Derivatives markets

904 Pages·69.311 MB·English

by  McDonald, Robert L(Contributor)

Derivatives Markets
Robert L. McDonald
Third Edition
ISBN 10: 1-292-02125-X
ISBN 13: 978-1-292-02125-6
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ISBN 10: 1-292-02125-X
ISBN 13: 978-1-292-02125-6
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Printed in the United States of America
111122221337033704771379197795795
P E A R S O N C U S T O M L I B R AR Y
Table of Contents
Glossary
Robert L. McDonald 1
1. Introduction to Derivatives
Robert L. McDonald 15
2. Insurance, Hedging, and Simple Strategies
Robert L. McDonald 37
3. An Introduction to Forwards and Options
Robert L. McDonald 39
4. Insurance, Collars, and Other Strategies
Robert L. McDonald 75
5. Introduction to Risk Management
Robert L. McDonald 103
6. Forwards, Futures, and Swaps
Robert L. McDonald 137
7. Commodity Forwards and Futures
Robert L. McDonald 139
8. Financial Forwards and Futures
Robert L. McDonald 171
9. Interest Rate Forwards and Futures
Robert L. McDonald 209
10. Swaps
Robert L. McDonald 247
11. Options
Robert L. McDonald 277
12. Parity and Other Option Relationships
Robert L. McDonald 279
I
333344445555666677036924582558146936773539133797713713
13. Binomial Option Pricing: Basic Concepts
Robert L. McDonald 307
14. Binomial Option Pricing: Selected Topics
Robert L. McDonald 337
15. The Black-Scholes Formula
Robert L. McDonald 363
16. Market-Making and Delta-Hedging
Robert L. McDonald 395
17. Exotic Options I
Robert L. McDonald 423
18. Financial Engineering and Applications
Robert L. McDonald 449
19. Financial Engineering and Security Design
Robert L. McDonald 451
20. Corporate Applications
Robert L. McDonald 483
21. Real Options
Robert L. McDonald 523
22. Advanced Pricing Theory and Applications
Robert L. McDonald 557
23. The Lognormal Distribution
Robert L. McDonald 559
24. Monte Carlo Valuation
Robert L. McDonald 587
25. Brownian Motion and Itô’s Lemma
Robert L. McDonald 617
26. The Black-Scholes-Merton Equation
Robert L. McDonald 641
27. Risk-Neutral and Martingale Pricing
Robert L. McDonald 663
28. Exotic Options II
Robert L. McDonald 697
29. Volatility
Robert L. McDonald 731
30. Interest Rate and Bond Derivatives
Robert L. McDonald 763
II
888888026678171719
31. Value at Risk
Robert L. McDonald 801
32. Credit Risk
Robert L. McDonald 827
Appendix: Continuous Compounding
Robert L. McDonald 861
Appendix: Jensen’s Inequality
Robert L. McDonald 867
References
Robert L. McDonald 871
Index 889
III
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Glossary
Absolutepriority Aprocedureforafirminbankruptcy notemayhaveapayoffbasedontheaveragedailystock
in which junior creditors are not paid unless more priceoverthelast20days(theAsiantail).
seniorcreditorshavebeenfullyrepaid.
Askprice Thepriceatwhichadealerormarket-maker
Accreting swap A swap where the notional amount offerstosellasecurity.Alsocalledtheofferprice.
increasesoverthelifeoftheswap. Asset swap A swap, typically involving a bond, in
Accrued interest The pro-rated portion of a bond’s whichfixedbondpaymentsareswappedforpayments
couponsincethepreviouscoupondate. basedonafloatingrate.
Affine function A function A(x) is affine if A(x)= Asset-backed security A financial claim to the cash
a+bL(x),whereL(x)isalinearfunctionofx.Note flows from a pool of assets. The regulatory defini-
thatf(x)=a+bxisaffinebutnotlinear. tion of an ABS in the United States is in 17 C.F.R.
§229.1101(c)(1).
Alpha-porting Using a futures overlay to transfer a
portfolioalpha(ameasureofsuperiorperformance) Asset-or-nothing call An option that pays a unit of
fromoneassetclasstoanother. theassetiftheassetpriceexceedsthestrikepriceat
expirationorzerootherwise.
Americanoption Anoptionthatmaybeexercisedat
anytimeduringitslife. Asset-or-nothing option An option that pays a unit
of the asset if the option is in-the-money or zero
Amortizingswap Aswapwherethenotionalamount
otherwise.
declinesoverthelifeoftheswap.
Asset-or-nothingput Anoptionthatpaysaunitofthe
Antitheticvariatemethod AtechniqueusedinMonte
assetiftheassetpriceislessthanthestrikepriceat
Carlovaluation,inwhicheachrandomdrawisusedto
expirationorzerootherwise.
createtwosimulatedpricesfromoppositetailsofthe
assetpricedistribution. Asymmetric butterfly spread A butterfly spread in
whichthedistancebetweenstrikepricesisnotequal.
Arbitrage Atransactiongeneratingapositivecashflow
At-the-money An option for which the price of the
eithertodayorinthefuturebysimultaneouslybuying
underlyingassetapproximatelyequalsthestrikeprice.
andsellingrelatedassets, withnonetinvestmentof
funds,andwithnorisk.
ArithmeticBrownianmotion Acontinuousstochastic Back-to-back transaction A transaction where a
process, x(t), in which the increments are given as dealerentersintooffsettingtransactionswithdifferent
dx(t)=αdt+σ dZ,wheredZistheincrementtoa parties,effectivelyservingasago-between.
Brownianprocess. Backwardequation SeeKolmogorovbackwardequa-
Asianoption Anoptioninwhichthepayoffatmaturity tion.
dependsuponanaverageoftheassetpricesoverthe Backwardation Aforwardcurveinwhichthefutures
lifeoftheoption. pricesarefallingwithtimetoexpiration.
Asian tail A reference price that is computed as an Barrel Aunitofvolumecommonlyusedinquotingoil
averageofrecentprices.Forexample,anequity-linked prices,equalto42gallons.
From DerivativesMarkets,ThirdEdition,RobertMcDonald.Copyright©2013byPearsonEduca-
tion,Inc.PublishedbyPearsonPrenticeHall.Allrightsreserved.
1
Glossary
Barrieroption Anoptionthathasapayoffdepending Bootstrapping This term has two meanings. First, it
upon whether, at some point during the life of the referstotheprocedurewherecouponbondsareused
option,thepriceoftheunderlyingassethasmovedpast togeneratethesetofzero-couponbondprices.Second,
areferenceprice(thebarrier).Examplesareknock-in it means the use of historical returns to create an
andknock-outoptions. empiricalprobabilitydistributionforreturns.
Basis The difference between the cash price of the Boundarycondition Thevalueofaderivativeclaimat
underlyingassetandthefuturesprice. acertaintime,orataparticularpriceoftheunderlying
asset.Forexample,aboundaryconditionforazero-
Basis point 1/100th of 1%, i.e., one ten-thousandth
couponbondisthatthebondatmaturityisworthits
(0.0001).
promisedmaturityvalue.
Basisrisk Thepossibilityofunexpectedchangesinthe
Boxspread Anoptionpositioninwhichthestockis
differencebetweenthepriceofanassetandtheprice
syntheticallypurchased(buycall,sellput)atoneprice
ofthecontracthedgingtheasset.
andsold(sellcall,buyput)atadifferentprice.When
Bearspread Thesaleofacall(orput)togetherwiththe constructedwithEuropeanoptions,theboxspreadis
purchaseofanotherwiseidenticalhigher-strikecall(or equivalenttoazero-couponbond.
put). Brownian motion A stochastic process in which the
Bermudanoption Anoptionthatcanonlybeexercised random variable moves continuously and follows a
atspecifiedtimesduringitslife. randomwalkwithnormallydistributed,independent
increments.NamedaftertheScottishbotanistRobert
Beta A Greek letter commonly used to denote the Brown, who in 1827 noticed that pollen grains sus-
slopecoefficientfromregressingthereturnonanasset pendedinwaterexhibitedcontinualmovement.Brow-
againstthereturnonthereturnonabroadmarketindex, nianmotionisalsocalledaWienerprocess.
suchastheS&P500.Betathusmeasurestheextentto
Bull spread The purchase of a call (or put) together
whichaparticularassetmovestogetherwiththeindex.
with the sale of an otherwise identical higher-strike
Becausebetameasurescomovement,itisameasureof
call(orput).
systematic risk—risk that cannot be diversified in a
portfolio. Bushel Aunitofdrymeasurecommonlyusedinquot-
inggrainprices.Abushelis4pecks,equaltoapproxi-
Bidprice Thepriceatwhichadealerormarket-maker
mately2150cubicinches.Bycomparison,acubicfoot
buysasecurity.
is1728cubicinches.
Bid-askspread Thedifferencebetweenthebidprice
Butterflyspread Apositioncreatedbybuyingacall,
andtheaskprice.
sellingtwocallsatahigherstrikeprice,andbuyinga
Binary option An option that has a payoff that is a fourthcallatastillhigherstrikeprice,withanequal
discreteamount—forexample,$1oroneshare.Also distancebetweenstrikeprices.Thebutterflyspreadcan
calledadigitaloption. alsobecreatedusingputsalone,orbybuyingastraddle
andinsuringitwiththepurchaseofout-of-the-money
Binomialtree Arepresentationofpossibleassetprice
callsandputs,orinavarietyofotherways.
movements over time, in which the asset price is
modeled as moving up or down by a given amount
eachperiod.
Calendar spread A spread position in which the
Blackformula AversionoftheBlack-Scholesformula boughtandsoldoptionsorfutureshavethesameun-
inwhichtheunderlyingassetisafuturespriceandthe derlyingassetbutdifferenttimestomaturity.
dividendyieldisreplacedwiththerisk-freerate. Calloption Acontractgivingthebuyertheright,but
not the obligation, to buy the underlying asset at a
Black-Scholesequation Thepartialdifferentialequa-
prespecifiedprice.
tionrelatingprice,delta,gamma,andtheta,thatmust
besatisfiedbyderivatives.TheBlack-Scholesformula Callprotection Aperiodduringwhichacallablebond
solvestheBlack-Scholesequation. cannotbecalled.
Black-Scholesformula Theformulagivingthepriceof Callschedule Acontractualfeatureofacallablebond,
aEuropeancalloptionasafunctionofthestockprice, specifying the price at which the company can buy
strikeprice,timetoexpiration,interestrate,volatility, thebondbackfrombondholdersatdifferentpointsin
anddividendyield. time.
2
Glossary
Callablebond Abondwheretheissuerhastheright Centrallimittheorem Oneofthemostimportantre-
tobuythebondbackfrombondholdersbypayinga sultsinstatistics,whichstatesthatthesumofindepen-
prespecifiedamount. dentandidenticallydistributedrandomvariableshasa
limitingdistributionthatisnormal.
Cap An options contract that serves as insurance
againstahighprice.(SeealsoInterestratecap.) Cheapesttodeliver Whenafuturescontractgivesthe
sellerachoiceofassettodelivertothebuyer,theasset
Caplet Acontractthatinsuresaborroweragainstahigh
thatismostprofitablefortheshorttodeliver.
interestrateonasingledate.Acollectionofcapletsis
aninterestratecap. Choleskydecomposition Aformulausedtoconstruct
a set of correlated random variables from a set of
Capped option An option with a maximum payoff,
uncorrelatedrandomvariables.
wheretheoptionisautomaticallyexercisediftheun-
derlyingassetreachesthepriceatwhichthemaximum Cleanprice Thepresentvalueofabond’sfuturecash
payoffisattained. flowslessaccruedinterest.
Clearinghouse Afinancialorganization,typicallyas-
Carry Anothertermforowninganasset,typicallyused
sociatedwithoneormoreexchanges,thatmatchesthe
torefertocommodities.(SeealsoCarrymarket and
buyandsellordersthattakeplaceduringthedayand
Costofcarry.)
keepstrackoftheobligationsandpaymentsrequired
Carrymarket Asituationwheretheforwardpriceis
ofthemembersoftheclearinghouse.
suchthatthereturnonacash-and-carryistherisk-free
Collar The purchase of a put and sale of a call at a
rate.
higherstrikeprice.
Carry trade A risky strategy in which an investor
Collarwidth Thedifferencebetweenthestrikeprices
borrowsatalowrateofinterestandlendsatahigh
ofthetwooptionsinacollar.
rateofinterest.Commoncarrytradesareborrowingin
onecurrencyandlendinginanother,orinfixedincome, Collateralized debt obligation A financial structure
borrowingshort-termandlendinglong-term. thatconsistsofapoolofassets, financedbyissuing
financialclaimsthatreapportionthereturnontheasset
Cash flow mapping A procedure in which the cash
pool.
flows of a given claim are assigned—or mapped—
Collect-on-deliveryoption Anoptionwherethepre-
to a set of benchmark claims. This provides a way
miumispaidonlywhentheoptionisexercised.
toapproximatetheclaimintermsofthebenchmark
claims. Commodityspread Offsettinglongandshortpositions
incloselyrelatedcommodities.(SeealsoCrackspread
Cashsettlement Aprocedurewheresettlemententails
andCrushspread.)
acashpaymentfromonepartytotheother,insteadof
deliveryofanasset. Compoundoption Anoptionthathasanoptionasthe
underlyingasset.
Cash-and-carry Thesimultaneousspotpurchaseand
forwardsaleofanassetorcommodity. Concave Shaped like the cross-section of an upside-
downbowl.
Cash-and-carryarbitrage Theuseofacash-and-carry
Conditional VaR (CVaR) The expected loss condi-
toeffectanarbitrage.
tional upon the VaR loss being exceeded. Another
Cash-or-nothing call An option that pays a fixed
namefortailVaR.
amount of cash if the asset price exceeds the strike
Constructive sale A term in tax law describing the
priceatexpirationorzerootherwise.
ownerofanassetenteringintoanoffsettingposition
Cash-or-nothing option An option that pays a fixed thatlargelyeliminatestheriskofholdingtheasset.
amountofcashiftheoptionisin-the-moneyorzero
Contango Aforwardcurveinwhichfuturespricesare
otherwise.
risingwithtimetoexpiration.
Cash-or-nothing put An option that pays a fixed
Contingent convertible bond A bond that becomes
amountofcashiftheassetpriceislessthanthestrike
convertibleonceacontingency(forexample,theshare
priceatexpirationorzerootherwise.
priceisgreaterthan$100for30days)hasoccurred.
CDO Seecollateralizeddebtobligation.
Continuation value The value of leaving an option
CDO-squared A collateralized debt obligation in unexercised.Youmakeanexercisedecisionbycom-
whichtheunderlyingassetpoolconsistsoftranches paringthecontinuationvaluetothevalueofimmediate
fromasetofdifferentcollateralizeddebtobligations. exercise.
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