Assumptions: No transaction cost, same rate for borrowing/lending, no default/counterparty risk


 Joleen Ferguson
 1 years ago
 Views:
Transcription
1 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, etc.) Three types of traders Hedger Attempts to reduce exposure to operating risk within firm Speculator Profiting from a bet that markets will move in a certain direction Arbitrageurs Profiting without any risk Forward contracts Forward A binding agreement (obligation) to buy/sell an asset or a commodity in the future, at a price set today Contract specifies: Features and quantity of the asset to be delivered Delivery logistics (time/date/place) Underlying Asset exchanged at maturity Long = S T K Short = K  S T Forward Price with No storage cost: F 0 = S 0 (1 + r ) T F 0 = Spot price + Opportunity cost Assumptions: No transaction cost, same rate for borrowing/lending, no default/counterparty risk E.g. Spot price is $450, risk free rate = 4%, F 0 = $477. Is there arbitrage opportunity? Theoretical forward price = 450 e (4% * 1) = => There is an arbitrate opportunity. How? Time 0 1 Year Sell 1 forward contract S T Borrow $ (468.36) Buy gold spot and sell it at time T (450) S T If F 0 = $460 Time 0 1 Year Buy 1 forward contract 0 S T 460 Short 1oz. gold 450 S T Borrow/repay the bank (450)
2 E.g. Bond is 1,074 and Forward price is 1,060. There are two $50 coupon payments semiannually. Rates are 8% (6mo.) and 9% (1yr) with continuous compounding. Theoretical forward price: 1074 * e Arbitrage follows: Time 0 6 month 1 Year Buy Forward S T Sell bond 1, S T Borrow/repay the bank Borrow/repay the bank 1, , Spot $600, rate is 5% (1 year continuous compounding). Storage cost is 2% continuously compounding proportionate to spot price. What is 1 year forward price? F 0 = 600e (5% + 2%)(1) = If F 0 = 650, how is arbitrage realized? F theoretical < F0 so we take a short position Today 1 year Sell 1 forward contract ST Borrow $ e 5% = Buy underlying including storage fees 600*(e 2% 1) ST Convenience yield Ownership of physical commodity provides benefits that are not obtained by the holders of contracts for future delivery. (c y )T F 0 = S 0 e S0 < F0: Contango occurs when c > y S0 > F0: Backwardation occurs when y >c Currency Forwards F 0 = S 0 e (rrf)t r : Tyear domestic riskfree interest rate rf : Tyear foreign riskfree interest rate S 0 : Spot exchange rate e.g. S0 = 2.30 r = 0.04 r f = 0.05, T = 1 F 0 = 2.30e ( ) = C$/ Synthetic Long Currency Forward Today One Year 1 2
3 e.g. The 8 month rate in the U.S. is 5% with semiannual compounding. The 8 month interest rate in France is 6% compounded continuously. The spot exchange rate is 1.89 US$/. The 8 month forward exchange rate is 1.95 is there an arbitrage opportunity? S 0 = $1.89/ F 0 = $1.95/ R C = mln(1+rm/m) = 2 ln(1+0.05/2) = (convert to domestic continuous rate) F hypothetical = S 0 e (rrf)(t) = 1.89e ( ) (8/12) = $/ Today 8 Months Sell Forward ST Borrow * 1.89 = 4.94% continuous Convert borrowed USD and invest in for 8 months ST Valuing a Forward Contract Value of a long forward contract Value of a short forward contract f = (F 0 K)e rt f = (K F 0 )e rt e.g. 1 year long forward contract on nondividend paying stock was entered when stock is at $40 and the risk free rate is 10% p.a., continuously compounded. What is forward price and initial value of forward contract? f 0 = 0 F 0 = 40e (10%) (1) = Six months later stock price is $45, what is forward price and value of forward contract? F 6m = 45e (10%)(0.5) = f 6m = F 6m F 0 e rf = e (10%)(.5) = 2.96 Margin Requirements Margin requirements are established based on the risk level of daily transactions. Underlyings which are highly volatile and prone to large daily fluctuations in spot price will have larger margin requirements relative to a more stable underlying. e.g. A company enters into a short futures contract to sell 5,000 bushels of wheat for 250 cents per bushel. The initial margin is $3,000 and the maintenance margin is $2,000. What price change would lead to a margin call? Under what circumstance could they withdraw $1500 from the margin account? Initial value: 250 cents / 100 * 5000 = 12, /12500 = MI% Trigger a margin call 1000/12500 = 8% 250 * 8% = 20 cent drop $1500 margin withdrawn 1500 /12,500 = 12% 250 * 12% = 30 cent gain
4 e.g. Suppose there are no storage costs for crude oil and the interest rate for borrowing or lending is 5% per annum. How could you have made money on January 8, 2007 by trading June 2007 and December 2007 contracts on crude oil? Prices below Open High Low Settle Change Jun Dec June 30 th S 0 = F hypo for June = S June (1+5%) 1/2 = 60.01(1.05) 1/2 = January June December Long 1 June future 0 S June Short 1 Dec future S Dec Borrow 5% buy oil in June Dec delivery S Dec Why do we need derivatives? CDS Trading Initiation (event) Creditworthiness exchange rate drops, foreign reserves, credit rating Risk regional CDS index, global CDS index Ex Debt GDP Hypothesis Effect driven by opacity & riskiness Benefits of CDS Initiation Facilitates risk sharing expansion of the risk return space Allows hedging of adverse selection risk Adverse selection, systematic risk Costs Many more to infer asset value Not that options push down the stock price but true value MSCI Emerging Markets Exposure ETF vs EM forwards 1. Forward Stack & Roll a. Liquidity b. Transaction costs 2. Full capitals w/ ETF vs. Margin a. Cost of Capital needs to be put up front for ETFs 3. Tracking Error a. Trading timing b. Premium/discount on ETF trading c. Dividend forecast error 4. Short position access is easier for forward contracts
5 Hedging example 1 Portfolio worth 100M, B = 1.2, index futures price = 1000, contract is $250 times index Change the beta to 0.5. a) What position should the company take? # contracts = (BB*)P N /F N = (1.2.5)(100,000,000/(250)(1000)) = 280 contracts b) Company wants to increase beta to 1.5, what position should they take? # contracts = B*B P N /F N = ( )(100,000,000/(250)(1000)) = 120 contracts Hedging example 2 Portfolio of 50 million, Beta of 0.87, the manager is concerned about the performance of the market over the next two months and plans to use three month future contracts on the S&P 500 to hedge the risk. The current index is 1,250, one contract is on $250 times the index, the risk free rate is 6% per annum and the dividend yield on the index is 3% per annum. The current three month futures price is 1,259. a) What position should fund manager take to hedge exposure to market over next 2 months. # contracts = B PN/FN = 0.87(50,000,000 / (250)(1254)) = => 138 b) Calculate effect of strategy if index in 2 months is 1100 or Assume 1mo future price is 0.25% higher than index level at this time. Index drops > 1100 Gain on short position = ( ) * 250 * 135 = 5,390,625 Loss of Portfolio = 3% * 2/12 = 0.5% ( )/1250 = 11.5% actual return R P 1% =.87 ( 11.5% 1%) = % Portfolio return = % => 50mil * = Net result: Gain of = 453,125 Interest rate forwards and futures Conversion Factor Example Maturity 21years 3m + days => round to 21 years 3 months Value today = ( i=1 3.5 /1.03 i + 100/ ) / 1.03 (1/2) = Adjust for actual interest 3.5/2 = = Conversion Factor /100 = Cash price for bond = ( /32) * = $ Example: Cheapest bond to deliver. Given: most recent settle = = Bond 1 = (93.25*1.0382) = 2.69 Bond 2 = (93.25 * ) = 1.87 Bond 3 = (93.25*1.2615) = 2.12 Accrued interest for Tbonds : Actual/Actual ratio Corporate & Municipal : 30/360
6 Forward Rate Agreement (FRA) Hedging Interest rate Risk Firm expects to receive 1 million in 6 months, they plan to invest the money for 3 months firm enters into a contract with a bank. Under the contract the firm will earn 5% per annum w/ quarterly compounding for the three money period starting in six months on a principal of 1 million. N = 1,000,000 Forward Rate = 5% 6mo LIBOR = 4.4% (annual rate w/ quarterly comp) No hedge 1,000,000 * 4.4/4 = 11,000 interest With hedge Long pay 11,000 Short pay 1,000,000 * (0.05/4) = 12,500 Diff of 1500 / (1 + (0.044/4)) = Settle (1mill ) (0.044/4) = 12,500 OR Settle = [L(R k R)(T 2 T 1 )] / [1 + R(T 2 T 1 )] 1,000,000 ( ) 0.25 / (1 + (0.044)(0.25) 1, Value of FRA Difference between Rk & R: 2 scalars: i) L (notional) ii)horizon (T2 T1), good rate for 1 year better than good rate for 1 month. Rk = 5% L = 1,000,000 3 months from now, invest for 3months Rf = R 2 T 2 R 1 T 1 / T 2 T 1 = (0.045)(0.5) (0.043)(0.25) /.25 = continuously comp. Convert to 1F2 = Value to the party receiving Rk is 1,000,000( )(0.25)e *0.5 = US Treasury Bonds Quoted in dollars and thirtyseconds e.g. a bond price of is equal to where 4/32 = e.g. Party Long: Receives 6% coupon US TBond Long <= Bond 6% Coupon $$$ => Short Conversion factor required for fairness. Consider 2 bonds Bond Coupon Yield FV Mat Value Conversion factor 1 7% 6.4% year = PV (coupons + FV) w/ r = 6% 2 5% 6.4% year Payment bond 1 = (95 21/32 * ) = Payment bond 2 = (95 21/32 * ) = 84.59
7 Bond 1 2 Market Price Invoice Price Invoice Market Bond 2 is cheapest to deliver for short party Conversion rules 1) 15 years to maturity 2) Discount rate for calculation is always 6% per annum with semiannual compounding 3) Round down to nearest 3 months DurationBased Hedge Ratio Optimal number of contracts to use for hedging is N* = PD P / F C D F FC = contract price for the interestrate future contract DF = duration of the asset underlying the futures contract at maturity of the future contract PL = value of the portfolio being hedged DP = duration of asset being hedged at maturity of the hedge e.g. Portfolio A consists of a oneyear zero coupon bond with a face value of $2000 and a 10year zero coupon bond with a face value of $6000. Portfolio B consists of a 5.95year zerocoupon bond with a face value of $5000. The current yield on all bonds is 10% per annum. a. Show that both portfolios have the same duration. b. Show the % changes in the values of the two portfolios for a 0.1% per annum increase in yields are the same. c. What are the % changes in the values of the two portfolios for a 5% per annum increase in yields? Method 1 D B = 5.95 (Since you get your payment at a later date) D A = 2000e (.1)(1) * e (.1)(10) *10 / 2000e (.1)(1) e (.1)(10) = 5.95 Method 2 Portfolio Proportion A 1 : D A1 = 1year PV = 2000e (.1)(1) = % A 2 : D A2 = 10 years PV = 6000e (.1)(10) = % D A = (.45)1 + (.55) 10 = 5.95 e.g. Suppose that on January 20 a corporate treasurer learns that US$10 million will be received on May 5. The funds will be needed for a major capital investment in November. The treasurer therefore plans to make a sixmonth Eurodollar deposit as soon as the funds are received. The treasurer is concerned that Eurodollar rates may decline between January 20 and May 5 and decides to hedge using the one June Eurodollar futures. On January 20 the June Eurodollar futures is quoted at a) What Eurodollar futures position should the company take? Explain. How many June Eurodollar futures contracts should the company use to hedge its exposure? b) On May 5, the June Eurodollar futures was quoted at 96.00, and the sixmonth Eurodollar deposit rate was 4.20% per annum with semiannual compounding. Determine the firm s profit or loss on the Eurodollar futures position.
8 Q is a Eurodollar futures quote, (100Q)% is the annualized Eurodollar futures interest rate for a threemonth period beginning on the 3 rd Wed. of the delivery month Price of 1 contract = 10,000[ (100Q)] Position of Treasurer Treasurer wants to be long for the protection from rate decrease Optimal Number of Contracts = N* = PD P / F C D F = 10(.5)/1(.25) = 20 Jan20: Price of 1 future = 10,000(10025( )) = 988,000 May5: Price of 1 future = 10,000(10025(10096)) = 990,000 Gain = 20(990, ,000) = 40,000 (10mil 40,000) (0.042/2) = 10,250, /10mil = 2.51% => 5.02% per annum Suppose the term structure of interest rates is flat in the US and Australia. The USD interest rate is 7% per annum and the AUD rate is 9% per annum. The current value of the AUD is 0.62 USD. Under the terms of a swap agreement, a financial institution pays 8% per annum in AUD and receives 4% per annum in USD. The principles in the two currencies are $12 million USD and $20 million AUD. Payments are exchanged every year, with one exchange having just taken place. The swap will last two more years. What is the value of the swap to the financial institution? Assume all interest rates are continuously compounded. Solution 1  Difference in Value between USD & AUD Bonds Institution: Short USD Bond & Long AUD Bonds PV USD Bond = 0.48e 0.07(1) e 0.07(2) = USD USD Coupon = 12million * 0.04 = 0.48 PV AUD Bond = 1.6e0.09(1) e0.09(2) = AUD Coupon =20million * 0.08 = 1.6 Value of swap = B 0 S 0 B F = (19.504) = => 795,000 Solution 2 Value as Series of Forward Exchange Agreements 1 st year forward exchange F 0 = S 0 e (RDRf)t = 0.62e ( )(1) = nd year forward F 0 =S 0 e (RDRf)t = 0.62e ( )(2) = Value of swap = (.48 (1.6*0.6077))e 0.07(1) + (12.48(21.6*.5957)e 0.07(2) = 795,000 Valuation of Equity Swaps To lower risk, the fund manager agrees to pay a dealer S&P 100 return for 8.75% fixed Index moves as follows I 0 =2500 I 6mo = 2600 I 12mo = 2570 R 6mo = 2600/ = 4% Fund manager pays => Swap dealer 0.04(1,000,000) = 40,000 Swap Dealer => Fund manager (1,000,000)(182/365) = 43,630 Period 1 Net payment: Swap dealer to fund manager = 3630 R 12mo 2570/ = 1.15% => 1,000,000 (0.0115) = 11,500 Period 2 Net payment: Swap dealer to fund manager =
9
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.
More information3. I. The twoyear riskfree rate in the is 8% per annum, continuously compounded
1. Calculate the price of a 1year forward contract on gold. Assume the storage cost for gold is $5.00 per ounce, with payment made at the end of the year. Spot gold is $290 per ounce and the riskfree
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 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 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 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 informationFinance 436 Futures and Options Review Notes for Midterm Exam
Finance 436 Futures and Options Review Notes for Midterm Exam Chapter 1 1. Derivative securities: concepts 2. Futures and forward contracts: definitions and comparison Exchange trading; contract size,
More informationLecture 12. Options Strategies
Lecture 12. Options Strategies Introduction to Options Strategies Options, Futures, Derivatives 10/15/07 back to start 1 Solutions Problem 6:23: Assume that a bank can borrow or lend money at the same
More 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 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 informationDetermination of Forward and Futures Prices. Chapter 5
Determination of Forward and Futures Prices Chapter 5 Fundamentals of Futures and Options Markets, 8th Ed, Ch 5, Copyright John C. Hull 2013 1 Consumption vs Investment Assets Investment assets are assets
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 informationIntroduction to derivatives
Introduction to derivatives Miloš Kopa based on 1 What is a Derivative? A derivative is an instrument whose value depends on, or is derived from, the value of another asset. Examples: futures, forwards,
More informationChapter 4 Interest Rates. Options, Futures, and Other Derivatives 8th Edition, Copyright John C. Hull
Chapter 4 Interest Rates 1 Types of Rates Treasury rates LIBOR rates Repo rates 2 Treasury Rates Rates on instruments issued by a government in its own currency 3 LIBOR and LIBID LIBOR is the rate of interest
More informationFinance 436 Futures and Options Review Notes for Midterm Exam II. Chapter 5
Finance 436 Futures and Options Review Notes for Midterm Exam II Chapter 5 1. Investment assets vs. consumption assets 2. Short selling 3. Forward price for an investment asset that provides no income
More informationForward and Futures Contracts
Forwards&Futures page 1 of 25 Forward and Futures Contracts Part I. Forward Contracts 1. Contract design and trading mechanics. 2. Finding forward price by an arbitrage argument: creating a synthetic forward.
More informationChapter 6 Interest Rate Futures. Options, Futures, and Other Derivatives, 9th Edition, Copyright John C. Hull
Chapter 6 Interest Rate Futures 1 Day Count Convention! Defines:! the period of time to which the interest rate applies! The period of time used to calculate accrued interest (relevant when the instrument
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 informationChapter 3: Commodity Forwards and Futures
Chapter 3: Commodity Forwards and Futures In the previous chapter we study financial forward and futures contracts and we concluded that are all alike. Each commodity forward, however, has some unique
More informationFutures Price d,f $ 0.65 = (1.05) (1.04)
24 e. Currency Futures In a currency futures contract, you enter into a contract to buy a foreign currency at a price fixed today. To see how spot and futures currency prices are related, note that holding
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 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 informationChapter 10 Forwards and Futures
Chapter 10 Forwards and Futures Road Map Part A Introduction to finance. Part B Valuation of assets, given discount rates. Part C Determination of riskadjusted discount rate. Part D Introduction to derivatives.
More informationProblem Set 2. Econ 236
Problem Set 2 Econ 236 Question 1............................................................................. 10 points On 22 April 2016, the settlement prices for the Jun 2016, Sep 2016 and Dec 2016
More informationFinance 436 Futures and Options Review Notes for Midterm Exam II. Chapter 5
Finance 436 Futures and Options Review Notes for Midterm Exam II Chapter 5 1. Investment assets vs. consumption assets 2. Short selling 3. Forward price for an investment asset that provides no income
More informationChapter 4 Interest Rates. Options, Futures, and Other Derivatives 9th Edition, Copyright John C. Hull
Chapter 4 Interest Rates 1 Types of Rates! Treasury rate! LIBOR! Fed funds rate! Repo rate 2 Treasury Rate! Rate on instrument issued by a government in its own currency 3 LIBOR! LIBOR is the rate of interest
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 informationReview for Exam 1. Instructions: Please read carefully
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 informationHedging Strategies Using Futures. Chapter 3
Hedging Strategies Using Futures Chapter 3 Fundamentals of Futures and Options Markets, 8th Ed, Ch3, Copyright John C. Hull 2013 1 The Nature of Derivatives A derivative is an instrument whose value depends
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 informationThis act of setting a price today for a transaction in the future, hedging. hedge currency exposure, short long long hedge short hedge Hedgers
Section 7.3 and Section 4.5 Oct. 7, 2002 William Pugh 7.3 Example of a forward contract: In May, a crude oil producer gets together with a refiner to agree on a price for crude oil. This price is for crude
More informationFina4500 Spring 2015 Extra Practice Problems Instructions
Extra Practice Problems Instructions: The problems are similar to the ones on your previous problem sets. All interest rates and rates of inflation given in the problems are annualized (i.e., stated as
More informationFigure S9.1 Profit from long position in Problem 9.9
Problem 9.9 Suppose that a European call option to buy a share for $100.00 costs $5.00 and is held until maturity. Under what circumstances will the holder of the option make a profit? Under what circumstances
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 informationForward Rate Agreements (FRAs) Interest Rate Futures (IRF)
Forward Rate Agreements (FRAs) Interest Rate Futures (IRF) Forwardforward A cash borrowing or deposit which starts on one forward date and ends on another forward. The term, amount and interest rate are
More informationReading: Chapter 19. 7. Swaps
Reading: Chapter 19 Chap. 19. Commodities and Financial Futures 1. The mechanics of investing in futures 2. Leverage 3. Hedging 4. The selection of commodity futures contracts 5. The pricing of futures
More informationLearning Curve Interest Rate Futures Contracts Moorad Choudhry
Learning Curve Interest Rate Futures Contracts Moorad Choudhry YieldCurve.com 2004 Page 1 The market in shortterm interest rate derivatives is a large and liquid one, and the instruments involved are
More informationLecture 3: Forward Contracts Steven Skiena. http://www.cs.sunysb.edu/ skiena
Lecture 3: Forward Contracts Steven Skiena Department of Computer Science State University of New York Stony Brook, NY 11794 4400 http://www.cs.sunysb.edu/ skiena Derivatives Derivatives are financial
More informationLecture 5: Forwards, Futures, and Futures Options
OPTIONS and FUTURES Lecture 5: Forwards, Futures, and Futures Options Philip H. Dybvig Washington University in Saint Louis Spot (cash) market Forward contract Futures contract Options on futures Copyright
More informationChapter 5 Determination of Forward and Futures Prices. Options, Futures, and Other Derivatives, 9th Edition, Copyright John C.
Chapter 5 Determination of Forward and Futures Prices 1 Consumption vs Investment Assets! Investment assets are assets held by significant numbers of people purely for investment purposes (Examples: gold,
More informationFIN 472 FixedIncome Securities Forward Rates
FIN 472 FixedIncome Securities Forward Rates Professor Robert B.H. Hauswald Kogod School of Business, AU InterestRate Forwards Review of yield curve analysis Forwards yet another use of yield curve forward
More informationChapter 23 INTERESTRATE FUTURES CONTRACTS
Chapter 23 INTERESTRATE FUTURES CONTRACTS FUTURES CONTRACT  contract to sell (deliver) or buy (take delivery of) a standardized quantity (or dollar amount) of an asset on a set date (settlement date)
More informationForward contracts and futures
Forward contracts and futures A forward is an agreement between two parties to buy or sell an asset at a predetermined future time for a certain price. Goal To hedge against the price fluctuation of commodity.
More informationLECTURE 10: MULTIPERIOD MODEL FUTURES & SWAPS
Lecture 10 Futures & Swaps (1) Markus K. Brunnermeier LECTURE 10: MULTIPERIOD MODEL FUTURES & SWAPS Lecture 10 Futures & Swaps (2) Overview 1. Futures o Forwards versus Futures Price o Interest Rate Forwards
More informationCall and Put. Options. American and European Options. Option Terminology. Payoffs of European Options. Different Types of Options
Call and Put Options A call option gives its holder the right to purchase an asset for a specified price, called the strike price, on or before some specified expiration date. A put option gives its holder
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 informationForward Markets. How Forwards Are Traded. Size of OTC and ExchangeTraded Markets
Forward Markets Prf. José Fajardo Getulio Vargas Foundation 1 How Forwards Are Traded In the overthecounter (OTC) market where traders working for banks, fund managers and corporate treasurers contact
More informationIntroduction, Forwards and Futures
Introduction, Forwards and Futures Liuren Wu Zicklin School of Business, Baruch College Fall, 2007 (Hull chapters: 1,2,3,5) Liuren Wu Introduction, Forwards & Futures Option Pricing, Fall, 2007 1 / 35
More informationUsing Derivatives to Manage Interest Rate Risk
Using Derivatives to Manage Interest Rate Risk Derivatives A derivative is any instrument or contract that derives its value from another underlying asset, instrument, or contract. Managing Interest Rate
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 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 informationIntroduction to Forwards and Futures
Introduction to Forwards and Futures Liuren Wu Zicklin School of Business, Baruch College Options Markets Liuren Wu (Baruch) Forwards and Futures Options Markets 1 / 29 Outline 1 Derivatives 2 Forwards
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 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 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 informationSwaps. Chapter 7 7.1
Swaps Chapter 7 7.1 Nature of Swaps A swap is an agreement to exchange cash flows at specified future times according to certain specified rules 7.2 An Example of a Plain Vanilla Interest Rate Swap An
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 informationWeb. Chapter FINANCIAL INSTITUTIONS AND MARKETS
FINANCIAL INSTITUTIONS AND MARKETS T Chapter Summary Chapter Web he Web Chapter provides an overview of the various financial institutions and markets that serve managers of firms and investors who invest
More informationDerivative: a financial instrument whose value depends (or derives from) the values of other, more basic, underlying values (Hull, p. 1).
Introduction Options, Futures, and Other Derivatives, 7th Edition, Copyright John C. Hull 2008 1 Derivative: a financial instrument whose value depends (or derives from) the values of other, more basic,
More informationForwards and Futures
Prof. Alex Shapiro Lecture Notes 16 Forwards and Futures I. Readings and Suggested Practice Problems II. Forward Contracts III. Futures Contracts IV. ForwardSpot Parity V. Stock Index ForwardSpot Parity
More informationBEAR: A person who believes that the price of a particular security or the market as a whole will go lower.
Trading Terms ARBITRAGE: The simultaneous purchase and sale of identical or equivalent financial instruments in order to benefit from a discrepancy in their price relationship. More generally, it refers
More informationCHAPTER 11 CURRENCY AND INTEREST RATE FUTURES
Answers to endofchapter exercises ARBITRAGE IN THE CURRENCY FUTURES MARKET 1. Consider the following: Spot Rate: $ 0.65/DM German 1yr interest rate: 9% US 1yr interest rate: 5% CHAPTER 11 CURRENCY
More informationSOCIETY OF ACTUARIES FINANCIAL MATHEMATICS. EXAM FM SAMPLE QUESTIONS Financial Economics
SOCIETY OF ACTUARIES EXAM FM FINANCIAL MATHEMATICS EXAM FM SAMPLE QUESTIONS Financial Economics June 2014 changes Questions 130 are from the prior version of this document. They have been edited to conform
More informationSOLUTION1. exercise 1
exercise 1 Stock BBB has a spot price equal to 80$ and a dividend equal to 10$ will be paid in 5 months. The on year interest rate is equal to 8% (c.c). 1. Calculate the 6 month forward price? 2. Calculate
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 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 informationCHAPTER 23: FUTURES, SWAPS, AND RISK MANAGEMENT
CHAPTER 23: FUTURES, SWAPS, AND RISK MANAGEMENT PROBLEM SETS 1. In formulating a hedge position, a stock s beta and a bond s duration are used similarly to determine the expected percentage gain or loss
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 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 informationCHAPTER 22: FUTURES MARKETS
CHAPTER 22: FUTURES MARKETS 1. a. The closing price for the spot index was 1329.78. The dollar value of stocks is thus $250 1329.78 = $332,445. The closing futures price for the March contract was 1364.00,
More informationChapter 16: Financial Risk Management
Chapter 16: Financial Risk Management Introduction Overview of Financial Risk Management in Treasury Interest Rate Risk Foreign Exchange (FX) Risk Commodity Price Risk Managing Financial Risk The Benefits
More informationCoupon Bonds and Zeroes
Coupon Bonds and Zeroes Concepts and Buzzwords Coupon bonds Zerocoupon bonds Bond replication Noarbitrage price relationships Zero rates Zeroes STRIPS Dedication Implied zeroes Semiannual compounding
More informationDerivative Users Traders of derivatives can be categorized as hedgers, speculators, or arbitrageurs.
OPTIONS THEORY Introduction The Financial Manager must be knowledgeable about derivatives in order to manage the price risk inherent in financial transactions. Price risk refers to the possibility of loss
More informationFinancial Derivatives Section 4 (of part II)
Financial Derivatives Section 4 (of part II) Swaps Michail Anthropelos anthropel@webmail.unipi.gr http://web.xrh.unipi.gr/faculty/anthropelos/ University of Piraeus Spring 2016 M. Anthropelos (Un. of Piraeus)
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 informationIntroduction to Futures Contracts
Introduction to Futures Contracts September 2010 PREPARED BY Eric Przybylinski Research Analyst Gregory J. Leonberger, FSA Director of Research Abstract Futures contracts are widely utilized throughout
More informationChapter 15  Options Markets
Chapter 15  Options Markets Option contract Option trading Values of options at expiration Options vs. stock investments Option strategies Optionlike securities Option contract Options are rights to
More informationChapter 5. Determination of Forward and Futures Prices. Joel R. Barber. Department of Finance. Florida International University.
Chapter 5 Determination of Forward and Futures Prices Joel R. Barber Department of Finance Florida International University Miami, FL 33199 I. Primer on Continuous Compounding Why? Thetraditioninoptionpricingistodiscount
More informationDetermination of Forward and Futures Prices
Determination of Forward and Futures Prices Chapter 5 5.1 Consumption vs Investment Assets Investment assets are assets held by significant numbers of people purely for investment purposes (Examples: gold,
More informationSAMPLE MIDTERM QUESTIONS
SAMPLE MIDTERM QUESTIONS William L. Silber HOW TO PREPARE FOR THE MID TERM: 1. Study in a group 2. Review the concept questions in the Before and After book 3. When you review the questions listed below,
More informationFIN 472 FixedIncome Securities Forward Rates
FIN 472 FixedIncome Securities Forward Rates Professor Robert B.H. Hauswald Kogod School of Business, AU InterestRate Forwards Review of yield curve analysis Forwards yet another use of yield curve forward
More informationDerivatives Pricing a Forward / Futures Contract
Derivatives Pricing a Forward / Futures Contract Professor André Farber Solvay Brussels School of Economics and Management Université Libre de Bruxelles Valuing forward contracts: Key ideas Two different
More informationSOCIETY OF ACTUARIES FINANCIAL MATHEMATICS EXAM FM SAMPLE QUESTIONS
SOCIETY OF ACTUARIES EXAM FM FINANCIAL MATHEMATICS EXAM FM SAMPLE QUESTIONS This page indicates changes made to Study Note FM0905. April 28, 2014: Question and solutions 61 were added. January 14, 2014:
More informationRisk Management and Governance Reminder on Derivatives. Prof. Hugues Pirotte
Risk Management and Governance Reminder on Derivatives Prof. Hugues Pirotte Quick presentation made in class of the main categories of derivatives and short reminder Prof. Hugues Pirotte 2 3 Commitments
More informationMONEY 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
More informationA) 1.8% B) 1.9% C) 2.0% D) 2.1% E) 2.2%
1 Exam FM Questions Practice Exam 1 1. Consider the following yield curve: Year Spot Rate 1 5.5% 2 5.0% 3 5.0% 4 4.5% 5 4.0% Find the four year forward rate. A) 1.8% B) 1.9% C) 2.0% D) 2.1% E) 2.2% 2.
More 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 informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
ECON 4110: Sample Exam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) Economists define risk as A) the difference between the return on common
More informationLecture 4: Properties of stock options
Lecture 4: Properties of stock options Reading: J.C.Hull, Chapter 9 An European call option is an agreement between two parties giving the holder the right to buy a certain asset (e.g. one stock unit)
More informationINVESTMENT DICTIONARY
INVESTMENT DICTIONARY Annual Report An annual report is a document that offers information about the company s activities and operations and contains financial details, cash flow statement, profit and
More informationFinancial Instruments. Chapter 2
Financial Instruments Chapter 2 Major Types of Securities debt money market instruments bonds common stock preferred stock derivative securities 12 Markets and Instruments Money Market debt instruments
More information2. Futures and Forward Markets Pricing
2. Futures and Forward Markets 2.2. Pricing An Arbitrage Opportunity? Gold spot price: $300 per oz Gold 1year forward price: $325 per oz Timetodelivery: one year Rate of interest per annum (with annual
More informationChapter 12. Forwards, Futures, and Swaps
IE 5441 1 Chapter 12. Forwards, Futures, and Swaps IE 5441 2 Pricing Principles Suppose that your uncle promises that he will give you an ounce of gold 1 year from now, which is worth $1,000 today. How
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 informationFINANCIAL MATHEMATICS MONEY MARKET
FINANCIAL MATHEMATICS MONEY MARKET 1. Methods of Interest Calculation, Yield Curve and Quotation... 2 1.1 Methods to Calculate Interest... 2 1.2 The Yield Curve... 6 1.3 Interpolation... 8 1.4 Quotation...
More informationPricing Forwards and Swaps
Chapter 7 Pricing Forwards and Swaps 7. Forwards Throughout this chapter, we will repeatedly use the following property of noarbitrage: P 0 (αx T +βy T ) = αp 0 (x T )+βp 0 (y T ). Here, P 0 (w T ) is
More 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 informationPricing Forwards and Futures
Pricing Forwards and Futures Peter Ritchken Peter Ritchken Forwards and Futures Prices 1 You will learn Objectives how to price a forward contract how to price a futures contract the relationship between
More informationMarket Linked Certificates of Deposit
Market Linked Certificates of Deposit This material was prepared by Wells Fargo Securities, LLC, a registered brokerdealer and separate nonbank affiliate of Wells Fargo & Company. This material is not
More informationCurrency Futures and Forward Contracts
Currency Futures and Forward Contracts by Geneviève Payette presented to Gregor Smith Queen s University January 28, 2005 In the past 30 years exchange rates have become much more volatile and less predictable
More information