FIN 472 FixedIncome Securities Forward Rates


 Pauline Lloyd
 5 years ago
 Views:
Transcription
1 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 deposits, loan commitments Introduction to synthetic FI securities FRAs, FRNs pricing and valuing: markedtomarket Preview of topics to come 2
2 Term Structure of Interest Rates r zero Yield curve Time to maturity 0 3m 6m 1yr 3yr 5yr 10yr 30yr slide 3 Yield Curve = Term Structure of IR r Flat Normal Inverted maturity slide 4
3 Determinants of the Yield Curve Federal Reserve Board sets a target level for the Fed Funds rate implementation? the rate at which depository institutions make uncollaterized overnight loans to one another. what do banks need Fed Funds for? so, the Fed controls what? Longterm rates reflect expectations of future rates: influenced by the monetary policy general economic outlook slide 5 Yield Curve Calculus Yield curves: term structure of interest rates time value of money representation pricing and arbitrage: spot rates Simple yield curve analysis: price  yield yield to maturity, discount yields, yield curves SO approximation of price changes due to parallel shifts: duration and convexity What about more realistic shifts? 6
4 Forward Contracts Definition: a contract to exchange a good at some future date for a price determined now prespecified price, prespecified date no cash/good exchange at contracting date Time line: now: price, quantity and future transaction date later: transaction carried out at prespecified terms Potential Problems? 7 Examples Forward contract on Treasury forward contract on zero: analytic interest whenissued market Forward Rate Agreement: FRA contract on a future loan/deposit standardized, especially in Euromarkets components: 3 dates, 2 quantities, 2 prices, 1 rate Loan commitment, forward deposit 8
5 Definition: Forward Rates A forward rate is a yield quoted now on a zerocoupon bond to be delivered in the future For example, a 2year rate 1year forward is the yield quoted today on a 2year zero starting one year from now and maturing 3 years from now Mechanics: Forward Rates Forward rates are embedded in the term structure. Suppose you own a zero that matures in 1 year and yields 6%: two alternative strategies Interest could accumulate at the same rate over the entire year or It could accumulate at one rate for the first half year and at another rate for the second half year such that the average is 6%. 10
6 Two Strategies, One Result: Finding 6M Forward Rates 6M forward rates are implied by the term structure: why? 0 1/ Strategy 1 Investing 0 P 1 at 6% for 1 year interest accumulates at the same rate throughout at the end of a half year you will have: 0P at the end of a year you will have 0 P
7 Strategy 2 Alternatively, invest 0 P 1 at say 4% for 6M, and then reinvest the proceeds at another rate, say 1 r 1, at the end of a half year you will have: 0P at the end of a year you will have 0P r The Arbitrage Argument These two strategies both have to result in a 6% yield for the year if that is, if and generally r 1 = r s 1 = 2 2 = r ( ) 2 ( ) 0P s P s
8 Forward Rates from Term Structure The spotrate curve implies forward rates under the assumption of no arbitrage having $100 to invest for three years do we want a threeyear spot return? how about a oneyear spot followed by two more years of spot returns.. 15 Spot Rates Graphically, we need to assess the time line of interest to us: z 2 z 1 1 f 1 The current 1Y spot rate is z 1 = % and the current 2Y spot rate z 2 = % % % 2/11/ Forward Rates Robert B.H. Hauswald
9 Implied Forward Rates In the absence of arbitrage we need to have: (1+ z 1 )*(1+ 1 f 1 ) = (1+z 2 ) 2 ( )*(1+ 1 f 1 ) = ( ) 2 ( )*(1+ 1 f 1 ) = f 1 = f 1 = % % % % 17 The Meaning of Forward Rates If we knew the future short (1Y) rate: 0(Today) 8% 1 10% 2 11% 3 11% then the price of a 4Y zero would be $1,000 P = ( )( )( )( ) slide 18
10 Short vs. Spot Rate r 1 = 8% r 1 = 10% r 3 = 11% r 4 = 11% Spot rate: the yield to maturity on zerocoupon bonds Short rate: the yield to maturity on a 1Y zerocoupon bond above we have the current and future short rates slide 19 From Future to Spot Rates r 1 = 8% r 1 = 10% r 3 = 11% r 4 = 11% y 1 = 8% ( ) = y 2 = 8.995% 3 ( ) 1 1 =? y 3 = 9.66% y 4 = 9.993% 2/11/2014 ShortTerm Credit Robert B.H. Hauswald 20
11 Manufacturing a Future Loan Suppose you will need a loan in two years from now for one year. How one can create such a loan today? Go short a threeyear zero coupon bond. Go long a twoyear zero coupon bond. Cash flows are then slide 21 Future Loan Rates (1 + y n ) n = (1 + y n1 ) n1 (1 + f n ) (1 + y n ) n (1 + y n1 ) n f n 3 slide 22
12 Locking in Future Loan Rates In other words we can lock now interest rate for a loan which will be taken in future To specify a forward interest rate one should provide information about today s date beginning date of the loan end date of the loan slide 23 The Arbitrage Argument Again Buy a two years bond Buy a one year bond and then use the money to buy another bond the price can be fixed today (1+r 2 )=(1+r 1 )(1+f 12 ) Term structure of instantaneous forward rates (1+r 3 ) 3 =(1+r 1 )(1+f 13 ) 2 = (1+r 1 )(1+f 12 )(1+f 23 ) slide 24
13 slide 25 Pricing Forward Contracts General principle: forward price = spot price x costofcarry otherwise? Holds for all forward transactions: FI FX commodities Other costs of carry items? ( 1 ) t F = P + r t 26
14 Valuation of a Forward Markingtomarket: fundamental valuation principle of financial positions only valid accounting approach: alternatives? principle: value positions at their fair market price Computation principle: reverse the transaction: conceptual squaring of position, i.e., compute the cost/gain arising from the offsetting transaction 27 Forward TBill Transaction What price is right? What principle is appropriate? Forward purchase of a 1Y Tbill for in 6M: data: 6M spot rate 10%, current price 80 forward price: 88, 84, 80? Mispricing of forward: forward < spot: spot > forward: Costofcarry: r 28
15 MarkingtoMarket t Example continued: F0 P0 ( 1 r t ) = + = +. = after 3 months: still 3M to go, price and rate changes spot price of 9M bill $90, interest rate 12% t current forward price: F90 P90 ( 1 r t ) = + = +. = Selling contract nets what? valuation? marked to market? Buy side of forward: markedtomarket V 29 t = F F r t 0 1+ T t Repurchase Agreements Definition: purchase of an asset with promise to reverse (sell back) the asset later Different forward contract: why? combination of spot and forward transaction spot: forward: Function: collateralized (or: secured) lending inventory finance short selling 30
16 Repo Rate Calculations Repo: $10m of 7.25%, 5/15/2016 Tbond protection against adverse price changesand default margin: haircut of 0.5% of market price 5/10/1986: full price = hair cut: $47, amount borrowed: 9,467, /13/1986: delivery and sold for full repo rate of 6%: forward rate that equates the underlying hedging of position 31 Forward Rate Agreement (FRA) Forward contract on interest rates Not a commitment of borrowing or lending Like any forward, value for buyer increases as underlying increases Here the underlying is an interest rate Payoff based on difference between market interest rate at settlement and the contract rate protection against interestrate uncertainty 32
17 A forward rate agreement (FRA) is a forward contract based on interest rates The buyer of an FRA agrees to pay a fixedrate coupon payment (at the exercise/contract rate) and receive a floatingrate payment against a notional principal amount at a specified future date. The buyer of an FRA will receive (pay) cash when the actual interest rate at settlement is greater (less) than the exercise/contract rate (specified fixedrate). The seller of an FRA agrees to make a floatingrate payment and receive a fixedrate payment against a notional principal amount at a specified future date. The seller of an FRA will receive (pay) cash when the actual interest rate at settlement is less (greater) than the exercise rate. Forward Rate Agreements OTC contract for the exchange of payments between two parties over a single future period one party pays fixed rate, the other variable one why would parties wish to exchange obligations? Example: $100m, 3/9 FRA, 5% fixed, 6M LIBOR /9: party A pays: party B pays: 34
18 FRA Time Structure deferment period contract period dealing date spot date fixing date settlement date maturity date contract rate agreed reference rate determined settlement sum paid Application of FRAs Life insurer has fixed policy loan rate that resets every year Exposure is that in 2nd half of policy year, rates will increase and policyholders withdraw cash to earn higher interest elsewhere Purchase of FRA with 6 month settlement will mitigate risk Rates increase, insurer receives cash Rates decrease, FRA payment from bond gains
19 Implicit Forward Rates Pricing an plainvanilla forward: 1 year loan or deposit in 1 year s time transaction details what are the alternatives? arbitrage reasoning: NFL The two legs: 2 1 two year investment: ( 1 + r2 ) 2 one year investments: ( 1+ r1 )( 1+ r 1, 2) > the arbitrage relation: ( 1+ r )( 1+ r ) ( 1 r ) 2 1 1, < + Forward Rates and Prices Generalize preceding example current future rate: 1 ( 1+ 0( )) = + t yt f s, t, t > s 0 s ( 1+ ys) later future rate, i.e., future rate at a future date? work it out! Forward price on zeros: + = ( 1 ft( T1, T2 )) ( ) ( 1+ y2 ) ( 1+ y ) T t 2 T1 t 1 1 T T 2 1 (, 1) (, ) P t T = P t T 38 3
20 Summary First derivative: forwards Key concepts: forward price markedtomarket implicit forward rates FRAs and FRNs: related derivatives synthetic security YC application 39 Appendix More on forwards legal issues methodological problem Continuous forward rates simple generalization Forward rate curve More on FRAs the pricing of floaters 40
21 Problems with Forwards Legal problem: fundamental default risk reneging potential insurance: posting margins, legal arrangements alternatives: exchange traded instruments: Analytic problem: implicit YC assumption common YC assumption underlying the valuation? is it realistic? alternatives? 41 Continuous Forward Rates Let P(t,s) be the price at time t of a pure discount bond maturing at time s > t. the yield to maturity R(t,T) is the internal rate of return at time t on a bond maturing at t+t. Then P(t, t+t) = exp[r(t,t)*t] R(t,T) =  log[p(t, t+t)]/t slide 42
22 From Forward Rates to YTM The integral of the forward rates gives the yield to maturity: t+ T 1 R ( t, T ) = F( t, s) ds T Alternatively, after substituting in and taking (partial) derivatives F( t, s) = log P( t, s) s t slide 43 Forward Rate Curve Use of the yield curve underlying assumption realistic? Construct forward rate curve from current YC familiarization with forward rates prediction tool for future (spot) YC: what hypothesis implicitly underlies such an approach to YC prediction important analytic tool, especially for more advanced yield curve modelling 44
23 FRA Contract Settlement Value On 1/1, an insurer enters an FRA contract for the period of 7/112/31, the contract rate is 5%, and the notional amount is $1 million If on 7/1 rates are 6%, a borrower without an FRA would pay $1,030,000 on 12/31 With an FRA, the amount of payment on 7/1 reflects PV of excess interest throughout contract period $5, 000 = $4, ( ) 2 FRAs and Forward Rates A contract entered at t=0, where the parties (a lender and a borrower) agree to let a certain interest rate R*, act on a prespecified principal, K, over some future time period [S,T]. Assuming continuous compounding we have at time S: K at time T: Ke R*(TS) Calculate the FRA rate R* which sets PV=0 hint: it is equal to forward rate slide 46
24 FRA Pricing Use YC to infer future LIBOR from implied forward rates necessary data: 6M rate for in 3M: fixed rate what else needs to be done? Settlement: at the end of the reference period: 3M netted: just the then prevailing net flow what is paid at start of contract? 47 Floaters Floating rate notes (FRNs): FIS (!) paying coupons linked to some other interest rate LIBOR, Treasury, prime + index linked security with premium Valuation: extend FRA idea calculate reset rates as implied forward rates from current YC add the spread discount back using, again, YC 48
FIN 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 informationInterest Rate and Currency Swaps
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)
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 informationSolutions 2. 1. For the benchmark maturity sectors in the United States Treasury bill markets,
FIN 472 Professor Robert Hauswald FixedIncome Securities Kogod School of Business, AU Solutions 2 1. For the benchmark maturity sectors in the United States Treasury bill markets, Bloomberg reported the
More informationFIN 683 Financial Institutions Management InterestRate Risk
FIN 683 Financial Institutions Management InterestRate Risk Professor Robert B.H. Hauswald Kogod School of Business, AU Interest Rate Risk FIs (financial institutions or intermediaries) face two core
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 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 informationTrading the Yield Curve. Copyright 19992006 Investment Analytics
Trading the Yield Curve Copyright 19992006 Investment Analytics 1 Trading the Yield Curve Repos Riding the Curve Yield Spread Trades Coupon Rolls Yield Curve Steepeners & Flatteners Butterfly Trading
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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 informationAsset Valuation Debt Investments: Analysis and Valuation
Asset Valuation Debt Investments: Analysis and Valuation Joel M. Shulman, Ph.D, CFA Study Session # 15 Level I CFA CANDIDATE READINGS: Fixed Income Analysis for the Chartered Financial Analyst Program:
More informationLOS 56.a: Explain steps in the bond valuation process.
The following is a review of the Analysis of Fixed Income Investments principles designed to address the learning outcome statements set forth by CFA Institute. This topic is also covered in: Introduction
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 informationUnderstanding 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
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 informationChapter 5 Financial Forwards and Futures
Chapter 5 Financial Forwards and Futures Question 5.1. Four different ways to sell a share of stock that has a price S(0) at time 0. Question 5.2. Description Get Paid at Lose Ownership of Receive Payment
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 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 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 informationThe new ACI Diploma. Unit 2 Fixed Income & Money Markets. Effective October 2014
The new ACI Diploma Unit 2 Fixed Income & Money Markets Effective October 2014 8 Rue du Mail, 75002 Paris  France T: +33 1 42975115  F: +33 1 42975116  www.aciforex.org The new ACI Diploma Objective
More informationHow To Understand A Rates Transaction
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 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 informationCHAPTER 11 INTRODUCTION TO SECURITY VALUATION TRUE/FALSE QUESTIONS
1 CHAPTER 11 INTRODUCTION TO SECURITY VALUATION TRUE/FALSE QUESTIONS (f) 1 The three step valuation process consists of 1) analysis of alternative economies and markets, 2) analysis of alternative industries
More informationFNCE 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
More informationHow To Invest In Stocks And Bonds
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
More informationTreasury 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
More informationChapter 12. Page 1. Bonds: Analysis and Strategy. Learning Objectives. INVESTMENTS: Analysis and Management Second Canadian Edition
INVESTMENTS: Analysis and Management Second Canadian Edition W. Sean Cleary Charles P. Jones Chapter 12 Bonds: Analysis and Strategy Learning Objectives Explain why investors buy bonds. Discuss major considerations
More informationDerivatives 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
More informationChapter 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
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 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 informationInvestments Analysis
Investments Analysis Last 2 Lectures: Fixed Income Securities Bond Prices and Yields Term Structure of Interest Rates This Lecture (#7): Fixed Income Securities Term Structure of Interest Rates Interest
More informationChapter Nine Selected Solutions
Chapter Nine Selected Solutions 1. What is the difference between book value accounting and market value accounting? How do interest rate changes affect the value of bank assets and liabilities under the
More informationBond 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 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 informationSingle Name Credit Derivatives:
Single ame Credit Derivatives: Products & Valuation Stephen M Schaefer London Business School Credit Risk Elective Summer 2012 Objectives To understand What singlename credit derivatives are How single
More informationTerm Structure of Interest Rates
Appendix 8B Term Structure of Interest Rates To explain the process of estimating the impact of an unexpected shock in shortterm interest rates on the entire term structure of interest rates, FIs use
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 informationFloatingRate Securities
FloatingRate Securities A floatingrate security, or floater, is a debt security whose coupon rate is reset at designated dates and is based on the value of a designated reference rate.  Handbook of
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 informationCreating ForwardStarting Swaps with DSFs
INTEREST RATES Creating Starting Swaps with s JULY 23, 2013 John W. Labuszewski Managing Director Research & Product Development 3124667469 jlab@cmegroup.com CME Group introduced its Deliverable Swap
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 informationYou 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
More informationChapter 11. Bond Pricing  1. Bond Valuation: Part I. Several Assumptions: To simplify the analysis, we make the following assumptions.
Bond Pricing  1 Chapter 11 Several Assumptions: To simplify the analysis, we make the following assumptions. 1. The coupon payments are made every six months. 2. The next coupon payment for the bond is
More informationFIN 683 Financial Institutions Management ForeignCurrency Risk
FIN 683 Financial Institutions Management ForeignCurrency Risk Professor Robert B.H. Hauswald Kogod School of Business, AU Global Banks Globalization of financial markets has increased foreign exposure
More informationZeroCoupon Bonds (Pure Discount Bonds)
ZeroCoupon Bonds (Pure Discount Bonds) The price of a zerocoupon bond that pays F dollars in n periods is F/(1 + r) n, where r is the interest rate per period. Can meet future obligations without reinvestment
More informationACI THE FINANCIAL MARKETS ASSOCIATION
ACI THE FINANCIAL MARKETS ASSOCIATION EXAMINATION FORMULAE 2009 VERSION page number INTEREST RATE..2 MONEY MARKET..... 3 FORWARDFORWARDS & FORWARD RATE AGREEMENTS..4 FIXED INCOME.....5 FOREIGN EXCHANGE
More informationInterest 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
More informationBond Market Overview and Bond Pricing
Bond Market Overview and Bond Pricing. Overview of Bond Market 2. Basics of Bond Pricing 3. Complications 4. Pricing Floater and Inverse Floater 5. Pricing Quotes and Accrued Interest What is A Bond? Bond:
More informationLecture 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
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 informationChapter 3 Fixed Income Securities
Chapter 3 Fixed Income Securities Road Map Part A Introduction to finance. Part B Valuation of assets, given discount rates. Fixedincome securities. Stocks. Real assets (capital budgeting). Part C Determination
More information2. Determine the appropriate discount rate based on the risk of the security
Fixed Income Instruments III Intro to the Valuation of Debt Securities LOS 64.a Explain the steps in the bond valuation process 1. Estimate the cash flows coupons and return of principal 2. Determine the
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 informationReview for Exam 1. Instructions: Please read carefully
Review for Exam 1 Instructions: Please read carefully The exam will have 25 multiple choice questions and 5 work problems covering chapter 1, 2, 3, 4, 14, 16. Questions in the multiple choice section will
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 informationMONEY MARKET FUND GLOSSARY
MONEY MARKET FUND GLOSSARY 1day SEC yield: The calculation is similar to the 7day Yield, only covering a one day time frame. To calculate the 1day yield, take the net interest income earned by the fund
More informationReview for Exam 1. Instructions: Please read carefully
Review for Exam 1 Instructions: Please read carefully The exam will have 20 multiple choice questions and 5 work problems. Questions in the multiple choice section will be either concept or calculation
More informationC(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 longterm fixed income securities are federal government bonds, corporate
More informationNotes for Lecture 2 (February 7)
CONTINUOUS COMPOUNDING Invest $1 for one year at interest rate r. Annual compounding: you get $(1+r). Semiannual compounding: you get $(1 + (r/2)) 2. Continuous compounding: you get $e r. Invest $1 for
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 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 informationInterest Rates and Bond Valuation
Interest Rates and Bond Valuation Chapter 6 Key Concepts and Skills Know the important bond features and bond types Understand bond values and why they fluctuate Understand bond ratings and what they mean
More information1.2 Structured notes
1.2 Structured notes Structured notes are financial products that appear to be fixed income instruments, but contain embedded options and do not necessarily reflect the risk of the issuing credit. Used
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 informationObligatory transactions on a specified date at a predetermined price
Obligatory transactions on a specified date at a predetermined price DERIVATIVE MARKET Bond Derivatives Bond Futures www.jse.co.za Johannesburg Stock Exchange A bond future is a contractual obligation
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 informationCollateral Fundamentals
COLLATERAL INITIATIVES COORDINATION FORUM Collateral Fundamentals A Dictionary Definition of Collateral: Something pledged as security for repayment of a loan, to be forfeited in the event of a default
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 informationHow To Calculate Interest Rate Derivative Options
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 informationDuration and convexity
Duration and convexity Prepared by Pamela Peterson Drake, Ph.D., CFA Contents 1. Overview... 1 A. Calculating the yield on a bond... 4 B. The yield curve... 6 C. Optionlike features... 8 D. Bond ratings...
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 informationPractice Set #2 and Solutions.
FIN672 Securities Analysis & Portfolio Management Professor Michel A. Robe Practice Set #2 and Solutions. What to do with this practice set? To help MBA students prepare for the assignment and the exams,
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 informationApplication of Interest Rate Swaps in Indian Insurance Industry Amruth Krishnan Rohit Ajgaonkar Guide: G.LN.Sarma
Institute of Actuaries of India Application of Interest Rate Swaps in Indian Insurance Industry Amruth Krishnan Rohit Ajgaonkar Guide: G.LN.Sarma 21 st IFS Seminar Indian Actuarial Profession Serving the
More informationDetermination 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
More informationBonds and the Term Structure of Interest Rates: Pricing, Yields, and (No) Arbitrage
Prof. Alex Shapiro Lecture Notes 12 Bonds and the Term Structure of Interest Rates: Pricing, Yields, and (No) Arbitrage I. Readings and Suggested Practice Problems II. Bonds Prices and Yields (Revisited)
More information