Quantitative Finance With Python: A Practical Guide to Investment Management, Trading, and Financial Engineering

Cover
Half Title
Series Page
Title Page
Copyright Page
Dedication
Contents
Foreword
Author
Contributors
Acknowledgments
SECTION I: Foundations of Quant Modeling
	CHAPTER 1: Setting the Stage: Quant Landscape
		1.1. INTRODUCTION
		1.2. QUANT FINANCE INSTITUTIONS
			1.2.1. Sell-Side: Dealers & Market Makers
			1.2.2. Buy-Side: Asset Managers & Hedge Funds
			1.2.3. Financial Technology Firms
		1.3. MOST COMMON QUANT CAREER PATHS
			1.3.1. Buy Side
			1.3.2. Sell Side
			1.3.3. Financial Technology
			1.3.4. What’s Common between Roles?
		1.4. TYPES OF FINANCIAL INSTRUMENTS
			1.4.1. Equity Instruments
			1.4.2. Debt Instruments
			1.4.3. Forwards & Futures
			1.4.4. Options
			1.4.5. Option Straddles in Practice
			1.4.6. Put-Call Parity
			1.4.7. Swaps
			1.4.8. Equity Index Total Return Swaps in Practice
			1.4.9. Over-the-Counter vs. Exchange Traded Products
		1.5. STAGES OF A QUANT PROJECT
			1.5.1. Data Collection
			1.5.2. Data Cleaning
			1.5.3. Model Implementation
			1.5.4. Model Validation
		1.6. TRENDS: WHERE IS QUANT FINANCE GOING?
			1.6.1. Automation
			1.6.2. Rapid Increase of Available Data
			1.6.3. Commoditization of Factor Premias
			1.6.4. Movement toward Incorporating Machine Learning/Artificial Intelligence
			1.6.5. Increasing Prevalence of Required Quant/Technical Skills
	CHAPTER 2: Theoretical Underpinnings of Quant Modeling: Modeling the Risk Neutral Measure
		2.1. INTRODUCTION
		2.2. RISK NEUTRAL PRICING & NO ARBITRAGE
			2.2.1. Risk Neutral vs. Actual Probabilities
			2.2.2. Theory of No Arbitrage
			2.2.3. Complete Markets
			2.2.4. Risk Neutral Valuation Equation
			2.2.5. Risk Neutral Discounting, Risk Premia & Stochastic Discount Factors
		2.3. BINOMIAL TREES
			2.3.1. Discrete vs. Continuous Time Models
			2.3.2. Scaled Random Walk
			2.3.3. Discrete Binomial Tree Model
			2.3.4. Limiting Distribution of Binomial Tree Model
		2.4. BUILDING BLOCKS OF STOCHASTIC CALCULUS
			2.4.1. Deterministic vs. Stochastic Calculus
			2.4.2. Stochastic Processes
			2.4.3. Martingales
			2.4.4. Brownian Motion
			2.4.5. Properties of Brownian Motion
		2.5. STOCHASTIC DIFFERENTIAL EQUATIONS
			2.5.1. Generic SDE Formulation
			2.5.2. Bachelier SDE
			2.5.3. Black-Scholes SDE
			2.5.4. Stochastic Models in Practice
		2.6. ITO’S LEMMA
			2.6.1. General Formulation & Theory
			2.6.2. Ito in Practice: Risk-Free Bond
			2.6.3. Ito in Practice: Black-Scholes Dynamics
		2.7. CONNECTION BETWEEN SDEs AND PDEs
			2.7.1. PDEs & Stochastic Processes
			2.7.2. Deriving the Black-Scholes PDE
			2.7.3. General Formulation: Feynman-Kac Formula
			2.7.4. Working with PDEs in Practice
		2.8. GIRSANOV’S THEOREM
			2.8.1. Change of Measure via Girsanov’s Theorem
			2.8.2. Applications of Girsanov’s Theorem
	CHAPTER 3: Theoretical Underpinnings of Quant Modeling: Modeling the Physical Measure
		3.1. INTRODUCTION: FORECASTING VS. REPLICATION
		3.2. MARKET EFFICIENCY AND RISK PREMIA
			3.2.1. Efficient Market Hypothesis
			3.2.2. Market Anomalies, Behavioral Finance & Risk Premia
			3.2.3. Risk Premia Example: Selling Insurance
		3.3. LINEAR REGRESSION MODELS
			3.3.1. Introduction & Terminology
			3.3.2. Univariate Linear Regression
			3.3.3. Multivariate Linear Regression
			3.3.4. Standard Errors & Significance Tests
			3.3.5. Assumptions of Linear Regression
			3.3.6. How are Regression Models used in Practice?
			3.3.7. Regression Models in Practice: Calculating High-Yield Betas to Stocks and
		3.4. TIME SERIES MODELS
			3.4.1. Time Series Data
			3.4.2. Stationary vs. Non-Stationary Series & Differencing
			3.4.3. White Noise & Random Walks
			3.4.4. Autoregressive Processes & Unit Root Tests
			3.4.5. Moving Average Models
			3.4.6. ARMA Models
			3.4.7. State Space Models
			3.4.8. How are Time Series Models used in practice?
		3.5. PANEL REGRESSION MODELS
		3.6. CORE PORTFOLIO AND INVESTMENT CONCEPTS
			3.6.1. Time Value of Money
			3.6.2. Compounding Returns
			3.6.3. Portfolio Calculations
			3.6.4. Portfolio Concepts in Practice: Benefit of Diversification
		3.7. BOOTSTRAPPING
			3.7.1. Overview
		3.8. PRINCIPAL COMPONENT ANALYSIS
		3.9. CONCLUSIONS: COMPARISON TO RISK NEUTRAL MEASURE
	CHAPTER 4: Python Programming Environment
		4.1. THE PYTHON PROGRAMMING LANGUAGE
		4.2. ADVANTAGES AND DISADVANTAGES OF PYTHON
		4.3. PYTHON DEVELOPMENT ENVIRONMENTS
		4.4. BASIC PROGRAMMING CONCEPTS IN PYTHON
			4.4.1. Language Syntax
			4.4.2. Data Types in Python
			4.4.3. Working with Built-in Functions
			4.4.4. Conditional Statements
			4.4.5. Operator Precedence
			4.4.6. Loops
			4.4.7. Working with Strings
			4.4.8. User-Defined Functions
			4.4.9. Variable Scope
			4.4.10. Importing Modules
			4.4.11. Exception Handling
			4.4.12. Recursive Functions
			4.4.13. Plotting/Visualizations
	CHAPTER 5: Programming Concepts in Python
		5.1. INTRODUCTION
		5.2. NUMPY LIBRARY
		5.3. PANDAS LIBRARY
		5.4. DATA STRUCTURES IN PYTHON
			5.4.1. Tuples
			5.4.2. Lists
			5.4.3. Array
			5.4.4. Differences between Lists and NumPy Arrays
			5.4.5. Covariance Matrices in Practice
			5.4.6. Covariance Matrices in Practice: Are Correlations Stationary?
			5.4.7. Series
			5.4.8. DataFrame
			5.4.9. Dictionary
		5.5. IMPLEMENTATION OF QUANT TECHNIQUES IN PYTHON
			5.5.1. Random Number Generation
			5.5.2. Linear Regression
			5.5.3. Linear Regression in Practice: Equity Return Decomposition by Fama-French Factors
			5.5.4. Autocorrelation Tests
			5.5.5. ARMA Models in Practice: Testing for Mean-Reversion in Equity Index Returns
			5.5.6. Matrix Decompositions
		5.6. OBJECT-ORIENTED PROGRAMMING IN PYTHON
			5.6.1. Principles of Object-Oriented Programming
			5.6.2. Classes in Python
			5.6.3. Constructors
			5.6.4. Destructors
			5.6.5. Class Attributes
			5.6.6. Class Methods
			5.6.7. Class Methods vs. Global Functions
			5.6.8. Operator Overloading
			5.6.9. Inheritance in Python
			5.6.10. Polymorphism in Python
		5.7. DESIGN PATTERNS
			5.7.1. Types of Design Patterns
			5.7.2. Abstract Base Classes
			5.7.3. Factory Pattern
			5.7.4. Singleton Pattern
			5.7.5. Template Method
		5.8. SEARCH ALGORITHMS
			5.8.1. Binary Search Algorithm
		5.9. SORT ALGORITHMS
			5.9.1. Selection Sort
			5.9.2. Insertion Sort
			5.9.3. Bubble Sort
			5.9.4. Merge Sort
	CHAPTER 6: Working with Financial Datasets
		6.1. INTRODUCTION
		6.2. DATA COLLECTION
			6.2.1. Overview
			6.2.2. Reading & Writing Files in Python
			6.2.3. Parsing Data from a Website
			6.2.4. Interacting with Databases in Python
		6.3. COMMON FINANCIAL DATASETS
			6.3.1. Stock Data
			6.3.2. Currency Data
			6.3.3. Futures Data
			6.3.4. Options Data
			6.3.5. Fixed Income Data
		6.4. COMMON FINANCIAL DATA SOURCES
		6.5. CLEANING DIFFERENT TYPES OF FINANCIAL DATA
			6.5.1. Proper Handling of Corporate Actions
			6.5.2. Avoiding Survivorship Bias
			6.5.3. Detecting Arbitrage in the Data
		6.6. HANDLING MISSING DATA
			6.6.1. Interpolation & Filling Forward
			6.6.2. Filling via Regression
			6.6.3. Filling via Bootstrapping
			6.6.4. Filling via K-Nearest Neighbor
		6.7. OUTLIER DETECTION
			6.7.1. Single vs. Multi-Variate Outlier Detection
			6.7.2. Plotting
			6.7.3. Standard Deviation
			6.7.4. Density Analysis
			6.7.5. Distance from K-Nearest Neighbor
			6.7.6. Outlier Detection in Practice: Identifying Anomalies in ETF Returns
	CHAPTER 7: Model Validation
		7.1. WHY IS MODEL VALIDATION SO IMPORTANT?
		7.2. HOW DO WE ENSURE OUR MODELS ARE CORRECT?
		7.3. COMPONENTS OF A MODEL VALIDATION PROCESS
			7.3.1. Model Documentation
			7.3.2. Code Review
			7.3.3. Unit Tests
			7.3.4. Production Model Change Process
		7.4. GOALS OF MODEL VALIDATION
			7.4.1. Validating Model Implementation
			7.4.2. Understanding Model Strengths and Weaknesses
			7.4.3. Identifying Model Assumptions
		7.5. TRADEOFF BETWEEN REALISTIC ASSUMPTIONS AND PARSIMONY IN MODELS
SECTION II: Options Modeling
	CHAPTER 8: Stochastic Models
		8.1. SIMPLE MODELS
			8.1.1. Black-Scholes Model
			8.1.2. Black-Scholes Model in Practice: Are Equity Returns Log-Normally Distributed?
			8.1.3. Implied Volatility Surfaces in Practice: Equity Options
			8.1.4. Bachelier Model
			8.1.5. CEV Model
			8.1.6. CEV Model in Practice: Impact of Beta
			8.1.7. Ornstein-Uhlenbeck Process
			8.1.8. Cox-Ingersol-Ross Model
			8.1.9. Conclusions
		8.2. STOCHASTIC VOLATILITY MODELS
			8.2.1. Introduction
			8.2.2. Heston Model
			8.2.3. SABR Model
			8.2.4. SABR Model in Practice: Relationship between Model Parameters and Volatility Surface
			8.2.5. Stochastic Volatility Models: Comments
		8.3. JUMP DIFFUSION MODELS
			8.3.1. Introduction
			8.3.2. Merton’s Jump Diffusion Model
			8.3.3. SVJ Model
			8.3.4. Variance Gamma Model
			8.3.5. VGSA Model
			8.3.6. Comments on Jump Processes
		8.4. LOCAL VOLATILITY MODELS
			8.4.1. Dupire’s Formula
			8.4.2. Local Volatility Model in Practice: S&P Option Local Volatility Surface
		8.5. STOCHASTIC LOCAL VOLATILITY MODELS
		8.6. PRACTICALITIES OF USING THESE MODELS
			8.6.1. Comparison of Stochastic Models
			8.6.2. Leveraging Stochastic Models in Practice
	CHAPTER 9: Options Pricing Techniques for European Options
		9.1. MODELS WITH CLOSED FORM SOLUTIONS OR ASYMPTOTIC APPROXIMATIONS
		9.2. OPTION PRICING VIA QUADRATURE
			9.2.1. Overview
			9.2.2. Quadrature Approximations
			9.2.3. Approximating a Pricing Integral via Quadrature
			9.2.4. Quadrature Methods in Practice: Digital Options Prices in Black-Scholes vs. Bachelier Model
		9.3. OPTION PRICING VIA FFT
			9.3.1. Fourier Transforms & Characteristic Functions
			9.3.2. European Option Pricing via Transform
			9.3.3. Digital Option Pricing via Transform
			9.3.4. Calculating Outer Pricing Integral via Quadrature
			9.3.5. Summary of FFT Algorithm
			9.3.6. Calculating Outer Pricing Integral via FFT
			9.3.7. Summary: Option Pricing via FFT
			9.3.8. Strike Spacing Functions
			9.3.9. Interpolation of Option Prices
			9.3.10. Technique Parameters
			9.3.11. Dependence on Technique Parameters
			9.3.12. Strengths and Weaknesses
			9.3.13. Variants of FFT Pricing Technique
			9.3.14. FFT Pricing in Practice: Sensitivity to Technique Parameters
		9.4. ROOT FINDING
			9.4.1. Setup
			9.4.2. Newton’s Method
			9.4.3. First Calibration: Implied Volatility
			9.4.4. Implied Volatility in Practice: Volatility Skew for VIX Options
		9.5. OPTIMIZATION TECHNIQUES
			9.5.1. Background & Terminology
			9.5.2. Global vs. Local Minima & Maxima
			9.5.3. First& Second-Order Conditions
			9.5.4. Unconstrained Optimization
			9.5.5. Lagrange Multipliers
			9.5.6. Optimization with Equality Constraints
			9.5.7. Minimum Variance Portfolios in Practice: Stock & Bond Minimum Variance Portfolio Weights
			9.5.8. Convex Functions
			9.5.9. Optimization Methods in Practice
		9.6. CALIBRATION OF VOLATILITY SURFACES
			9.6.1. Optimization Formulation
			9.6.2. Objective Functions
			9.6.3. Constraints
			9.6.4. Regularization
			9.6.5. Gradient-Based vs. Gradient-Free Optimizers
			9.6.6. Gradient-Based Methods with Linear Constraints
			9.6.7. Practicalities of Calibrating Volatility Surfaces
			9.6.8. Calibration in Practice: BRLJPY Currency Options
	CHAPTER 10: Options Pricing Techniques for Exotic Options
		10.1. INTRODUCTION
		10.2. SIMULATION
			10.2.1. Overview
			10.2.2. Central Limit Theorem & Law of Large Numbers
			10.2.3. Random Number Generators
			10.2.4. Generating Random Variables
			10.2.5. Transforming Random Numbers
			10.2.6. Transforming Random Numbers: Inverse Transform Technique
			10.2.7. Transforming Random Numbers: Acceptance Rejection Method
			10.2.8. Generating Normal Random Variables
			10.2.9. Quasi Random Numbers
			10.2.10. Euler Discretization of SDEs
			10.2.11. Simulating from Geometric Brownian Motion
			10.2.12. Simulating from the Heston Model
			10.2.13. Simulating from the Variance Gamma Model
			10.2.14. Variance Reduction Techniques
			10.2.15. Strengths and Weaknesses
			10.2.16. Simulation in Practice: Impact of Skew on Lookback Options Values in the Heston Model
		10.3. NUMERICAL SOLUTIONS TO PDEs
			10.3.1. Overview
			10.3.2. PDE Representations of Stochastic Processes
			10.3.3. Finite Differences
			10.3.4. Time & Space Grid
			10.3.5. Boundary Conditions
			10.3.6. Explicit Scheme
			10.3.7. Implicit Scheme
			10.3.8. Crank-Nicolson
			10.3.9. Stability
			10.3.10. Multi-Dimension PDEs
			10.3.11. Partial Integro Differential Equations
			10.3.12. Strengths & Weaknesses
			10.3.13. American vs. European Digital Options in Practice
		10.4. MODELING EXOTIC OPTIONS IN PRACTICE
	CHAPTER 11: Greeks and Options Trading
		11.1. INTRODUCTION
		11.2. BLACK-SCHOLES GREEKS
			11.2.1. Delta
			11.2.2. Gamma
			11.2.3. Delta and Gamma in Practice: Delta and Gamma by Strike
			11.2.4. Theta
			11.2.5. Theta in Practice: How Does Theta Change by Option Expiry?
			11.2.6. Vega
			11.2.7. Practical Uses of Greeks
		11.3. THETA VS. GAMMA
		11.4. MODEL DEPENDENCE OF GREEKS
		11.5. GREEKS FOR EXOTIC OPTIONS
		11.6. ESTIMATION OF GREEKS VIA FINITE DIFFERENCES
		11.7. SMILE ADJUSTED GREEKS
			11.7.1. Smile Adjusted Greeks in Practice: USDBRL Options
		11.8. HEDGING IN PRACTICE
			11.8.1. Re-Balancing Strategies
			11.8.2. Delta Hedging in Practice
			11.8.3. Vega Hedging in Practice
			11.8.4. Validation of Greeks Out-of-Sample
		11.9. COMMON OPTIONS TRADING STRUCTURES
			11.9.1. Benefits of Trading Options
			11.9.2. Covered Calls
			11.9.3. Call & Put Spreads
			11.9.4. Straddles & Strangles
			11.9.5. Butterflies
			11.9.6. Condors
			11.9.7. Calendar Spreads
			11.9.8. Risk Reversals
			11.9.9. 1x2s
		11.10. VOLATILITY AS AN ASSET CLASS
		11.11. RISK PREMIA IN THE OPTIONS MARKET: IMPLIED VS. REALIZED VOLATILITY
			11.11.1. Delta-Hedged Straddles
			11.11.2. Implied vs. Realized Volatility
			11.11.3. Implied Volatility Premium in Practice: S&P 500
		11.12. CASE STUDY: GAMESTOP REDDIT MANIA
	CHAPTER 12: Extraction of Risk Neutral Densities
		12.1. MOTIVATION
		12.2. BREDEN-LITZENBERGER
			12.2.1. Derivation
			12.2.2. Breeden-Litzenberger in the Presence of Imprecise Data
			12.2.3. Strengths and Weaknesses
			12.2.4. Applying Breden-Litzenberger in Practice
		12.3. CONNECTION BETWEEN RISK NEUTRAL DISTRIBUTIONS AND MARKET INSTRUMENTS
			12.3.1. Butterflies
			12.3.2. Digital Options
		12.4. OPTIMIZATION FRAMEWORK FOR NON-PARAMETRIC DENSITY EXTRACTION
		12.5. WEIGTHED MONTE CARLO
			12.5.1. Optimization Directly on Terminal Probabilities
			12.5.2. Inclusion of a Prior Distribution
			12.5.3. Weighting Simulated Paths Instead of Probabilities
			12.5.4. Strengths and Weaknesses
			12.5.5. Implementation of Weighted Monte Carlo in Practice: S&P Options
		12.6. RELATIONSHIP BETWEEN VOLATILITY SKEW AND RISK NEUTRAL DENSITIES
		12.7. RISK PREMIA IN THE OPTIONS MARKET: COMPARISON OF RISK NEUTRAL VS. PHYSICAL MEASURES
			12.7.1. Comparison of Risk Neutral vs. Physical Measure: Example
			12.7.2. Connection to Market Implied Risk Premia
			12.7.3. Taking Advantage of Deviations between the Risk Neutral & Physical Measure
		12.8. CONCLUSIONS & ASSESSMENT OF PARAMETRIC VS. NON-PARAMETRIC METHODS
SECTION III: Quant Modeling in Different Markets
	CHAPTER 13: Interest Rate Markets
		13.1. MARKET SETTING
		13.2. BOND PRICING CONCEPTS
			13.2.1. Present Value & Discounting Cashflows
			13.2.2. Pricing a Zero Coupon Bond
			13.2.3. Pricing a Coupon Bond
			13.2.4. Daycount Conventions
			13.2.5. Yield to Maturity
			13.2.6. Duration & Convexity
			13.2.7. Bond Pricing in Practice: Duration and Convexity vs. Maturity
			13.2.8. From Yield to Maturity to a Yield Curve
		13.3. MAIN COMPONENTS OF A YIELD CURVE
			13.3.1. Overview
			13.3.2. FRA’s & Eurodollar Futures
			13.3.3. Swaps
		13.4. MARKET RATES
		13.5. YIELD CURVE CONSTRUCTION
			13.5.1. Motivation
			13.5.2. Libor vs. OIS
			13.5.3. Bootstrapping
			13.5.4. Optimization
			13.5.5. Comparison of Methodologies
			13.5.6. Bootstrapping in Practice: US Swap Rates
			13.5.7. Empirical Observations of the Yield Curve
			13.5.8. Fed Policy and the Yield Curve
		13.6. MODELING INTEREST RATE DERIVATIVES
			13.6.1. Linear vs. Non-Linear Payoffs
			13.6.2. Vanilla vs. Exotic Options
			13.6.3. Most Common Interest Rate Derivatives
			13.6.4. Modeling the Curve vs. Modeling a Single Rate
		13.7. MODELING VOLATILITY FOR A SINGLE RATE: CAPS/FLOORS
			13.7.1. T-Forward Numeraire
			13.7.2. Caplets/Floorlets via Black’s Model
			13.7.3. Stripping Cap/Floor Volatilities
			13.7.4. Fitting the Volatility Skew
		13.8. MODELING VOLATILITY FOR A SINGLE RATE: SWAPTIONS
			13.8.1. Annuity Function & Numeraire
			13.8.2. Pricing via the Bachelier Model
			13.8.3. Fitting the Volatility Skew with the SABR Model
			13.8.4. Swaption Volatility Cube
		13.9. MODELING THE TERM STRUCTURE: SHORT RATE MODELS
			13.9.1. Short Rate Models: Overview
			13.9.2. Ho-Lee
			13.9.3. Vasicek
			13.9.4. Cox Ingersol Ross
			13.9.5. Hull-White
			13.9.6. Multi-Factor Short Rate Models
			13.9.7. Two Factor Gaussian Short Rate Model
			13.9.8. Two Factor Hull-White Model
			13.9.9. Short Rate Models: Conclusions
		13.10. MODELING THE TERM STRUCTURE: FORWARD RATE MODELS
			13.10.1. Libor Market Models: Introduction
			13.10.2. Log-Normal Libor Market Model
			13.10.3. SABR Libor Market Model
			13.10.4. Valuation of Swaptions in an LMM Framework
		13.11. EXOTIC OPTIONS
			13.11.1. Spread Options
			13.11.2. Bermudan Swaptions
		13.12. INVESTMENT PERSPECTIVE: TRADED STRUCTURES
			13.12.1. Hedging Interest Rate Risk in Practice
			13.12.2. Harvesting Carry in Rates Markets: Swaps
			13.12.3. Swaps vs. Treasuries Basis Trade
			13.12.4. Conditional Flattener/Steepeners
			13.12.5. Triangles: Swaptions vs. Mid-Curves
			13.12.6. Wedges: Caps vs. Swaptions
			13.12.7. Berm vs. Most Expensive European
		13.13. CASE STUDY: INTRODUCTION OF NEGATIVE RATES
	CHAPTER 14: Credit Markets
		14.1. MARKET SETTING
		14.2. MODELING DEFAULT RISK: HAZARD RATE MODELS
		14.3. RISKY BOND
			14.3.1. Modeling Risky Bonds
			14.3.2. Bonds in Practice: Comparison of Risky & Risk-Free Bond Duration
		14.4. CREDIT DEFAULT SWAPS
			14.4.1. Overview
			14.4.2. Valuation of CDS
			14.4.3. Risk Annuity vs. IR Annuity
			14.4.4. Credit Triangle
			14.4.5. Mark to Market of a CDS
			14.4.6. Market Risks of CDS
		14.5. CDS VS. CORPORATE BONDS
			14.5.1. CDS Bond Basis
			14.5.2. What Drives the CDS-Bond Basis?
		14.6. BOOTSTRAPPING A SURVIVAL CURVE
			14.6.1. Term Structure of Hazard Rates
			14.6.2. CDS Curve: Bootstrapping Procedure
			14.6.3. Alternate Approach: Optimization
		14.7. INDICES OF CREDIT DEFAULT SWAPS
			14.7.1. Credit Indices
			14.7.2. Valuing Credit Indices
			14.7.3. Index vs. Single Name Basis
			14.7.4. Credit Indices in Practice: Extracting IG & HY Index Hazard Rates
		14.8. MARKET IMPLIED VS EMPIRICAL DEFAULT PROBABILITIES
		14.9. OPTIONS ON CDS & CDX INDICES
			14.9.1. Options on CDS
			14.9.2. Options on Indices
		14.10. MODELING CORRELATION: CDOS
			14.10.1. CDO Subordination Structure
			14.10.2. Mechanics of CDOs
			14.10.3. Default Correlation & the Tranche Loss Distribution
			14.10.4. A Simple Model for CDOs: One Factor Large Pool Homogeneous Model
			14.10.5. Correlation Skew
			14.10.6. CDO Correlation in Practice: Impact of Correlation on Tranche Valuation
			14.10.7. Alternative Models for CDOs
		14.11. MODELS CONNECTING EQUITY AND CREDIT
			14.11.1. Merton’s Model
			14.11.2. Hirsa-Madan Approach
		14.12. MORTGAGE BACKED SECURITIES
		14.13. INVESTMENT PERSPECTIVE: TRADED STRUCTURES
			14.13.1. Hedging Credit Risk
			14.13.2. Harvesting Carry in Credit Markets
			14.13.3. CDS Bond Basis
			14.13.4. Trading Credit Index Calendar Spreads
			14.13.5. Correlation Trade: Mezzanine vs. Equity Tranches
	CHAPTER 15: Foreign Exchange Markets
		15.1. MARKET SETTING
			15.1.1. Overview
			15.1.2. G10 Major Currencies
			15.1.3. EM Currencies
			15.1.4. Major Players
			15.1.5. Derivatives Market Structure
		15.2. MODELING IN A CURRENCY SETTING
			15.2.1. FX Quotations
			15.2.2. FX Forward Valuations
			15.2.3. Carry in FX Markets: Do FX forward Realize?
			15.2.4. Deliverable vs. Non-Deliverable Forwards
			15.2.5. FX Triangles
			15.2.6. Black-Scholes Model in an FX Setting
			15.2.7. Quoting Conventions in FX Vol. Surfaces
		15.3. VOLATILITY SMILES IN FOREIGN EXCHANGE MARKETS
			15.3.1. Persistent Characteristics of FX Volatility Surfaces
			15.3.2. FX Volatility Surfaces in Practice: Comparison across Currency Pairs
		15.4. EXOTIC OPTIONS IN FOREIGN EXCHANGE MARKETS
			15.4.1. Digital Options
			15.4.2. One Touch Options
			15.4.3. One-Touches vs. Digis in Practice: Ratio of Prices in EURJPY
			15.4.4. Asian Options
			15.4.5. Barrier Options
			15.4.6. Volatility & Variance Swaps
			15.4.7. Dual Digitals
		15.5. INVESTMENT PERSPECTIVE: TRADED STRUCTURES
			15.5.1. Hedging Currency Risk
			15.5.2. Harvesting Carry in FX Markets
			15.5.3. Trading Dispersion: Currency Triangles
			15.5.4. Trading Skewness: Digital Options vs. One Touches
		15.6. CASE STUDY: CHF PEG BREAK IN 2015
	CHAPTER 16: Equity & Commodity Markets
		16.1. MARKET SETTING
		16.2. FUTURES CURVES IN EQUITY & COMMODITY MARKETS
			16.2.1. Determinants of Futures Valuations
			16.2.2. Futures Curves of Hard to Store Assets
			16.2.3. Why Are VIX & Commodity Curves Generally in Contango?
			16.2.4. Futures Curves In Practice: Excess Contango in Natural Gas & VIX
		16.3. VOLATILITY SURFACES IN EQUITY & COMMODITY MARKETS
			16.3.1. Persistent Characteristics of Equity & Commodity Volatility Surfaces
		16.4. EXOTIC OPTIONS IN EQUITY & COMMODITY MARKETS
			16.4.1. Lookback Options
			16.4.2. Basket Options
		16.5. INVESTMENT PERSPECTIVE: TRADED STRUCTURES
			16.5.1. Hedging Equity Risk
			16.5.2. Momentum in Single Stocks
			16.5.3. Harvesting Roll Yield via Commodity Futures Curves
			16.5.4. Lookback vs. European
			16.5.5. Dispersion Trading: Index vs. Single Names
			16.5.6. Leveraged ETF Decay
		16.6. CASE STUDY: NAT. GAS SHORT SQUEEZE
		16.7. CASE STUDY: VOLATILITY ETP APOCALYPSE OF 2018
SECTION IV: Portfolio Construction & Risk Management
	CHAPTER 17: Portfolio Construction & Optimization Techniques
		17.1. THEORETICAL BACKGROUND
			17.1.1. Physical vs. Risk-Neutral Measure
			17.1.2. First-& Second-Order Conditions, Lagrange Multipliers
			17.1.3. Interpretation of Lagrange Multipliers
		17.2. MEAN-VARIANCE OPTIMIZATION
			17.2.1. Investor Utility
			17.2.2. Unconstrained Mean-Variance Optimization
			17.2.3. Mean-Variance Efficient Frontier
			17.2.4. Mean-Variance Fully Invested Efficient Frontier
			17.2.5. Mean-Variance Optimization in Practice: Efficient Frontier
			17.2.6. Fully Invested Minimum Variance Portfolio
			17.2.7. Mean-Variance Optimization with Inequality Constraints
			17.2.8. Most Common Constraints
			17.2.9. Mean-Variance Optimization: Market or Factor Exposure Constraints
			17.2.10. Mean-Variance Optimization: Turnover Constraint
			17.2.11. Minimizing Tracking Error to a Benchmark
			17.2.12. Estimation of Portfolio Optimization Inputs
		17.3. CHALLENGES ASSOCIATED WITH MEAN-VARIANCE OPTIMIZATION
			17.3.1. Estimation Error in Expected Returns
			17.3.2. Mean-Variance Optimization in Practice: Impact of Estimation Error
			17.3.3. Estimation Error of Variance Estimates
			17.3.4. Singularity of Covariance Matrices
			17.3.5. Mean-Variance Optimization in Practice: Analysis of Covariance Matrices
			17.3.6. Non-Stationarity of Asset Correlations
		17.4. CAPITAL ASSET PRICING MODEL
			17.4.1. Leverage & the Tangency Portfolio
			17.4.2. CAPM
			17.4.3. Systemic vs. Idiosyncratic Risk
			17.4.4. CAPM in Practice: Efficient Frontier, Tangency Portfolio and Leverage
			17.4.5. Multi-Factor Models
			17.4.6. Fama-French Factors
		17.5. BLACK-LITTERMAN
			17.5.1. Market Implied Equilibrium Expected Returns
			17.5.2. Bayes’ Rule
			17.5.3. Incorporating Subjective Views
			17.5.4. The Black-Litterman Model
		17.6. RESAMPLING
			17.6.1. Resampling the Efficient Frontier
			17.6.2. Resampling in Practice: Comparison to a Mean-Variance Efficient Frontier
		17.7. DOWNSIDE RISK BASED OPTIMIZATION
			17.7.1. Value at Risk (VaR)
			17.7.2. Conditional Value at Risk (CVaR)
			17.7.3. Mean-VaR Optimal Portfolio
			17.7.4. Mean-CVaR Optimal Portfolio
		17.8. RISK PARITY
			17.8.1. Introduction
			17.8.2. Inverse Volatility Weighting
			17.8.3. Marginal Risk Contributions
			17.8.4. Risk Parity Optimization Formulation
			17.8.5. Strengths and Weaknesses of Risk Parity
			17.8.6. Asset Class Risk Parity Portfolio in Practice
		17.9. COMPARISON OF METHODOLOGIES
	CHAPTER 18: Modeling Expected Returns and Covariance Matrices
		18.1. SINGLE & MULTI-FACTOR MODELS FOR EXPECTED RETURNS
			18.1.1. Building Expected Return Models
			18.1.2. Employing Regularization Techniques
			18.1.3. Regularization Techniques in Practice: Impact on Expected Return Model
			18.1.4. Correcting for Serial Correlation
			18.1.5. Isolating Signal from Noise
			18.1.6. Information Coefficient
			18.1.7. Information Coefficient in Practice: Rolling IC of a Short Term FX Reversal
			18.1.8. The Fundamental Law of Active Management: Relationship between Information Ratio & Information Coefficient
		18.2. MODELING VOLATILITY
			18.2.1. Estimating Volatility
			18.2.2. Rolling & Expanding Windows Volatility Estimates
			18.2.3. Exponentially Weighted Moving Average Estimates
			18.2.4. High Frequency & Range Based Volatility Estimators
			18.2.5. Mean-Reverting Volatility Models: GARCH
			18.2.6. GARCH in Practice: Estimation of GARCH(1,1) Parameters to Equity Index Returns
			18.2.7. Estimation of Covariance Matrices
			18.2.8. Correcting for Negative Eigenvalues
			18.2.9. Shrinkage Methods for Covariance Matrices
			18.2.10. Shrinkage in Practice: Impact on Structure of Principal Components
			18.2.11. Random Matrix Theory
	CHAPTER 19: Risk Management
		19.1. MOTIVATION & SETTING
			19.1.1. Risk Management in Practice
			19.1.2. Defined vs. Undefined Risks
			19.1.3. Types of Risk
		19.2. COMMON RISK MEASURES
			19.2.1. Portfolio Value at Risk
			19.2.2. Marginal VaR Contribution
			19.2.3. Portfolio Conditional Value at Risk
			19.2.4. Marginal CVaR Contribution
			19.2.5. Extreme Loss, Stress Tests & Scenario Analysis
		19.3. CALCULATION OF PORTFOLIO VaR AND CVaR
			19.3.1. Overview
			19.3.2. Historical Simulation
			19.3.3. Monte Carlo Simulation
			19.3.4. Strengths and Weaknesses of Each Approach
			19.3.5. Validating Our Risk Calculations Out-of-Sample
			19.3.6. VaR in Practice: Out of Sample Test of Rolling VaR
		19.4. RISK MANAGEMENT OF NON-LINEAR INSTRUMENTS
			19.4.1. Non-Linear Risk
			19.4.2. Hedging Portfolios via Scenarios
		19.5. RISK MANAGEMENT IN RATES & CREDIT MARKETS
			19.5.1. Introduction
			19.5.2. Converting from Change in Yield to Change in Price
			19.5.3. DV01 and Credit Spread 01: Risk Management via Parallel Shifts
			19.5.4. Partial DV01’s: Risk Management via Key Rate Shifts
			19.5.5. Jump to Default Risk
			19.5.6. Principal Component Based Shifts
	CHAPTER 20: Quantitative Trading Models
		20.1. INTRODUCTION TO QUANT TRADING MODELS
			20.1.1. Quant Strategies
			20.1.2. What is Alpha Research?
			20.1.3. Types of Quant Strategies
		20.2. BACK-TESTING
			20.2.1. Parameter Estimation
			20.2.2. Modeling Transactions Costs
			20.2.3. Evaluating Back-Test Performance
			20.2.4. Most Common Quant Traps
			20.2.5. Common Performance Metrics
			20.2.6. Back-Tested Sharpe Ratios
			20.2.7. In-Sample and Out-of-Sample Analysis
			20.2.8. Out-of-Sample Performance & Slippage
		20.3. COMMON STAT-ARB STRATEGIES
			20.3.1. Single Asset Momentum & Mean-Reversion Strategies
			20.3.2. Cross Asset Autocorrelation Strategies
			20.3.3. Pairs Trading
			20.3.4. Pairs Trading in Practice: Gold vs. Gold Miners
			20.3.5. Factor Models
			20.3.6. PCA-Based Strategies
			20.3.7. PCA Decomposition in Practice: How Many Principal Components Explain the S&P 500?
			20.3.8. Risk Premia Strategies
			20.3.9. Momentum in Practice: Country ETFs
			20.3.10. Translating Raw Signals to Positions
		20.4. SYSTEMATIC OPTIONS BASED STRATEGIES
			20.4.1. Back-Testing Strategies Using Options
			20.4.2. Common Options Trading Strategies
			20.4.3. Options Strategy in Practice: Covered Calls on NASDAQ
		20.5. COMBINING QUANT STRATEGIES
		20.6. PRINCIPLES OF DISCRETIONARY VS. SYSTEMATIC INVESTING
	CHAPTER 21: Incorporating Machine Learning Techniques
		21.1. MACHINE LEARNING FRAMEWORK
			21.1.1. Machine Learning vs. Econometrics
			21.1.2. Stages of a Machine Learning Project
			21.1.3. Parameter Tuning & Cross Validation
			21.1.4. Classes of Machine Learning Algorithms
			21.1.5. Applications of Machine Learning in Asset Management & Trading
			21.1.6. Challenges of Using Machine Learning in Finance
		21.2. SUPERVISED VS. UNSUPERVISED LEARNING METHODS
			21.2.1. Supervised vs. Unsupervised Learning
			21.2.2. Supervised Learning Methods
			21.2.3. Regression vs. Classification Techniques
			21.2.4. Unsupervised Learning Methods
		21.3. CLUSTERING
			21.3.1. What is Clustering?
			21.3.2. K-Means Clustering
			21.3.3. Hierarchical Clustering
			21.3.4. Distance Metrics
			21.3.5. Optimal Number of Clusters
			21.3.6. Clustering in Finance
			21.3.7. Clustering in Practice: Asset Class & Risk-on Risk-off Clusters
		21.4. CLASSIFICATION TECHNIQUES
			21.4.1. What is Classification?
			21.4.2. K-Nearest Neighbor
			21.4.3. Probit Regression
			21.4.4. Logistic Regression
			21.4.5. Support Vector Machines
			21.4.6. Confusion Matrices
			21.4.7. Classification Problems in Finance
			21.4.8. Classification in Practice: Using Classification Techniques in an Alpha Signal
		21.5. FEATURE IMPORTANCE & INTERPRETABILITY
			21.5.1. Feature Importance & Interpretability
		21.6. OTHER APPLICATIONS OF MACHINE LEARNING
			21.6.1. Delta Hedging Schemes & Optimal Execution via Reinforcement Learning
			21.6.2. Credit Risk Modeling via Classification Techniques
			21.6.3. Incorporating Alternative Data via Natural Language Processing (NLP) Algorithms and Other Machine
Learning Techniques
			21.6.4. Volatility Surface Calibration via Deep Learning
Bibliography
Index