it is always exactly three months between each payment. Let s consider the specifics of the most common form of a swap, called a plain vanilla swap. This involves the swapping of a floating-rate (LIBOR) payment for a fixed-rate payment, which is quoted as a spread over the U.S. Treasury rate of the same maturity. Examples of swaps and their pricing structure are shown in Exhibit 1. The swap rate quotes in Exhibit 1 are for the case where the floating-rate is based on the prevailing 6-month LIBOR rate where the floating and fixed payments are made semi-annually. 2 Exhibit 1 reveals that if you want to receive the fixed rate in a two-year swap, you will receive 6.06 percent and pay six-month LIBOR. If you want to pay the fixed rate, you will pay a fixed rate of 6.09 percent and receive six-month LIBOR. The difference between the ask and the bid is the amount that the dealer makes as a profit or spread on the swap by receiving 6.09 percent and paying out 6.06% on the fixed-rate part of the deal. LIBOR LIBOR Party A Party B has fixed, wants Dealer has floating, floating rate 6.06% 6.09% wants fixed rate Dealer profit.03% 2 The convention for a plain vanilla swap is that LIBOR payments are based on the rate in effect at the beginning of the period. This means that the interest due on the payment date equals the 3-month LIBOR in effect at the beginning of the quarter times the notional principal.

3 -3- All of the dates for payment are specified in the contract. At the inception of the swap no principal is exchanged, and the payments, both floating and fixed, are based on an amount called the notional principal. Assume a notional amount of \$100 million for convenience and a signing date of June 17, The terms of a two-year swap would be that one party pays the three-month LIBOR that prevails at the beginning of each quarter and in return receives 6.06 percent of \$100 million paid quarterly (\$ million). The fixed payment is made every three months and the floating payment is reset every three months to the new LIBOR rate in effect at that time. The payment schedule looks as follows: Type of Payment 9/17/95 12/17/95 3/17/96 6/17/96 9/17/96 12/17/96 3/17/97 6/17/97 Fixed \$1.515 mill. \$1.515 mill. \$1.515 mill. \$1.515 mill. \$1.515 mill. \$1.515 mill. \$1.515 mill. \$1.515 mill. Floating 3 mo LIBOR 3 mo LIBOR 3 mo LIBOR 3 mo LIBOR 3 mo LIBOR 3 mo LIBOR 3 mo LIBOR 3 mo LIBOR Swaps are often quoted as U.S. Treasury yields + basis points. For example, the quote of 6.06 percent represents a 15 basis-point spread over the prevailing two-year U.S. Treasury rate of 5.91 percent. The pricing of an interest-rate swap involves determining what fixed rate to accept today in exchange for receiving the floating-rate flows. Pricing Interest-Rate Swaps Example Like most other derivative-based financial instruments, interest-rate swaps are priced on the basis of arbitrage. Assume that you own a three-year (\$50 million face value) bond with an interest rate equal to the three-month LIBOR rate. 3 You are aware that LIBOR has been fairly volatile over the last five years (see Figure 1) and you would like to eliminate the interest-rate risk that you face for the LIBOR rate over the next three years. Interest payments are due quarterly on the 17th of September, December, March and June of each year and are calculated by taking the three-month LIBOR rate at the beginning of each quarter times the \$50 million of face value. Thus, if today was June 17 and the current three-month LIBOR was 5.75 percent, the first interest payment would be 5.75 percent / 4 = percent of \$50 million for a payment of \$718,875 due on September Note that usually such a bond would have a rate equal to LIBOR plus some number of basis points (for example, LIBOR + 50 basis points). 4 We will assume that it is exactly one-fourth of a year between interest payments. In reality the actual number of days would be used to calculate the fraction of the year in each quarter.

4 -4- Eurodollar Futures Eurodollar futures contracts can be used to lock in the forward LIBOR interest rates. Exhibit 2 shows the Eurodollar futures contract specifications, and Exhibit 3 shows Eurodollar futures prices for June 17, A futures contract is a contract between two parties: one who agrees to buy (long position) at a set price and a seller (short position) who agrees to sell at that price. In this case the underlying asset is the rate on a Eurodollar 90-day deposit. For example, the September Eurodollar deposit rate is 5.74 percent, which means that a three-month deposit would earn percent for the three months beginning September 17. When two parties agree on a futures contract they are agreeing on the forward LIBOR rate which is quoted as a Eurodollar futures price as follows: Eurodollar Futures Price = 100 (agreed upon rate 4) * 100 Thus, if the both sides agreed on a rate of percent for the three months, the Eurodollar Futures price would be As another example, Exhibit 3 shows that the contract that matures in September 1996 has a quoted settle price of which implies an annualized rate of 5.98 percent ([100 - Eurodollar Futures Price]/100). Based on this price, the implied annual forward rate is 5.98 percent or percent for the three-month period, September-December. Hedging with Eurodollar Futures In the case of the three-year loan with a \$50 million face value and an interest rate equal to three-month LIBOR, the interest-rate risk of the floating rate could be eliminated by using Eurodollar futures. Since we would want to receive money when interest rates rise and pay when they drop, we should take a short (sell) position in the Eurodollar futures contracts. Suppose we used a short position to hedge the interest-rate risk of the interest payment due December 17, We would take a short position in 50 Eurodollar futures contracts (\$50,000,000) to hedge our exposure. In doing so, we would fix our interest-rate costs at 5.98 percent. To demonstrate this, assume as above that the actual three-month rate turns out to be 6.25 percent. On our \$50 million loan we would owe \$781,250 in interest, where \$50,000,000 [LIBOR] Interest = 4 A short (sell) position in 50 contracts would have resulted in the receipt of a total of \$33,750 (\$675 50) in settlement payments. 5 The hedge therefore reduces the net interest cost to \$747,500 (\$781,250 5 Settlement payment to the futures short position for one contract is determined as: \$1,000,000 (Actual Rate Futures Rate)/4 Thus, for an actual rate of 6.25% and a futures rate of 5.98% the payment is: \$1,000,000 ( )/4 = \$1,000,000( ) = \$675.

5 -5- \$33,750). In percentage terms this is percent for the quarter (\$747,500/\$50,000,000) or 5.98 percent annualized. If LIBOR turned out to be 5.25 percent, our interest due on the \$50 million would be percent (5.25 percent / 4), or \$656,250. The short position in the 50 Eurodollar futures contracts would require a payout of \$91,250 (\$1,825 50) and the total cost would be \$747,500 (\$656,250 + \$ 91,250) or 5.98 percent annualized. A simple way of viewing the use of Eurodollar futures contracts is the following. Taking the sell side of a Eurodollar futures contract pays off the difference between the forward rate, F and the spot rate, S, or (F-S) x \$1million. Hence the combination of a position of paying the spot rate on \$1 million plus taking the sell side of a Eurodollar futures contract results in a payment of Loan + sell-side futures = fixed rate S + (F-S) = F The result converts a variable rate payment into a fixed rate payment. Thus, in this example, the Eurodollar futures contracts can be used to hedge the interest-rate risk and convert a series of unknown future three-month LIBOR rates into a series of known payments. Exhibit 4 shows the interest rate payments and LIBOR rates that can be locked in today using the Eurodollar futures contracts in Exhibit 3. 6 Because the hedging process allows us to know what all the LIBOR payments will be, we can solve for the fixed-rate payments by setting the present value of the LIBOR payments equal to the present value of the fixed payments. Swaps Determining spot rates from Eurodollar futures The usual swap transaction involves swapping from floating into a fixed equal payment. Above we saw that using futures allows us to costlessly convert the uncertain future LIBOR payments into a series of fixed payments. The fixed payments are the certainty equivalent of the LIBOR payments. They are equivalent. It is the same as choosing between four quarters and a dollar bill. You consider them equivalent because you can costlessly change from one to the other. Consequently, the present value of the fixed payments and the floating LIBOR payments should be the same. When we consider swaps, the issue is: what series of fixed equal payments has the same present value as the LIBOR payments? 6 Because futures contracts are marked to market daily, they may require periodic cash flows prior to the interest payments being hedged. This makes the hedging process more complicated than presented here and emphasizes the convenience aspect of using swaps to hedge rather than a series of futures contracts.

6 -6- The first step is to calculate the present value of the LIBOR payments. To do this we need the appropriate discount rates for each payment. This is the LIBOR spot rate. Spot rates can be estimated directly from the Eurodollar futures (forward) rates. Assume that the current 3-month LIBOR rate is 5.50 percent and that the futures rates are those shown in Exhibits 3 and 4. Then the spot rate for the first payment, S 3 mos, is percent (.055/4) for the three months or 5.50 percent annualized. The spot rate for the second payment, S 6mos is 5.62 percent and is computed as follows: (1 + S 6mos /4) 2 = (1 + S 3mos /4) 1 (1 + F 4-6mos /4) 1 S 6mos = {[(1 + S 3mos /4) 1 (1 + F 4-6mos /4) 1 ] ½ 1} 4 S 6mos = {[( /4) 1 ( /4) 1 ] ½ 1} 4 S 6mos = 5.62%. Spot rates for each interest-payment period are shown in Exhibit 5. 7 Pricing Interest-Rate Swaps Once the spot rates are estimated, the swap can be priced, i.e., the fixed rate that will be exchanged for the LIBOR rate can be computed. The process is to calculate the present value of the fixed hedged payments that result from the Eurodollar futures position using the spot rates as the discount rates (see Exhibit 6). The present value of the LIBOR payments from the Eurodollar hedged position is \$8,251,448. In order to find the fixed (annual) swap rate, FC, we need the rate that has the same present value as the present value of the Eurodollar futures hedged, or FC/4 \$50 mill. FC/4 \$50 mill. FC/4 \$50 mill. FC/4 \$50 mill. \$8,251,448 = (1+ S3mos /4) (1+S6mos/4 ) (1+ S9mos /4) (1+S36mos/4). Solving for FC/4, we find that a quarterly payment of \$754,934 has a present value of \$8,251,448. On 7 The annualized rates are determined based on the quarter for which the rate is computed. For the threeyear swap there are 36 months and 12 quarters. Therefore the final spot rate is S 36mos and is computed as: /12 S36mos = {[(1+ S33mos /4 ) (1+ F34-36mos /4 ) ] 1} (1+ S 36mos /4 ) = (1+ S33mos /4 ) x(1+ F34-36mos /4 ) If we assume that S 33 mos has already been computed as 6.012% and the three-month forward rate for months 34-36, F 34-36mos, is taken from Exhibit 3 as the futures rate for March 1998 or 6.56%, S 36 mos is: S 36 mos = {[( /4) 11 ( /4)] 1/12-1} 4 S 36 mos = {[( ) (1.0164)] 1/12-1} 4 S 36 mos = 6.057%.

7 -7- a percentage basis the swap rate (fixed rate) is 1.51% per quarter (\$754,934/\$50 million) or 6.04 percent annualized.

8 -8- Exhibit 1 VALUATION OF PLAIN VANILLA INTEREST-RATE SWAPS Swap-Rate Quotes U.S. DOLLAR SECURITY TIME BID ASK CHANGE OPEN HIGH LOW PRV CLS U.S.\$SWAPS ABSOLUTE \$SWAPS2 Index \$SWAP3 Index \$SWAP4 Index \$SWAP5 Index \$SWAP7 Index \$SWAP10 Index \$SWAP15 Index \$SWAP20 Index \$SWAP30 Index SEMI-ANN (ACT/ACT) VS 6-MO U.S.\$LIBOR LONDON INTERBANK LIUS06M INDEX

9 -9- Exhibit 2 VALUATION OF PLAIN VANILLA INTEREST-RATE SWAPS Eurodollar Futures Contract Specifications Commodity: Three-month Eurodollar Time Deposits Ticker Symbol: ED Contract Size: \$1,000,000 Contract Months: March, June, September, December Minimum Price Change: 1 bp (basis point) = \$25 Price Limit: None Trading Hours (Chicago Time): Last Day of Trading: 7:20 am - 2:00 pm (last day-9:30 am) Second London business day prior to the third Wednesday of the delivery month. Delivery: No delivery for Eurodollar futures. Settlement is in cash. Final settlement on last day of trading.

10 -10- Exhibit 3 VALUATION OF PLAIN VANILLA INTEREST-RATE SWAPS Yield Open Open High Low Settle Chg Settle Chg Interest Sep ,429 Dec ,942 Mar ,932 Jun ,783 Sep ,515 Dec ,111 Mar ,782 Jun ,897 Sep ,127 Dec ,035 Mar ,246 Jun ,456 Sep ,385 Dec ,166 Mar ,628 Jun ,432 Sep ,042 Dec ,599 Mar ,988 Jun ,272 Sep ,235 Dec ,460 Mar ,156 Jun ,810 Sep ,228 Dec ,870 Eurodollar 90-day Futures Contract Prices (WSJ June 17, 1995)

11 -11- Exhibit 4 VALUATION OF PLAIN VANILLA INTEREST-RATE SWAPS Interest Payments from using Eurodollar Futures Contracts Futures Rates Notional Interest Date (Forward Rates) Amount Payment Jun \$50 million \$ Sep million 687,500 (.0550/4 \$50M) Dec million 717,500 (.0574/4 \$50M) Mar million 710,000 Jun million 711,250 Sep million 728,750 Dec million 747,500 Mar million 773,750 June million 780,000 Sep million 791,250 Dec million 801,250 Mar million 817,500 Jun \$50 million \$820,000

12 -12- Exhibit 5 VALUATION OF INTEREST-RATE SWAPS Estimation of Spot Rates Date Futures Rates Date From To (Forward Rates) From To Months Spot Rates Jun-95 Sep June-95 Sep % Sep-95 Dec Jun-95 Dec Dec-95 Mar Jun-95 Mar Mar-96 Jun Jun-95 Jun Jun-96 Sep Jun-95 Sep Sep-96 Dec Jun-95 Dec Dec-96 Mar Jun-95 Mar Mar-97 Jun Jun-95 Jun Jun-97 Sep Jun-95 Sep Sep-97 Dec Jun-95 Dec Dec-97 Mar Jun-95 Mar Mar-98 Jun Jun-95 Jun %

13 -13- Exhibit 6 VALUATION OF PLAIN VANILLA INTEREST-RATE SWAPS Present Value of Eurodollar Futures Hedged Interest Payments Date Spot LIBOR Present From To Months Rates Payments Value Jun-95 Sep % 687,500 \$678,175 Jun-95 Dec , ,755 Jun-95 Mar , ,795 Jun-95 Jun , ,428 Jun-95 Sep , ,075 Jun-95 Dec , ,287 Jun-95 Mar , ,562 Jun-95 Jun , ,380 Jun-95 Sep , ,422 Jun-95 Dec , ,110 Jun-95 Mar , ,783 Jun-95 Jun % 820, ,676 Total Present Value \$8,251,448

14 -14- Figure 1 VALUATION OF PLAIN VANILLA INTEREST-RATE SWAPS LIBOR 3-Month Rates Interest Rates (%) /1/90 11/1/90 2/1/91 5/1/91 8/1/91 11/1/91 2/1/92 5/1/92 8/1/92 11/1/92 2/1/93 5/1/93 8/1/93 11/1/93 2/1/94 5/1/94 8/1/94 11/1/94 2/1/95 5/1/95 8/1/95 time (Monthly)

### 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 and Currency Swaps

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)

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

### Interest rate Derivatives

Interest rate Derivatives There is a wide variety of interest rate options available. The most widely offered are interest rate caps and floors. Increasingly we also see swaptions offered. This note will

### a. On what day would the 1% filter rule have issued its first signal? Was this a buy or a sell signal? At what price did the trade occur?

Answers to Chapter #7 Exercises 1. Examine the daily closing price data on the DM/\$ rate in file E07.WK1 that was used to construct Figure 7.5. Suppose you were using a 1% filter rule to trade the DM and

### 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

### 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

### 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

### 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

### 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,

### 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

### 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:

### 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

### 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

### 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 PRICING. Robert T. Daigler. Florida International University. and. Visiting Scholar. Graduate School of Business

EURODOLLAR FUTURES PRICING Robert T. Daigler Florida International University and Visiting Scholar Graduate School of Business Stanford University 1990-91 Jumiaty Nurawan Jakarta, Indonesia The Financial

### In terms of expected returns, MSFT should invest in the U.K.

Rauli Susmel Dept. of Finance Univ. of Houston FINA 4360 International Financial Management 12/4/02 Chapter 21 Short-term Investing MNCs have many choices for investing Home return(usd) = deposit interest

### 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...

### Chapter 7 Swaps. Options, Futures, and Other Derivatives, 9th Edition, Copyright John C. Hull

Chapter 7 Swaps 1 Nature of Swaps A swap is an agreement to exchange cash flows at specified future times according to certain specified rules 2 An Example of a Plain Vanilla Interest Rate Swap! An agreement

### 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

### 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

### 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:

### Hedging Borrowing Costs with Eurodollar Futures

Hedging Borrowing Costs with Eurodollar Futures DTN/The Progressive Farmer 2010 Ag Summit December 9, 2010 James Boudreault, CFA Financial Research & Product Development CME Group Agenda 1. Introduction

### 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,

### 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

### BINOMIAL OPTION PRICING

Darden Graduate School of Business Administration University of Virginia BINOMIAL OPTION PRICING Binomial option pricing is a simple but powerful technique that can be used to solve many complex option-pricing

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

### CME Eurodollar Futures An Introduction

CME Eurodollar Futures An Introduction CME Interest Rate Products October 26, 2005 What are Eurodollars? Markets developed in London in 1950 s and 60 s Time deposits denominated in U.S. dollars in commercial

### 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

### 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

### Chapter 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

### MONEY MARKET FUTURES. FINANCE TRAINER International Money Market Futures / Page 1 of 22

MONEY MARKET FUTURES 1. Conventions and Contract Specifications... 3 2. Main Markets of Money Market Futures... 7 3. Exchange and Clearing House... 8 4. The Margin System... 9 5. Comparison: Money Market

### 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

### 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.

### 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

### 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

### 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

### Treasury Floating Rate Notes

Global Banking and Markets Treasury Floating Rate Notes DATE: April 2012 Recommendation summary The USD 7trn money market should support significant FRN issuance from the Treasury. This would diversify

### 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 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

### 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

### 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

### 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

### 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

### 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

### Creating Forward-Starting Swaps with DSFs

INTEREST RATES Creating -Starting Swaps with s JULY 23, 2013 John W. Labuszewski Managing Director Research & Product Development 312-466-7469 jlab@cmegroup.com CME Group introduced its Deliverable Swap

### Foreign Exchange Market: Chapter 7. Chapter Objectives & Lecture Notes FINA 5500

Foreign Exchange Market: Chapter 7 Chapter Objectives & Lecture Notes FINA 5500 Chapter Objectives: FINA 5500 Chapter 7 / FX Markets 1. To be able to interpret direct and indirect quotes in the spot market

### In this chapter we will learn about. Treasury Notes and Bonds, Treasury Inflation Protected Securities,

2 Treasury Securities In this chapter we will learn about Treasury Bills, Treasury Notes and Bonds, Strips, Treasury Inflation Protected Securities, and a few other products including Eurodollar deposits.

### CHAPTER 27. Short-Term Financial Planning. Chapter Synopsis

CHAPTER 27 Short-Term Financial Planning Chapter Synopsis 27.1 Forecasting Short-Term Financing Needs The first step in short-term financial planning is to forecast the company s future cash flows. This

### 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 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

### 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

### 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

### 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

### Understanding Futures on the DTCC GCF Repo Index

Understanding Futures on the DTCC GCF Repo Index White Paper June 2014 This material may not be reproduced or redistributed in whole or in part without the express, prior written consent of Intercontinental

### 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

### Floating rate Payments 6m Libor. Fixed rate payments 1 300000 337500-37500 2 300000 337500-37500 3 300000 337500-37500 4 300000 325000-25000

Introduction: Interest rate swaps are used to hedge interest rate risks as well as to take on interest rate risks. If a treasurer is of the view that interest rates will be falling in the future, he may

### A guide to managing foreign exchange risk

A guide to managing foreign exchange risk CPA Australia Ltd ( CPA Australia ) is one of the world s largest accounting bodies with more than 122,000 members of the financial, accounting and business profession

### The Market for Foreign Exchange

The Market for Foreign Exchange Chapter Objective: 5 Chapter Five This chapter introduces the institutional framework within which exchange rates are determined. It lays the foundation for much of the

### 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,

### Understanding interest

& California Debt and Investment Advisory Commission Understanding interest rate swap math pricing CDIAC #06-11 January 2007 & California Debt and Investment Advisory Commission Understanding interest

The TED spread trade: illustration of the analytics using Bloomberg Aaron Nematnejad January 2003 1 The views, thoughts and opinions expressed in this article represent those of the author in his individual

### Class Note on Valuing Swaps

Corporate Finance Professor Gordon Bodnar Class Note on Valuing Swaps A swap is a financial instrument that exchanges one set of cash flows for another set of cash flows of equal expected value. Swaps

### Learning Curve An introduction to the use of the Bloomberg system in swaps analysis Received: 1st July, 2002

Learning Curve An introduction to the use of the Bloomberg system in swaps analysis Received: 1st July, 2002 Aaron Nematnejad works in the fixed income analytics team at Bloomberg L.P. in London. He graduated

### Comparing Eurodollar Strips to Interest Rate Swaps

Comparing Eurodollar Strips to Interest Rate Swaps By Ira G. Kawaller * While interest rate swaps and strips of eurodollar futures can serve as substitutes for each other, use of futures necessarily fosters

### Pricing and Strategy for Muni BMA Swaps

J.P. Morgan Management Municipal Strategy Note BMA Basis Swaps: Can be used to trade the relative value of Libor against short maturity tax exempt bonds. Imply future tax rates and can be used to take

### Modeling VaR of Swaps. Dr Nitin Singh IIM Indore (India)

Modeling VaR of Swaps Dr Nitin Singh IIM Indore (India) nsingh@iimidr.ac.in Modeling VaR of Swaps @Risk application Palisade Corporation Overview of Presentation Swaps Interest Rate Swap Structure and

### 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

### Risk Hedging Strategies for Business Enterprises A Case Study of Rio Tinto

International Journal of Business and Social Science Vol. 6, No. 5; May 2015 Risk Hedging Strategies for Business Enterprises A Case Study of Rio Tinto Li Xuepei Electronic Banking Center Industrial and

### Solutions 2. 1. For the benchmark maturity sectors in the United States Treasury bill markets,

FIN 472 Professor Robert Hauswald Fixed-Income Securities Kogod School of Business, AU Solutions 2 1. For the benchmark maturity sectors in the United States Treasury bill markets, Bloomberg reported the

### Interest Rate Swaps and Fixed Income Portfolio Analysis

White Paper Interest Rate Swaps and Fixed Income Portfolio Analysis Copyright 2014 FactSet Research Systems Inc. All rights reserved. Interest Rate Swaps and Fixed Income Portfolio Analysis Contents Introduction...

### FORWARD RATE AGREEMENT (FRA)

FORWARD RATE AGREEMENT (FRA) 1. Terminology... 3 2. Hedging with FRAs... 9 3. Determination of Forward Interest Rates (FRA)... 11 3.1 The Principle of Forward Interest Rates... 11 3.2 Highest and Lowest

### You just paid \$350,000 for a policy that will pay you and your heirs \$12,000 a year forever. What rate of return are you earning on this policy?

1 You estimate that you will have \$24,500 in student loans by the time you graduate. The interest rate is 6.5%. If you want to have this debt paid in full within five years, how much must you pay each

### 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

### 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

### Eris Interest Rate Swap Futures: Flex Contract Specifications

Eris Interest Rate Swap Futures: Flex Contract Specifications Trading Hours Contract Structure Contract Size Trading Conventions Swap Futures Leg Conventions Effective Date Cash Flow Alignment Date ( CFAD

### 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)

### 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

### CHAPTER 6. Accounting and the Time Value of Money. 2. Use of tables. 13, 14 8 1. a. Unknown future amount. 7, 19 1, 5, 13 2, 3, 4, 7

CHAPTER 6 Accounting and the Time Value of Money ASSIGNMENT CLASSIFICATION TABLE (BY TOPIC) Topics Questions Brief Exercises Exercises Problems 1. Present value concepts. 1, 2, 3, 4, 5, 9, 17 2. Use of

### 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

### Whitepaper. Eurodollar and Euribor Futures in Fixed Income Portfolio Analysis. White Paper

White Paper Whitepaper Eurodollar and Euribor Futures in Fixed Income Portfolio Analysis Copyright 2015 FactSet Research Systems Inc. All rights reserved. Eurodollar and Euribor Futures in Fixed Income

### 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

### 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

### Hedging Interest-Rate Risk: A Primer in Instruments. & Accounting. September 29, 2015. Presented by: Ruth Hardie

Hedging Interest-Rate Risk: A Primer in Instruments September 29, 2015 & Accounting Presented by: Ruth Hardie Hedge Trackers, LLC Integrated Derivative Management Interest Rate, Foreign Currency and Commodities

### 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

### Chapter 1 - Introduction

Chapter 1 - Introduction Derivative securities Futures contracts Forward contracts Futures and forward markets Comparison of futures and forward contracts Options contracts Options markets Comparison of

### January 1, Year 1 Equipment... 100,000 Note Payable... 100,000

Illustrations of Accounting for Derivatives Extension of Chapter 11 Web This reading illustrates the accounting for the interest rate swaps in Examples 13 and 14 in Chapter 11. Web problem DERIVATIVE 1

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

### The Short Dated Interest Rate Market Trading JIBAR Futures

JOHANNESBURG STOCK EXCHANGE Interest Rates The Short Dated Interest Rate Market Trading JIBAR Futures JIBAR Futures are Short Term Interest Rate (STIR) Futures based on the 3-month JIBAR (Johannesburg

### Lecture 12/13 Bond Pricing and the Term Structure of Interest Rates

1 Lecture 1/13 Bond Pricing and the Term Structure of Interest Rates Alexander K. Koch Department of Economics, Royal Holloway, University of London January 14 and 1, 008 In addition to learning the material

### MCQ on International Finance

MCQ on International Finance 1. If portable disk players made in China are imported into the United States, the Chinese manufacturer is paid with a) international monetary credits. b) dollars. c) yuan,

### The CDS market: A primer

The CDS market: A primer Including computational remarks on Default Probabilities online Roland Beck, Risk Analysis Group Folie 2 The CDS market: A primer Credit Default Swaps Short Introduction CDS are

### The new world under FAS 133: Cross-Currency Interest Rate Swaps

The new world under FAS 133: Cross-Currency Interest Rate Swaps As many US listed companies are fast realizing, the accounting requirements under Financial Accounting Standard No. 133 generate reported

### 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

### 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

### Pearson Education Limited Edinburgh Gate Harlow Essex CM20 2JE England and Associated Companies throughout the world

Pearson Education Limited Edinburgh Gate Harlow Essex CM20 2JE England and Associated Companies throughout the world Visit us on the World Wide Web at: www.pearsoned.co.uk Pearson Education Limited 2014

### OPTIONS ON SHORT-TERM INTEREST RATE FUTURES*

OPTIONS ON SHORT-TERM INTEREST RATE FUTURES* Anatoli Kuprianov Options are contracts that give their owners the right, but not the obligation, to buy or sell a specified item at a set price on or before