A Primer for Financial Engineering: Financial Signal Processing and Electronic Trading

156 Pages·2015·2.09 MB·english

by  Ali N. Akansu

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
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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
Introduction 5
sell high, and make profit coupled with a favorable risk level. Professional
traders predefine and strictly follow a set of systematic rules (trading
strategies) in analyzing the market data to detect investment opportunities
as well as to intelligently decide how to react to those opportunities. In
Chapter4,wefocusonquantitative(rulesbased)tradingstrategies.First,we
present the terminology used in trading including long and short positions,
buy, sell, short-sell, and buy-to-cover order types, and several others. We
introduce the concepts like cost of trading, back-testing (a method to test
a trading strategy using historical data), and performance measures for a
trading strategy such as profit and loss (P&L) equitation and Sharpe ratio.
Then, we cover the three most commonly used trading strategies. The first
oneiscalledpairstradingwheretherawmarketdataisanalyzedtolookfor
indicatorsidentifyingshortlivedrelative priceinefficiencies betweenapair
of assets (Section 4.5). The second one is called statistical arbitrage where
the trader seeks arbitrage opportunities due to price inefficiencies across
industries (Section 4.6). The last one is called trend following where one
tracksstrongupwardordownwardtrendsinordertoprofitfromsuchaprice
move (Section 4.7). In the latter, we also discuss common trend detection
algorithms and their ties to linear-time invariant filters. At the end of each
section,weproviderecipesthatsummarizetheimportantstepsofthegiven
tradingstrategy.Inaddition,wealsoprovidetheMATLABimplementations
of these strategies for the readers of further interest. We conclude the
chapter with a discussion on trading in multiple frequencies where traders
gain a fine grained control over the cycle of portfolio rebalancing process
(Section4.8).
Returnandriskarethetwoinseparableandmostimportantperformance
metrics of a financial investment. It is quite analogous with the two
inseparable metrics of rate and distortion in rate-distortion theory [5]. In
Section 3.3.1.2,we define the risk of a portfolio in terms of the correlation
matrix of the return processes for the assets in the portfolio, P. For a
portfolio of N assets, there are N(N − 1)/2 unknown cross-correlations
and they need to be estimated through market measurements in order
ˆ
to form the empirical correlation matrix, P. It is a well-known fact that
ˆ
P contains significant amount of inherent market noise. In Chapter 5,
we revisit random matrix theory and leverage the asymptotically known
behavior of the eigenvalues of random matrices in order to identify the
ˆ
noise component in P, and utilize eigenfiltering for its removal from
measurements.Laterinthechapter,weextendthismethodfortheportfolios
formed with statistical arbitrage (or any form of strategy that involves