Derivatives: Theory and Practice of Trading, Valuation, and Risk Management

381 Pages·2020·14.065 MB·English

by  Jiří Witzany

Springer Texts in Business and Economics
Jiří Witzany
Derivatives
Theory and Practice of Trading,
Valuation, and Risk Management
Springer Texts in Business and Economics
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ř
Ji í Witzany
Derivatives
Theory and Practice of Trading,
Valuation, and Risk Management
JiříWitzany
FacultyofFinance&Accounting
UniversityofEconomicsPrague
Prague,CzechRepublic
ISSN2192-4333 ISSN2192-4341 (electronic)
SpringerTextsinBusinessandEconomics
ISBN978-3-030-51750-2 ISBN978-3-030-51751-9 (eBook)
https://doi.org/10.1007/978-3-030-51751-9
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Preface
The goal of this book is to cover basic and advanced topics in the valuation and
modeling of (financial and commodity) derivatives, their institutional framework,
andtheirriskmanagement.Itisdedicatedmainlytograduatestudentsandfinancial
markets practitioners, but it may also be of interest to researchers in the fields of
derivativesvaluation,stochasticmodeling,andriskmanagement.
The book is based on its preceding version, Witzany (2013b), and on financial
derivatives lecture notes, Witzany (2011), for thenewly established financialengi-
neeringmaster’sdegreeprogramstudentsattheUniversityofEconomicsinPrague.
Compared to those publications, the text has been substantially revised and
extended,toincludenewregulatoryrequirementssuchasBaselIII,theFundamental
Review of the Trading Book (FRTB), the Interest Rate Risk of the Banking Book
(IRRB), or the Internal Capital Assessment Process (ICAAP). There is also a
detailed treatment of the counterparty credit risk, stochastic volatility estimation
methodssuchasMCMCandparticlefilters,andtheconceptofmodel-freevolatility,
VIXindexdefinition,andtherelatedvolatilitytrading.
Thefirstfourchapterscanbeusedinanintroductoryderivativescourseandcover
thebasictopics,i.e.,forwards,futures,interestrateswaps,andoptions,includingthe
Black–Scholesformuladerivationinthecontextofbinomialtreesandthecontinu-
oustimestochasticmodelingapproach.Regardingstochasticmodeling,wesystem-
aticallyuseanintuitiveapproachbasedontheconceptofbinomialtreesextendedto
continuoustimeusingtheconceptofinfinitesimals.Moredetailsonthefoundation
ofinfinitesimalsandofclassicalstochasticcalculusaregiveninappendicesAandB.
The fifth chapter focuses on risk management issues. It deals not only with the
elementary principles but also with more advanced topics such as value at risk
estimationtechniques,orcreditvaluationadjustment(CVA),whichcurrentlypres-
ent a challenge to financial institutions and researchers. The chapter explains the
principlesofseveralrecentimportantregulationsthathaveafundamentalimpacton
all risk managers, namely the Fundamental Review of the Trading Book, which
replaces the concept of value at risk with the conditional value at risk, operational
risk, or ICAAP modeling requirements. The last three chapters deal with more
advanced derivative topics. The valuation of interest rate options is not possible
without deeper stochasticcalculus foundationsintroduced inChap.6.Thischapter
alsocoverstheclassicalBacheliermodel,whichhasfoundnewapplicationsintimes
v
vi Preface
of negative interest rates. Besides the standard market model, in Chap. 7 we
investigate the most well-known short-rate and term-structure models. The last
chapter discusses a number of exotic derivatives, such as binary options, warrants,
barrierorAsianoptions,andvariousalternativestochasticmodelsthathavebecome
anecessityduetoempiricalphenomenasuchasvolatilitysmile,skew,orsurface.It
turns out that the volatility of asset return is itself stochastic. Its modeling and
estimationhavebeenthesubjectofintensiveresearchduringrecentyears.Selected
recent interesting results and advanced estimation approaches are covered in this
chapter. The chapter concludes with the definition of the VIX volatility index and
looks at volatility trading, which has become a relatively new phenomenon on the
derivativesmarket.
The readers are certainly also encouraged to study other global derivatives
textbooksthatprovidemorefocusanddetailsonvariousothertopics,suchasHull
(2018), Wilmott (2006), Cipra (2010), and the mathematically more advanced
Shreve (2004, 2005). Czech readers are also recommended Dvořák (2011) or
Cipra(2008).
Although the materials presented here have been thoroughly checked, some
mistakesmayremain,andIwillwelcomeanyfurtherremarksorrecommendations
[email protected].
Prague,CzechRepublic JiříWitzany
February2020
Acknowledgments
This book has been supported by the the Czech Science Foundation Grant 18-
05244SandVSEInstitutionalGrantIP00040.
vii
Contents
1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2 ForwardsandFutures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3 InterestRateDerivatives. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4 OptionMarkets,Valuation,andHedging. . . . . . . . . . . . . . . . . . . . 77
5 MarketRiskMeasurementandManagement. . . . . . . . . . . . . . . . . 141
6 StochasticInterestRatesandtheStandardMarketModel. . . . . . . 223
7 InterestRateModels. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261
8 ExoticOptions,VolatilitySmile,andAlternativeStochastic
Models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289
AppendixA:InfinitesimalsandtheElementaryStochasticCalculus. . . . 347
AppendixB:APrimerofClassicalStochasticCalculus. . . . . . . . . . . . . 355
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363
Index. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 369
iixx
1
Introduction
Derivatives are financial instruments that are built on (derived from) more basic
underlying assets. They are designed to transfer risk easily between different
counterparties. Instruments such as forwards, futures, swaps, or options are nowa-
daysnormallyusedbybanks,assetmanagers,orcorporatetreasurersforhedgingor
speculation.Tradingwithderivativeshasbecomeincreasinglyimportantinthelast
30yearsthroughouttheworld.Ithasbeenmadeeasierduetoelectroniccommuni-
cationandsettlementsystems,andhasgrownexponentiallyinrecentyears.Onthe
other hand, derivatives are closely related to many bank failures and even many
financialcrises,includingtheglobalfinancialcrisisof2007–2008.Thegoalofthis
bookisnottomakederivativesmorepopular,buttounderstandtheirnature;infact,
our point of view will be rather critical. In order to understand modern financial
markets, it has become necessary to know how derivatives work, how they can be
used,andhowtheyarepriced.Thistextaimstogiveanoverviewofthebasic(plain
vanilla) derivatives as well of the more complex (exotic) ones. We will focus not
onlyonthemechanicsoftradingandsettlement,butalsoonthemoredifficultissues
of valuation, hedging, and risk management in general. In order to understand the
valuation and hedging techniques, we have to develop and apply the necessary
mathematicalandstatisticaltools.
Derivatives are financial instruments whose values dependon themarket prices
of one or more basic underlying instruments. The settlement of derivatives always
takestimeinthefuture,andtheirpayoffcanusuallybecalculatedrelativelyeasilyat
that time. However, it is generally more difficult to value derivatives before settle-
ment, because the payoff, dependent on prices in the future, is not known. When
valuing derivatives, we necessarily have to deal with the uncertainty of the future
prices of the underlying assets. Derivatives also allow the elimination of physical
settlement.Thisis, inparticular,anadvantageofcommodityderivatives.Investors
may invest, hedge, or speculate on oil, wheat or cows without physically dealing
withanyoftheseassets.Thecontractscanbe,and,infact,themajorityofthemare,
settled financially, without the physical settlement of the underlying commodities.
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