<s> FIFTH EDITION
JOHN C. HULL
  
Options, Futures,AND
Other Derivatives
FIFTH EDITION
JOHN C. HULLS Options, Futures, and Other Derivatives is unique in that it is botha best-selling college textbook and the “bible” in trading rooms throughout the world.
The Fifth Edition continues to offer the most current topics in the field with the additionare A LM eee
m CyarreR 4 “Hedging Strategies Using Futures,” a new chapter on the use offutures for hedging.
m CHAPTER 20 “More on Models and Numerical Procedures.”
| Osu ee tec Bac MMRnonstandard swap products.
m CHAPTER 27 “Credit Derivatives,” explains how these products work and how theyRT Mee
m CHAPTER 28 “Real Options,” provides realistic examples showing how the realoptions approach can be used in capital investment appraisal.
m CHAPTER 29 “Insurance, Weather, and Energy Derivatives,” explainsnon-traditional derivatives and their role in risk management.
m CuHarTeR 30 “Derivatives, Mishaps, and What We Can Learn From Them.”A new version of DerivaGem Software (Version 1.50) comes with every copy of the text. It includes a
new Applications Builder module. Updates to the software can be downloaded fromwww.preniiall.com/hull.
ISBN 0-13-0050St-5
Prentice Hall
90000Education | Upper Saddle River, New Jersey 07458 | |
Pearson
 
a ae P awww. prenhall.com
9"780130"090560
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OPTIONS, FUTURES,& OTHER DERIVATIVES
John C. Hull
Maple Financial Group Professor of Derivatives and Risk ManagementDirector, Bonham Center for FinanceJoseph L. Rotman School of ManagementUniversity of Toronto
eatin eeTall
PRENTICE HALL, UPPER SADDLE RIVER, NEW JERSEY 07458CONTENTS
 
                        
 
            
1. Tintroduction ..........cccccecceessceesseeeerseeseseassenausecnensseeeeesenseeuensauescessuseesesens vel1.1 Exchange-traded markets....00... 0c ect ener ee tnteentneee eens el1.2. Over-the-counter markets . 21.3. Forward contracts........ 21.4 Futures contracts... Ld1.5 Options ........... 61.6 Types of traders . 101.7 Other derivatives 14
Summary 15Questions and problems 16ASSIQMNMENt QUESIONS 00.2... 00. c ce eeeee cece cree cneeeeeanaaeeeeceeneneeeeteeeaaerereeeeeaeanees 17
2. Mechanics of futures markets ..........:ccscsssccscsescessssscsvsenscssenescasseoversssassens sesscesseccceescensees 1D2.1. Trading futures contracts............. 192.2. Specification of the futures contract .... . 202.3. Convergence of futures price to spot price. . 232.4 Operation of margins.......0.. ee 242.5 | Newspaper Quotes.......... 0c ceeccceceeeee cece eee eee eee enenee ee eeet nee eeees see saa bent eeeteeaeees 272.6 Keynes and Hicks....0...00...0 ce cccceee cece ceeeeetneeeeneeeeeeeeentettnetennseeeaneeeeueeeeaaes 312.7 Delivery......00...... 312.8 Types of traders 322.9 Regulation .......... 33
2.10 Accounting and tax... cece 352.11 Forward contracts vs. futures contracts.. . 36SUMMALY 00.0 ee ern Ee EEE EEE EEE net eee etree eee 37Suggestions for further reading ....... 00... ..ce cc ceeeeneec nerve ener ene etetneecateeeeaneet eee 38Questions and problemsASSIgNMENt QUESTIONS 1.00... cece eee eect eee eens e eee a eee eee ane te nee neetae eta eeea teen ees
3. Determination of forward and futures prices ..............0.:c:cscccceecceceeeeenenseneneeeneesesueeetaneeeeenee 413.1 Investment assets vs. consumption assets ..............c0eeceeceeeeseeeeneeneeee Al3.2 Short selling 0.0.0... ceccec cece eeces eee eeebeaa eee eeeneeeneseeeensseneeeeeees 43.3. Measuring interest rates .423.4 Assumptions and notation.......0..... 443.5 Forward price for an investment asset . 453.6 Known income..............0.:cccceeeees .473.7 Known yield............... .493.8 Valuing forward contracts....0......cce eee 493.9 Are forward prices and futures prices equal?... 51
3.10 Stock index futures... eee 523.11 Forward and futures contracts on currencies 553.12 Futures on commodities 0.0.0.0... . 58
            
   
            
 
      
 
x Contents3.13 Cost Of Carry ee cence eee trne reece rin reeet rane tee eenieeeeteteaenesteetaereceegaes 603.14 Delivery options ......... cess cence e ee eene eens .. 603.15 Futures prices and the expected future spol price...........cceceeeeceeesceseeeeeeeeeeen anes 61
SUMIMALY 200. cee ee een en EE EEE EEE E EEE TREE SEE FEE eager 63Suggestions for further reading .. .. 64Questions and problems ........ 65ASSIQMMeENE QUESLIONS 10... ... cece cece ence ce tee ete ce tent ee nete cae enedeeegaaseeaeseeaeteanreenes 67Appendix 3A: Proof that forward and futures prices are equal when interestrates are constant4. Hedging strategies using futures ..............:0000664.1 Basic principles ..............ceeeeeeeeee
42 Arguments for and against hedging . .
4.3 Basis risk 00... eeee tere eee 75
4.4 Minimum variance hedge ratio ......0...ccccccceceeeeccueceeeeecueeetaeeeeaeeeeeeeeeaerennenees 78
4.5 Stock index futures ...
46 Rolling the hedge forward .. . 86Summary... eee .. 87Suggestions for further reading ...............cc cc eeceeee eee eseeeeeceetaeeeeceteaaeeceeeeaeeenees 88Questions and problems 00.2.0... 0... ee reenter nee 88Assignment questions ............ceccccsceeeeeeeeeeeeeeteteneeseeesneneeeetens -- 90Appendix 4A: Proof of the minimum variance hedge ratio formula................... 92
5. Interest rate markets ...........ssseeeeee beeeweencecweesaseecesasneseceraeeseecstsausesstaeueeesseeueeeeseseensnsenees 93
5.1 Types of rates 93
5.2 Zero rates .... . 94
5.3. Bond pricing ........... 94
5.4 Determining zero rates.. .. 96
5.5 Forward rates ...........0... .. 98
5.6 Forward rate agreements ............ 00. cccc cece eee eeeeee eee nett ete eet eed ecne tensed seta teneees 100
5.7 Theories of the term structure 0.0... cecee cc ccceeereeeeeeeeeeteueeesetenes cibeeeeeeeenene 102
5.8 Day count conventions ...... .. 102
5.9 Quotations ............606 103
5.10 Treasury bond futures... 0.0 ee ener etree ete 1045.11 Eurodollar futures5.12 The LIBOR zero curve . eee$.13 Duration... 1125.14 Duration-based hedging strategies.
Summary ........:. cee
Suggestions for further reading.
Questions and problems .....
ASSIQNMENt QUESTIONS 0.00.0. icc cece eee c eee ee tence ener terrane eta beet nbee nes eaa rete
G6. SWaps.....cseccssccsecsesccseceeseesteeneesesenenseeseneessnsneeseeseneeaesenseeeeseeeeereereneeesennsseesernseeseeenens
6.1 Mechanics of interest rate swaps .
6.2 The comparative-advantage argument .........0...ceeeeceeecenee ences cece ntbe cae ceuenenens 131
6.3 Swap quotes and LIBOR Zero rates .... 0... cece cee cec sete nee een een eeeeeeeeeeasenseaenes 134
6.4 Valuation of interest rate swaps ... .136
6.5 Currency swaps... 140
6.6 Valuation of currency SWAPS..... 0.0 ccecec cee ee eee n eee e eect tebe e cere tenses sa teen eee ea dan eeees 143
6.7 Credit risk... cece ee eee e cece eee ce tcc ened ten ne neneeeeteteeeete eens seta nebeneeeteress 145Summary 146Suggestions for further reading. 147Questions and problems ........ 147
 
ASSIQNMENL QUESTIONS 2.0.0... cece cece cee ce cece et ee nee e deta een eee send eedeeaeeeebeneneeetanenes 149      
 
            
Contents xi7. Mechanics of options markets...........cccsssssesecenseeensseceeescaeeeeeanseeneeeeneeseen eee cenescee ans seeenenege 151FA Underlying assets.....000..0000.c cc cccce cece ee eee eee e ee ene e ete te tab et ata eee tad eeeteiteetanetene® 1517.2 Specification of stock Options .... 00... eaeccceee eee es cee e stent eee nee et ante et et eteneeeeed 1527.3. Newspaper quotes............. 15574 Trading ............. 1577.5 Commissions 1577.6  Margins......... cece ceeeeeeee neces .. 1587.7 The options clearing corporation ... 1607.8 Regulation 00... EE EEE deere 1617.9 Taxation... cece ee cee ect e ee nteee nn eeteneeees veeteteteeeesneee 1617.10 Warrants, executive stock options, and convertibles .. 1627AL Over-the-counter markets 000.0000... eee . 163SUMIMALY oo... cee cece cere renee ee EEE EE EU LE EE ES sda nan Eee Ee SEE ane Ee EE eRe tba 163Suggestions for further reading .........0..000 ccc ccc cceeceeceeececceeetcseceuecsateueeeuersees 164Questions and problems .Assignment questions 0.0.0.0... .cc ccc cceeecceceteeeece cee neeeeeeesneneeeeseeenuneeseseesevaanenes8. Properties of stock Options..........::sscccseccssssccssseesseavsesseeeeeeescesneesensnsraeeneeensseseneseseeenssens 1678.1 Factors affecting option prices... we 1678.2 Assumptions and notation ............0000.0 eee . 1708.3. Upper and lower bounds for option prices AT]8.4 Put-call parity 0.0. eee eee eeee reste 1748.5 Early exercise: calls on a non-dividend-paying stock .. 1758.6 Early exercise: puts on a non-dividend-paying stock ..8.7 Effect of dividends8.8 Empirical researchSUMMALY 00... ee cece ee erect ee eee nee enn EEE E EHEC EEE EEE ee On Eset anes cea bree tea Ee teeSuggestions for further reading .. 181Questions and problems ..... .. 182ASSIQMMENt QUESTIONS 0.0... i eee eect eee cette teen et en tenet ete a tenet ee eet aee te taenee nies 1839. Trading strategies involving options ................0.scccceececeeceeeeeceseeceenececeaneeuacessuansssecesraneneees 1859.1 Strategies involving a single option and a stock ........ ieee ceceeeeeeeeenereeeeeeees 1859.2 Spreads 0... eee e eee e se ee tte eeea bees . 1879.3 Combinations .. 1949.4 Other payoffs... 197Summary .......c eee 197Suggestions for further reading .. 198Questions and problems ........ .- 198
10. Introduction to binomial trees...
10.110.210.310.410.510.610.710.8
         
Assignment questions ...
A one-step binomial model .
Risk-neutral valuation ..... »--203Two-step binomial trees 1.2.00. ..... ccc csee nsec eec ence neee ete eee ee teeeesaeeeeeseeaaeeeaeeetees 205A put example 00.0.0 ieeee cere eee ce renee eee e ee eben ects enbeeee teen nneeeeteeeeeeeags 208American options .-209
Delta... eee .Matching volatility with uv and d.........ce ees 211Binomial trees im practice 0.0.0.0... cece eee neeee 212SUMMALY .0... eee eee eeSuggestions for further reading ..Questions and problems ... .Assignment Questions ........0.ccccccceetcseeec eee teeeeee ee eeetn be ttaa este cneetnnneesineeesanees 215xii
Contents
11. A model of the behavior of stock prices ..............ccccescceessccessensnseeuecessecenngscuuescssenseeueseason 216
          
    
  
      
          
11.1 The Markov property ...0... ee 21611.2 Continuous-lime slochastic processes 21711.3. The process for stock prices........... 22211.4 Review of the model .. 22311.5 The parameters ..... 22511.6 It6’s lemma.......... 22611.7 The lognormal! property .. 227Summary .0........ eee 228Suggestions for further reading. 229Questions and probiems........ .229Assignment Questions .........0...ccccceceee set eseeeeeeceee tees ee eeeeesaeneeeeeen ne ceneeesteeteed 230Appendix 11A: Derivation of It6’s lemma .........00.....eccccceeeeeceteeeuneteceeeeaeeees 23212. The Black-Scholes model..............s0ssseeeeeeeeee 23412.1 Lognormal property of stock prices . 23412.2 The distribution of the rate of return . . 23612.3) The expected return... cece teen tee ee net rte etre reese teen es teats 23712.4 Volatility... cece cece eeen cece cece eeeeeceeeeeeeeeeaeeneeeeaeaesegeeaaeeeeegenietseeeetneees 23812.5 Concepts underlying the Black-Scholes-Merton differential equation . -.24112.6 Derivation of the Black-Scholes—Merton differential equation ....... 24212.7. Risk-neutral valuation ..00...00. 0c cece ee ner ee nner rte geen ree ei ee 24412.8 Black-Scholes pricing formulas............ ccc cece teen cere teeeeeeaeneeretenaaes 24612.9 Cumulative normal distribution function........ 24812.10 Warrants issued by a company on its own stock. 24912.11 Implied volatilities 00.00. eeeceeennneceeeaneebeeeeaeaeteseeeaeeesetaaeeeeeeeaes 25012.12 The causes of volatility 000... eect e cere tener cette tees ennet ieee ta eeer tenets 25112.13 Dividends... 252Summary ....0.... ee ..256Suggestions for further reading .......00..00000000.. i .257Questions and problems ..258Assignment questions ..............c0ccccceeeeeeceeeeeeenbete eens .261Appendix 12A: Proof of Black-Scholes—Merton formula 1.2.0.0... cceeeeeeeeeeeeeee 262
Appendix 12B: Exact procedure for calculating the values of American calls ondividend-paying stocks ..00....... ccc eeceecenee ee ereeeeeeteteeenereeans 265
Appendix 12C: Calculation of cumulative probability in bivariate normal
CistribUtion 00... cece enter eeeeteeeteeteaaeeeeeeuineneeeanneneees 26613. Options on stock indices, currencies, and fUtures.............:cccsesceseececsseesenceeserseesensnseeerneneee 26713.1 Results for a stock paying a known dividend yield. 26713.2. Option pricing formulas........ cece eee eee . 26813.3. Options on stock indices . 27013.4 Currency options........ 27613.5 Futures options ......0 ee eect erences 27813.6 Valuation of futures options using binomial trees .. . 28413.7 Futures price analogy ....00.. 0. -. 28613.8  Black’s model for valuing futures Options ..0............. cee ee cee eteeeeceeenetnceeenennees 28713.9 Futures options vs. spot Options 00... .cccccccceeecceneeeeeeeenaeeeeeeeueneeeesataneeessenees 288SUMMALY «20... eters 289Suggestions for further reading. .290Questions and problems ..............000cccceeeceeeee reese ceed eee eeeeneeett et eeneeeeeeneea ceed 291
ASSIZNMENE QUESTIONS 00.0... cece ee cece recent eee een eeeeseeaaeteeeteanneseeeenieetseraaeneeed 294Appendix 13A: Derivation of differential equation satisfied by a derivativedependent on a stock providing a dividend yield ............00... 295 
               
       
Contents xiiiAppendix 13B: Derivation of differential equation satisfied by a derivativedependent on a futures price ......... beceteeeeseeeeceeaen ees eee 29714. The Greek letters.............. sean +29914.1 Illustration ....0000 29914.2. Naked and covered positions.. ..-30014.3. A stop-loss strategy 0.2.2... cc cece cece cece eee ce cece e tcc becca bance ceeeeeecaeeteeeeeteeeeeeees 30014.4 Delta hedging ........ 2. eee ceeeeeeeeeececeeteeeceteeeeeeneeeeneeaaaaenauaneneagieaeeaeeneee 30214.5 Theta........ ..30914.6 Gamma... cece sete reece eeteeneennees 31214.7 Relationship between delta, theta, and gamma ............:ccccceeeececeeceneeeeeeeeeeeeues 31514.8 Vega ec ee cece ee eee e eee e tea a bee ee cea ee tReet een etee see aaaeneeeeteee tana eeeeeeitegs 31614.9) Rho... .31814.10 Hedging in practice. 31914.11 Scenario analysis 00000000... ee cee cece eee tect eeteent ee tbe eet cette tetenenee 31914.12 Portfolio iNSUrANCe 0... eee cece eeeeeeeen ae eneeeesaeaeeeeeeseaeeeseeeesenaaeeeeeeeseeaes 32014.13 Stock market volatility. ..323SUMMALY ... 0. eect eeee eee -323Suggestions for further reading .. ..324Questions and problems ........ ..326ASSIQMMENL QUESLIONS ......... 0. cee eee cece ec ce nese e ete ate teeeaneeteees ...327Appendix 14A: Taylor series expansions and hedge parameters ........00...0..00065 32915. Volatility smiles..........ssccssssceeevesesccrseeseeccenseneecenasesseeseeeesseuseesnassenansscseresseeueeseneensees 33015.1 Put-call parity revisited... cece eterno rece ener een eet eee tenet eee 33015.2 Foreign currency options.. 33115.3. Equity options 2.0.0.0... cece ceseeeeeeeeeeeeeeeeeeteeee .. 33415.4 The volatility term structure and volatility surfaces.. ..33615.5 Greek letters cece ence ce eeeeeeeesan settee 33715.6 When a single large jump is anticipated... «33815.7 Empirical research .....000..... cece +339SUMMALY 0.0.0... eee eee eee ee 341Suggestions for further reading .. . 341Questions and problems ........ . 343Assignment Questions ........0...cccceeeeeeeenneeeeeeeaeeeeeeeaeneeseeneeaeaeeeeeeeenaeereeteeea 344Appendix 15A: Determining implied risk-neutral distributions from volatility
16. Value at risk
16.116.216.316.416.516.616.716.816.9
0 345
The VaR measure...
 
Historical simulation ...........0 0. ccc ccceeeeeeeeeceeeeeeeereeceeeeeeeeaneseeaaeneasanaeaaaeaeaaea 348Model-building approach............ ec ceeececceeneececeneeneeteeeteeeeeeeenesteeetegeenoenees 350Linear model .......0.... 352
          
Quadratic model.....Monte Carlo simulation ...Comparison of approaches...Stress testing and back testingPrincipal components analysisSummary .0.... 0... cee eee eee eee ees
Suggestions for further reading «364Questions and problems......... » 365ASSIQNMENE QUCSLIONS 0.20.00... ee eee ce cece eens ceee eee eeeeeeeaaeeeeeeeeeeaeeeeteseannaereeeeeea 366Appendix 16A: Cash-flow mapping ........00.0...0066 0 ccceececcc cece ceeetetecteeteeteeetees 368
Appendix 16B: Use of the Cornish—Fisher expansion to estimate VaR .............. 370xiv
Contents
     
 
        
17. Estimating volatilities and correlations........ «37217.1 Estimating volatility ........ cc ceececceeee eee eeeeteeeee 37217.2 The exponentially weighted moving average model 37417.3. The GARCH(1, 1) model... eee 37617.4 Choosing between the models... 37717.5 Maximum likelihood methods oe ..37817.6 Using GARCH(, 1) to forecast future volatility .. ..38217.7 Correlations... 0.0... ccc ee ee nee eneee tees . 385
SUMMALY 0... eee cece cnet cere ee ne ec ee tetera eaten teeta eee aneeeeneetedgeeeeeeceentaes 388Suggestions for further reading ........0.. 00... ccccc cece eee ec cece eetbeee ees seee sec eteceeeenes 388Questions and problems “Assignment Questions ......0.00. 0. cccceeceeeeee cece cette eee e tne teen ee eb eb nett teteeeeseeeeete nied
18. Numerical procedures...........ccsssccssssccsesceneescenescssnseanecsaneesasseeeaneeeeecanenenansesuncceaeesneesees18.1 Binomial trees18.2 Using the binomial tree for options on indices, currencies, and futures
contracts 39918.3. Binomial model for a dividend-paying stock 40218.4 Extensions to the basic tree approach............ 40518.5 Alternative procedures for constructing trees 40618.6 Monte Carlo simulation ......0.0000 ee 41018.7 Variance reduction procedures .. 41418.8 Finite difference methods..............0ceeeeeeee 41818.9 Analytic approximation to American option prices 427AY01 001000 ee 427Suggestions for further reading ..............0ccccceeecee ccc eeeeeceeeeaeteeeetaeseeeeaeeterees 428Questions and problems .
19. Exotic options
 
approximation to American option prices ofa
nd af Baranc_Aded and Whalew A22NG Of Barone-Aaesi ana Wiaicy ...-..... eee eee 455
 
        
    
19.1 Packages 0.0... .ccc ccc ceecc cece cece eee e eke enee debe cece ee sete a ebb eta eed eteedeetdeeaeeneceeeeenias 43519.2. Nonstandard American options 43619.3. Forward start options.......... ..43719.4 Compound options ., 43719.5 Chooser options .... 4381