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A Primer for Financial Engineering A Primer for Financial Engineering Financial Signal Processing and Electronic Trading AliN.Akansu NewJerseyInstituteofTechnology Newark,NJ and MustafaU.Torun AmazonWebServices,Inc. Seattle,WA AMSTERDAM (cid:129) BOSTON (cid:129) HEIDELBERG (cid:129) LONDON NEW YORK (cid:129) OXFORD (cid:129) PARIS (cid:129) SAN DIEGO SAN FRANCISCO (cid:129) SINGAPORE (cid:129) SYDNEY (cid:129) TOKYO Academic Press is an imprint of Elsevier AcademicPressisanimprintofElsevier 125LondonWall,London,EC2Y5AS,UK 525BStreet,Suite1800,SanDiego,CA92101-4495,USA 225WymanStreet,Waltham,MA02451,USA TheBoulevard,LangfordLane,Kidlington,OxfordOX51GB,UK Copyright©2015ElsevierInc.Allrightsreserved. Nopartofthispublicationmaybereproducedortransmittedinanyformorbyanymeans,electronicor mechanical,includingphotocopying,recording,oranyinformationstorageandretrievalsystem, withoutpermissioninwritingfromthepublisher.Detailsonhowtoseekpermission,further informationaboutthePublisher’spermissionspoliciesandourarrangementswithorganizationssuchas theCopyrightClearanceCenterandtheCopyrightLicensingAgency,canbefoundatourwebsite: www.elsevier.com/permissions. Thisbookandtheindividualcontributionscontainedinitareprotectedundercopyrightbythe Publisher(otherthanasmaybenotedherein). Notices Knowledgeandbestpracticeinthisfieldareconstantlychanging.Asnewresearchandexperience broadenourunderstanding,changesinresearchmethods,professionalpractices,ormedicaltreatment maybecomenecessary. Practitionersandresearchersmustalwaysrelyontheirownexperienceandknowledgeinevaluating andusinganyinformation,methods,compounds,orexperimentsdescribedherein.Inusingsuch informationormethodstheyshouldbemindfuloftheirownsafetyandthesafetyofothers,including partiesforwhomtheyhaveaprofessionalresponsibility. Tothefullestextentofthelaw,neitherthePublishernortheauthors,contributors,oreditors,assume anyliabilityforanyinjuryand/ordamagetopersonsorpropertyasamatterofproductsliability, negligenceorotherwise,orfromanyuseoroperationofanymethods,products,instructions,orideas containedinthematerialherein. LibraryofCongressCataloging-in-PublicationData AcatalogrecordforthisbookisavailablefromtheLibraryofCongress BritishLibraryCataloguinginPublicationData AcataloguerecordforthisbookisavailablefromtheBritishLibrary ForinformationonallAcademicPresspublications visitourwebsiteathttp://store.elsevier.com/ ISBN:978-0-12-801561-2 DEDICATION ToDaria, FredandIrma ToTubaandmyparents PREFACE This book presents the authors’ professional reflections on finance, includ- ing their exposure to and interpretations of important problems historically addressed by experts in quantitative finance, electronic trading, and risk engineering. The book is a compilation of basic concepts and frameworks infinance,writtenbyengineers,foratarget audienceinterested inpursuing a career in financial engineering and electronic trading. The main goal of the book is to share the authors’ experiences as they have made a similar transitionintheirprofessionalcareers. ItisawellrecognizedphenomenonontheStreetthatmanyengineersand programmers working in the industry are lacking the very basic theoretical knowledgeandthenomenclatureofthefinancialsector.Thisbookattempts tofillthatvoid.Thematerialcoveredinthebookmayhelpsomeofthemto betterappreciatethemathematical fundamentalsoffinancialtools,systems, and services they implement and are utilized by their fellow investment bankers, portfolio managers, risk officers, and electronic traders of all varieties includinghighfrequencytraders. This book along with [1] may serve as textbook for a graduate level introductory course in Financial Engineering. The examples given in the book,andtheirMATLABcodes,providereaderswithproblemsandproject topicsforfurtherstudy. TheauthorshavebenefitedovertheyearsfromtheiraffiliationwithProf. MarcoAvellanedaofCourantInstituteofMathematicalSciencesattheNew YorkUniversity.Thankyou,Marco. AliN.Akansu MustafaU.Torun February2015 viii 11 CHAPTER Introduction 1.1 DISCLAIMER.................................................................. 7 Financialengineersbringtheirknowledgebaseandperspectivestoservethe financialindustryforapplications includingthedevelopmentofhigh-speed hardware and software infrastructure in order to trade securities (financial assets) within microseconds or faster, the design and implementation of high-frequency trading algorithms and systems, and advanced trading and risk management solutions for large size investment portfolios. A well- equipped financial engineer understands how the markets work, seeks to explain the behavior of the markets, develops mathematical and stochastic models for various signals related to the financial assets (such as price, return, volatility, comovement) through analyzing available financial data as well as understanding the market microstructure (studies on modeling the limit order book activity), then builds trading and risk management strategies using those models, and develops execution strategies to get in and out of investment positions in an asset. The list of typical questions financialengineersstrivetoanswerinclude • “What is the arrival rate of market orders and its variation in the limit orderbookofasecurity?” • “Howcanonepartition averylargeorderintosmallerorderssuchthatit won’tbesubjecttosignificantmarketimpact?” • “How does the cross correlation of two financial instruments vary in time?” • “Do high frequency traders have positive or negative impact on the marketsandwhy?” • “Can Flash Crashof May 6,2010happenagain in thefuture? What was thereasonbehindit?Howcanwepreventsimilarincidentsinthefuture?” and many others. We emphasize that these and similar questions and problems have been historically addressed in overlapping fields such as finance, economics, econometrics, and mathematical finance (also known as quantitative finance). They all pursue a similar path of applied study. Mostly, the theoretical frameworks and tools of applied mathematics, APrimerforFinancialEngineering.http://dx.doi.org/10.1016/B978-0-12-801561-2.00001-0 1 ©2015ElsevierInc.Allrightsreserved. 2 APrimerforFinancialEngineering statistics, signalprocessing,computer engineering, high-performance com- puting, information analytics, and computer communication networks are utilized to better understand and to address such important problems that frequently arise in finance. We note that financial engineers are sometimes called “quants” (experts in mathematical finance) since they practice quan- titativefinancewiththeheavyuseofthestate-of-the-art computingdevices andsystemsforhigh-speeddataprocessingandintelligentdecisionmaking inreal-time. Although the domain specifics of application is unique as expected, the interest and focus of a financial engineer is indeed quite similar to what a signalprocessingengineerdoesinprofessionallife.Regardlessoftheappli- cation focus, the goal is to extract meaningful information out of observed and harvested signals (functions or vectors that convey information) with built-in noise otherwise seem random, to develop stochastic models that mathematically describe those signals, to utilize those models to estimate andpredictcertain informationtomakeintelligentandactionabledecisions to exploit price inefficiencies in the markets. Although there has been an increasing activity in the signal processing and engineering community for financeapplicationsoverthelastfewyears(forexample,seespecialissues of IEEE Signal Processing Magazine [2] and IEEE Journal of Selected Topics in Signal Processing [3], IEEE ICASSP and EURASIP EUSIPCO conference special sessions and tutorials on Financial Signal Processing and Electronic Trading, and the edited book Financial Signal Processing and Machine Learning [1]), inter-disciplinary academic research activity, industry-universitycollaborations,andthecross-fertilizationarecurrentlyat theirinfancy.Thisisatypicalphaseintheinter-disciplinaryknowledgegen- erationprocesssincethedisciplinesofinterestgothroughtheirownlearning processes themselves to understand and assess the common problem area from their perspectives and propose possible improvements. For example, speech, image, video, EEG, EKG, and price of a stock are all described as signals,buttheinformationrepresentedandconveyedbyeachsignalisvery differentthantheothersbyitsverynature.IntheforewordofAndrewPole’s book on statistical arbitrage [4], Gregory van Kipnis states “A description with any meaningful detail at all quickly points to a series of experiments fromwhichanalertlistenercantrytoreverse-engineerthe[trading]strategy. Thatiswhyquantpractitionerstalkingeneralities thatareonlyunderstand- ablebythemathematicallytrained.”Sinceoneofthemaingoalsoffinancial engineers is to profit from their findings of market inefficiencies comple- mentedwithexpertiseintrading,“talkingingeneralities”isunderstandable. Introduction 3 However, we believe, as it is the case for every discipline, financial engi- neering has its own “dictionary” of terms coupled with a crowded toolbox, andanyonewellequippedwithnecessaryanalyticalandcomputationalskill setcanlearnandpracticethem.Weconcurthatasolidmathematicaltraining and knowledge base is a must requirement to pursue financial engineering in the professional level. However, once a competent signal processing engineerarmedwiththetheoryofsignalsandtransformsandcomputational skill set understands the terminology and the finance problems of interest, it then becomes quite natural to contribute to the field as expected. The main challenge has been to understand, translate, and describe finance problems from an engineering perspective. The book mainly attempts to fill that void by presenting, explaining, and discussing the fundamentals, the concepts and terms, and the problems of high interest in financial engineering rather than their mathematical treatment in detail. It should be considered as an entry point and guide, written by engineers, for engineers to explore and possibly move to the financial sector as the specialty area. Thebookprovidesmathematicalprincipleswithcitedreferencesandavoids rigor for the purpose. We provide simple examples and their MATLAB codes to fix the ideas for elaboration and further studies. We assume that the reader does not have any finance background and is familiar with signals and transforms, linear algebra, probability theory, and stochastic processes. We start with a discussion on market structures in Chapter 2. We high- light the entities of the financial markets including exchanges, electronic communication networks (ECNs), brokers, traders, government agencies, and many others. We further elaborate their roles and interactions in the global financial ecosystem. Then, wedelve into sixmostcommonly traded financial instruments. Namely, they are stocks, options, futures contracts, exchange traded funds (ETFs), currency pairs (FX), and fixed income securities. Each one of these instruments has its unique financial structure and properties, andserves adifferent purpose.Oneneedstounderstandthe purpose, financial structure, and properties of such a financial instrument in order to study and model its behavior in time, intelligently price it, and develop trading and risk management strategies to profit from its usually short lived inefficiencies in the market. In Chapter 2, we also provide the definitions of a wide range of financial terms including buy-side and sell-sidefirms,fundamental,technical,andquantitativefinanceandtrading, traders, investors, and brokers, European and American options, initial publicoffering(IPO),andothers. 4 APrimerforFinancialEngineering We cover the fundamentals of quantitative finance in Chapter 3. Each topicdiscussedinthischapter couldeasily beextended inanentire chapter of its own. However, our goal in Chapter 3 is to introduce the very basic concepts and structures as well as to lay the framework for the following chapters. We start with the price models and present continuous- and discrete-time geometric Brownian motion. Price models with local and stochastic volatilities, the definition of return and its statistical properties such as expected return and volatility are discussed in this chapter. After discussing the effect of sampling on volatility and price models with jumps,we delve into the modern portfolio theory (MPT) where we discuss the portfolio optimization, finding the best investment allocation vector for measured correlation (covariance/co-movement) structure of portfolio assets and targeted return along with its risk. Next, Section 3.4 revisits the capital asset pricing model (CAPM) that explains the expected return of a financial asset in terms of a risk-free asset and the expected return of the market portfolio. We cover various relevant concepts in Section 3.4 including the capital market line, market portfolio, and the security market line.Then,werevisittherelativevalueandfactormodelswherethereturnof anassetisexplained(regressed)bythereturnsofotherassetsorbyasetof factorssuchasearnings,inflation,interestrate,andothers.WeendChapter3 by revisiting a specific type offactor that is referred to as eigenportfolio as detailed inSection3.5.4.Ourdiscussiononeigenportfolioslaystheground topresentapopulartradingstrategycalledstatisticalarbitrage(Section4.6) in addition to filter the built-in market noise in the empirical correlation matrixofassetreturns(Section5.1.4). Ashighlighted inChapter 4,thepractice offinance, traders, and trading strategies may be grouped in the three major categories. These groups are called fundamental, technical, and quantitative due to their characteristics. Thefirstgroupdealswiththefinancialsofcompaniessuchasearnings,cash flow, and similar metrics. The second one is interested in the momentum, support, and trends in “price charts” of the markets. Financial engineers mostly practice quantitative finance, the third group, since they approach financialproblemsthroughmathematicalandstochasticmodels,implement- ingandexecutingthembyutilizingtherequiredcomputationaldevicesand tradinginfrastructure. Incontrasttoinvestingintoafinancialasset(buyingandholdingasecu- rityforrelativelylongperiods),tradingseeksshort-termpriceinefficiencies or trends in the markets. Thegoal in trading is simple. It is to buy low and

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hardware and software infrastructure in order to trade securities (financial assets) within In the foreword of Andrew Pole's book on to present a popular trading strategy called statistical arbitrage (Section 4.6) in addition to filter the
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