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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 Stages of a Quant Project
1.4.1 Data Collection
1.4.2 Data Cleaning
1.4.3 Model Implementation
1.4.4 Model Validation
1.5 Trends: What has changed in the last few years, and where is Quant Finance going?
1.5.1 Change in Inflation Regime
1.5.2 Automation
1.5.3 Rapid Increase of Available Data
viii. 1.5.4 Commoditization of Factor Premia
1.5.5 Increased Popularity of Multi-Strategy Hedge Funds
1.5.6 Proliferation of Artificial Intelligence, Machine Learning and Large Language Models
1.5.7 Increasing Prevalence of Required Quant/Technical Skills
1.5.8 Increased Regulatory Complexity and the Potential for Democratization
Chapter 2 ▪ Setting the Stage: Landscape of Financial Instruments
2.1 Equity Instruments
2.1.1 Overview & Mechanics
2.1.2 Public Equity
2.1.3 Modeling Equity via a Discounted Dividend Growth Model
2.1.4 Private Equity
2.1.5 Private Equity vs. Public Equity Returns in Practice
2.1.6 Preferred Stock
2.2 Debt Instruments
2.2.1 Overview & Mechanics
2.2.2 Sovereign Bonds
2.2.3 Corporate Bonds
2.2.4 Municipal Bonds
2.2.5 Municipal Bond Valuation in Practice
2.2.6 Inflation Linked Bonds
2.2.7 Convertible Bonds
2.2.8 Green Bonds
2.3 Forwards & Futures
2.4 Options
2.4.1 Mechanics
2.4.2 Option Straddles in Practice
2.4.3 Put-Call Parity
2.5 Swaps
2.5.1 Mechanics
2.5.2 Equity Index Total Return Swaps in Practice
2.5.3 Over-The-Counter vs. Exchange Traded Products
ix. Chapter 3 ▪ Theoretical Underpinnings of Quant Modeling: Modeling the Risk Neutral Measure
3.1 Introduction
3.2 Risk Neutral Pricing & No Arbitrage
3.2.1 Risk Neutral vs. Actual Probabilities
3.2.2 Theory of No Arbitrage
3.2.3 Complete Markets
3.2.4 Risk Neutral Valuation Equation
3.2.5 Risk Neutral Discounting, Risk Premia & Stochastic Discount Factors
3.3 Binomial Trees
3.3.1 Discrete vs. Continuous Time Models
3.3.2 Scaled Random Walk
3.3.3 Discrete Binomial Tree Model
3.3.4 Limiting Distribution of Binomial Tree Model
3.4 Building Blocks of Stochastic Calculus
3.4.1 Deterministic vs. Stochastic Calculus
3.4.2 Stochastic Processes
3.4.3 Martingales
3.4.4 Brownian Motion
3.4.5 Properties of Brownian Motion
3.5 Stochastic Differential Equations
3.5.1 Generic SDE Formulation
3.5.2 Bachelier SDE
3.5.3 Black-Scholes SDE
3.5.4 Stochastic Models in Practice
3.6 Ito's Lemma
3.6.1 General Formulation & Theory
3.6.2 Ito in Practice: Risk-Free Bond
3.6.3 Ito in Practice: Black-Scholes Dynamics
3.7 Connection between SDEsand PDEs
3.7.1 PDEs & Stochastic Processes
3.7.2 Deriving the Black-Scholes PDE
3.7.3 General Formulation: Feynman-Kac Formula
3.7.4 Working with PDEs in Practice
x. 3.8 Girsanov's Theorem
3.8.1 Change of Measure via Girsanov's Theorem
3.8.2 Applications of Girsanov's Theorem
Chapter 4 ▪ Theoretical Underpinnings of Quant Modeling: Modeling the Physical Measure
4.1 Introduction: Forecasting vs. Replication
4.2 Market Efficiency and Risk Premia
4.2.1 Efficient Market Hypothesis
4.2.2 Market Anomalies, Behavioral Finance & Risk Premia
4.2.3 Risk Premia Example: Selling Insurance
4.3 Linear Regression Models
4.3.1 Introduction & Terminology
4.3.2 Univariate Linear Regression
4.3.3 Multivariate Linear Regression
4.3.4 Standard Errors & Significance Tests
4.3.5 T-Statistics, P-Values & Statistical Significance
4.3.6 Assumptions of Linear Regression
4.3.7 How Are Regression Models Used in Practice?
4.3.8 Regression Models in Practice: Calculating High-Yield Betas to Stocks and Bonds
4.4 Time Series Models
4.4.1 Time Series Data
4.4.2 Stationary vs. Non-Stationary Series & Differencing
4.4.3 White Noise & Random Walks
4.4.4 Autoregressive Processes & Unit Root Tests
4.4.5 Moving Average Models
4.4.6 ARMA Models
4.4.7 State Space Models
4.4.8 How Are Time Series Models Used in practice?
4.5 Panel Regression Models
4.6 Core Portfolio and Investment Concepts
4.6.1 Time Value of Money
4.6.2 Compounding Returns
4.6.3 Portfolio Calculations
4.6.4 Portfolio Concepts in Practice: Benefit of Diversification
xi. 4.7 Bootstrapping
4.7.1 Overview
4.8 Principal Component Analysis
4.9 Conclusions: Comparison to Risk Neutral Measure Modeling
Section II Fundamentals of Coding and Data Analysis
Chapter 5 ▪ Python Programming Environment
5.1 The Python Programming Language
5.2 Advantages and disadvantages of Python
5.3 Python Development Environments
5.4 Basic Programming Concepts in Python
5.4.1 Language Syntax
5.4.2 Data Types in Python
5.4.3 Working with Built-in Functions
5.4.4 Conditional Statements
5.4.5 Operator Precedence
5.4.6 Loops
5.4.7 Working with Strings
5.4.8 User-Defined Functions
5.4.9 Variable Scope
5.4.10 Importing Modules
5.4.11 Exception Handling
5.4.12 Recursive Functions
5.4.13 Plotting/Visualizations
5.5 Working in a Multi-Programmer Environment
Chapter 6 ▪ Programming Concepts in Python
6.1 Introduction
6.2 NumPy Library
6.3 Pandas Library
6.4 Data Structures in Python
6.4.1 Tuples
6.4.2 Lists
6.4.3 Array
xii. 6.4.4 Differences between Lists and NumPy Arrays
6.4.5 Covariance Matrices in Practice
6.4.6 Covariance Matrices in Practice: Are Correlations Stationary?
6.4.7 Series
6.4.8 DataFrame
6.4.9 Dictionary
6.5 Implementation of Quant Techniques in Python
6.5.1 Random Number Generation
6.5.2 Linear Regression
6.5.3 Linear Regression in Practice: Equity Return Decomposition by Fama-French Factors
6.5.4 Autocorrelation Tests
6.5.5 ARMA Models in Practice: Testing for Mean-Reversion in Equity Index Returns
6.5.6 Matrix Decompositions
6.6 Object-Oriented Programming in Python
6.6.1 Principles of Object-Oriented Programming
6.6.2 Classes in Python
6.6.3 Constructors
6.6.4 Destructors
6.6.5 Class Attributes
6.6.6 Class Methods
6.6.7 Class Methods vs. Global Functions
6.6.8 Operator Overloading
6.6.9 Inheritance in Python
6.6.10 Polymorphism in Python
6.7 Design Patterns
6.7.1 Types of Design Patterns
6.7.2 Abstract Base Classes
6.7.3 Factory Pattern
6.7.4 Singleton Pattern
6.7.5 Template Method
6.8 Search Algorithms
6.8.1 Binary Search Algorithm
6.9 Sort Algorithms
6.9.1 Selection Sort
xiii. 6.9.2 Insertion Sort
6.9.3 Bubble Sort
6.9.4 Merge Sort
Chapter 7 ▪ Working with Financial Datasets
7.1 Introduction
7.2 Data Collection
7.2.1 Overview
7.2.2 Reading & Writing Files in Python
7.2.3 Parsing Data from a Website
7.2.4 Interacting with Databases in Python
7.3 Common Financial Datasets
7.3.1 Stock Data
7.3.2 Currency Data
7.3.3 Futures Data
7.3.4 Options Data
7.3.5 Fixed Income Data
7.4 Common Financial Data Sources
7.5 Cleaning Different Types of Financial Data
7.5.1 Proper Handling of Corporate Actions
7.5.2 Avoiding Survivorship Bias
7.5.3 Detecting Arbitrage in the Data
7.6 Handling Missing Data
7.6.1 Interpolation & Filling Forward
7.6.2 Filling via Regression
7.6.3 Filling via Bootstrapping
7.6.4 Filling via K-Nearest Neighbor
Chapter 8 ▪ Data Science Techniques in Finance
8.1 Introduction: What is Data Science?
8.2 Exploratory Data Analysis
8.2.1 Single vs. Multivariate Exploratory Data Analysis
8.2.2 Data Visualization
8.2.3 Statistical Analysis of Data
8.2.4 Factor & Principal Component Analysis
xiv. 8.2.5 t-distributed Stochastic Neighbor Embedding
8.2.6 EDA in Practice
8.3 Machine Learning Techniques for Data Science
8.3.1 Overview of Machine Learning for Data Science
8.3.2 Supervised vs. Unsupervised Learning
8.3.3 Structured vs. Unstructured Data
8.4 Transforming Data using SQL
8.4.1 Modifying Data via Insert, Update and Delete Statements
8.4.2 Retrieving Data via Select Statements
8.4.3 Retrieving Data from Multiple Tables via JOINs
8.4.4 Aggregating Data via a Group by Clause
8.5 Dimensionality Reduction
8.5.1 Principal Component Analysis
8.5.2 Autoencoder
8.5.3 Dimensionality Reduction in Practice: Reducing the Dimensionality of a Covariance Matrix Using PCA
8.6 Python Tools for Big Data
8.6.1 Working with Large Datasets
8.6.2 Memory & Large Datasets
8.6.3 Parallel Computing
8.6.4 Spark & Hadoop
8.7 Outlier Detection
8.7.1 Single vs. Multi-Variate Outlier Detection
8.7.2 Plotting
8.7.3 Standard Deviation
8.7.4 Density Analysis
8.7.5 Distance from K Nearest Neighbor
8.7.6 Outlier Detection in Practice: Identifying Anomalies in ETF Returns
Chapter 9 ▪ Model Validation
9.1 Why is Model Validation so important?
9.2 How do we ensure our models are correct?
9.3 Components of a Model Validation Process
9.3.1 Model Documentation
9.3.2 Code Review
xv. 9.3.3 Unit Tests
9.3.4 Production Model Change Process
9.4 Goals of Model Validation
9.4.1 Validating Model Implementation
9.4.2 Understanding Model Strengths and Weaknesses
.4.3 Identifying Model Assumptions
9.5 Tradeoff Between Realistic Assumptions and Parsimony in Models
Section III Options Modeling
Chapter 10 ▪ Stochastic Models
10.1 Simple Models
10.1.1 Black-Scholes Model
10.1.2 Black-Scholes Model in Practice: Are Equity Returns Log-Normally Distributed?
10.1.3 Implied Volatility Surfaces in Practice: Equity Options
10.1.4 Bachelier Model
10.1.5 CEV Model
10.1.6 CEV Model in Practice: Impact of Beta
10.1.7 Ornstein-Uhlenbeck Process
10.1.8 Cox-Ingersol-Ross Model
10.1.9 Conclusions
10.2 Stochastic Volatility Models
10.2.1 Introduction
10.2.2 Heston Model
10.2.3 SABR Model
10.2.4 SABR Model in Practice: Relationship between Model Parameters and Volatility Surface
10.2.5 Stochastic Volatility Models: Comments
3.1 Introduction
10.3.2 Merton's Jump Diffusion Model
10.3.3 SVJ Model
10.3.4 Variance Gamma Model
10.3.5 VGSA Model
10.3.6 Comments on Jump Processes
xvi. 10.4 Local Volatility Models
10.4.1 Dupire's Formula
10.4.2 Local Volatility Model in Practice: S&P Option Local Volatility Surface
10.5 Stochastic Local Volatility Models
10.6 Practicalities of Using these Models
10.6.1 Comparison of Stochastic Models
10.6.2 Leveraging Stochastic Models in Practice
Chapter 11 ▪ Options Pricing Techniques for European Options
11.1 Models with Closed Form Solutions or Asymptotic Approximations
11.2 Option Pricing via Quadrature
11.2.1 Overview
11.2.2 Quadrature Approximations
11.2.3 Approximating a Pricing Integral via Quadrature
11.2.4 Quadrature Methods in Practice: Digital Options Prices in Black-Scholes vs. Bachelier Model
11.3 Option Pricing via FFT
11.3.1 Fourier Transforms & Characteristic Functions
11.3.2 European Option Pricing via Transform
11.3.3 Digital Option Pricing via Transform
11.3.4 Calculating Outer Pricing Integral via Quadrature
11.3.5 Summary of FFT Algorithm
11.3.6 Calculating Outer Pricing Integral via FFT
11.3.7 Summary: Option Pricing via FFT
11.3.8 Strike Spacing Functions
11.3.9 Interpolation of Option Prices
11.3.10 Technique Parameters
11.3.11 Dependence on Technique Parameters
11.3.12 Strengths and Weaknesses
11.3.13 Variants of FFT Pricing Technique
11.3.14 FFT Pricing in Practice: Sensitivity to Technique Parameters
11.4 Root Finding
11.4.1 Setup
xvii. 11.4.2 Newton's Method
11.4.3 First Calibration: Implied Volatility
11.4.4 Implied Volatility in Practice: Volatility Skew for VIX Options
11.5 Optimization Techniques
11.5.1 Background & Terminology
11.5.2 Global vs. Local Minima & Maxima
11.5.3 First- & Second-Order Conditions
11.5.4 Unconstrained Optimization
11.5.5 Lagrange Multipliers
11.5.6 Optimization with Equality Constraints
11.5.7 Minimum Variance Portfolios in Practice: Stock & Bond Minimum Variance Portfolio Weights
11.5.8 Convex Functions
11.5.9 Optimization Methods in Practice
11.6 Calibration of Volatility Surfaces
11.6.1 Optimization Formulation
11.6.2 Objective Functions
11.6.3 Constraints
11.6.4 Regularization
11.6.5 Gradient-Based vs. Gradient-Free Optimizers
11.6.6 Gradient-Based Methods with Linear Constraints
11.6.7 Practicalities of Calibrating Volatility Surfaces
11.6.8 Calibration in Practice: BRLJPY Currency Options
Chapter 12 ▪ Options Pricing Techniques for Exotic Options
12.1 Introduction
12.2 Simulation
12.2.1 Overview
12.2.2 Central Limit Theorem & Law of Large Numbers
12.2.3 Random Number Generators
12.2.4 Generating Random Variables
12.2.5 Transforming Random Numbers
12.2.6 Transforming Random Numbers: Inverse Transform Technique
xviii. 12.2.7 Transforming Random Numbers: Acceptance Rejection Method
12.2.8 Generating Normal Random Variables
12.2.9 Quasi Random Numbers
12.2.10 Euler Discretization of SDEs
12.2.11 Simulating from Geometric Brownian Motion
12.2.12 Simulating from the Heston Model
12.2.13 Simulating from the Variance Gamma Model
12.2.14 Variance Reduction Techniques
12.2.15 Strengths and Weaknesses
12.2.16 Simulation in Practice: Impact of Skew on Lookback Options Values in the Heston Model
12.3 Numerical Solutions to PDEs
12.3.1 Overview
12.3.2 PDE Representations of Stochastic Processes
12.3.3 Finite Differences
12.3.4 Time & Space Grid
12.3.5 Boundary Conditions
12.3.6 Explicit Scheme
12.3.7 Implicit Scheme
12.3.8 Crank-Nicolson
12.3.9 Stability
12.3.10 Multi-Dimension PDEs
12.3.11 Partial Integro Differential Equations
12.3.12 Strengths & Weaknesses
12.3.13 American vs. European Digital Options in Practice
12.4 Modeling Exotic Options in Practice
Chapter 13 ▪ Greeks and Options Trading
13.1 Introduction
13.2 Black-Scholes Greeks
13.2.1 Delta
13.2.2 Gamma
13.2.3 Delta and Gamma in Practice: Delta and Gamma by Strike
13.2.4 Theta
xix. 13.2.5 Theta in Practice: How Does Theta Change by Option Expiry?
13.2.6 Vega
13.2.7 Practical Uses of Greeks
13.3 Theta vs. Gamma
13.4 Model Dependence of Greeks
13.5 Greeks for Exotic Options
13.6 Estimation of Greeks via Finite Differences
13.7 Smile Adjusted Greeks
13.7.1 Smile Adjusted Greeks in Practice: USDBRL Options
13.8 Hedging in Practice
13.8.1 Re-Balancing Strategies
13.8.2 Delta Hedging in Practice
13.8.3 Vega Hedging in Practice
13.8.4 Validation of Greeks Out-of-Sample
13.9 Common Options Trading Structures
13.9.1 Benefits of Trading Options
13.9.2 Covered Calls
13.9.3 Call & Put Spreads
13.9.4 Straddles & Strangles
13.9.5 Butterflies
13.9.6 Condors
13.9.7 Calendar Spreads
13.9.8 Risk Reversals
13.9.9 1x2s
13.10 Volatility As An Asset Class
13.11 Risk Premia in the Options Market: Implied vs. Realized Volatility
13.11.1 Delta-Hedged Straddles
13.11.2 Implied vs. Realized Volatility
13.11.3 Implied Volatility Premium in Practice: S&P 500
13.12 Case Study: Gamestop Reddit Mania
Chapter 14 ▪ Extraction of Risk Neutral Densities
14.1 Motivation
14.2 Breden-Litzenberger
xx. 14.2.1 Derivation
14.2.2 Breeden-Litzenberger in the Presence of Imprecise Data
14.2.3 Strengths and Weaknesses
14.2.4 Applying Breden-Litzenberger in Practice
14.3 Connection between Risk Neutral Distributions and Market Instruments
14.3.1 Butterflies
14.3.2 Digital Options
14.4 Optimization Framework for Non-Parametric Density Extraction
14.5 Weigthed Monte Carlo
14.5.1 Optimization Directly on Terminal Probabilities
14.5.2 Inclusion of a Prior Distribution
.5.3 Weighting Simulated Paths Instead of Probabilities
14.5.4 Strengths and Weaknesses
14.5.5 Implementation of Weighted Monte Carlo in Practice: S&P Options
14.6 Relationship between Volatility Skew and Risk Neutral Densities
14.7 Risk Premia in the Options Market: Comparison of Risk Neutral vs. Physical Measures
14.7.1 Comparison of Risk Neutral vs. Physical Measure: Example
14.7.2 Connection to Market Implied Risk Premia
14.7.3 Taking Advantage of Deviations between the Risk Neutral & Physical Measure
14.8 Conclusions & Assessment of Parametric vs. Non-Parametric methods
Section IV Quant Modeling in Different Markets
Chapter 15 ▪ Interest Rate Markets
15.1 Market Setting
15.2 Bond Pricing Concepts
15.2.1 Present Value & Discounting Cashflows
15.2.2 Pricing a Zero Coupon Bond
15.2.3 Pricing a Coupon Bond
15.2.4 Daycount Conventions
xxi. 15.2.5 Yield to Maturity
15.2.6 Duration & Convexity
15.2.7 Bond Pricing in Practice: Duration and Convexity vs. Maturity
15.2.8 From Yield to Maturity to a Yield Curve
15.3 Main Components of a Yield Curve
15.3.1 Overview
15.3.2 FRAs & SOFR Futures
15.3.3 Swaps
15.3.4 Libor vs. SOFR & The Decommissioning of Libor
15.4 Market Rates
15.5 Yield Curve Construction
15.5.1 Motivation
15.5.2 Bootstrapping
15.5.3 Optimization
15.5.4 Comparison of Methodologies
15.5.5 Bootstrapping in Practice: US Swap Rates
15.5.6 Empirical Observations of the Yield Curve
15.5.7 Fed Policy and the Yield Curve
15.6 Inflation Linked Assets
15.6.1 Importance of Inflation Linked Assets
15.6.2 Inflation Linked Bonds
15.6.3 Inflation Swaps
15.6.4 Breakeven Inflation Rates
15.7 Modeling Interest Rate Derivatives
15.7.1 Linear vs. Non-Linear Payoffs
15.7.2 Vanilla vs. Exotic Options
15.7.3 Most Common Interest Rate Derivatives
15.7.4 Modeling the Curve vs. Modeling a Single Rate
15.8 Modeling Volatility for a Single Rate: Caps/Floors
15.8.1 T-Forward Numeraire
15.8.2 Caplets/Floorlets via Black's Model
15.8.3 Stripping Cap/Floor Volatilities
15.8.4 Fitting the Volatility Skew
15.9 Modeling Volatility for a Single Rate: Swaptions
15.9.1 Annuity Function & Numeraire
xxii. 15.9.2 Pricing via the Bachelier Model
15.9.3 Fitting the Volatility Skew with the SABR Model
15.9.4 Swaption Volatility Cube
15.10 Modeling the Term Structure: Short Rate Models
15.10.1 Short Rate Models: Overview
15.10.2 Ho-Lee
15.10.3 Vasicek
15.10.4 Cox Ingersol Ross
15.10.5 Hull-White
15.10.6 Multi-Factor Short Rate Models
15.10.7 Two Factor Gaussian Short Rate Model
15.10.8 Two Factor Hull-White Model
15.10.9 Short Rate Models: Conclusions
15.11 Modeling the Term Structure: Forward Rate Models
15.11.1 Libor Market Models: Introduction
15.11.2 Log-Normal Libor Market Model
15.11.3 SABR Libor Market Model
15.11.4 Valuation of Swaptions in an LMM Framework
15.12 Exotic Options
15.12.1 Spread Options
15.12.2 Bermudan Swaptions
15.13 Investment Perspective: Traded Structures
15.13.1 Hedging Interest Rate Risk in Practice
15.13.2 Harvesting Carry in Rates Markets: Swaps
15.13.3 Swaps vs. Treasuries Basis Trade
15.13.4 Conditional Flattener/Steepeners
15.13.5 Triangles: Swaptions vs. Mid-Curves
.7 Berm vs. Most Expensive European
15.14 Case Study: Introduction of Negative Rates
15.15 Case Study: Post-Covid Inflation Shock
Chapter 16 ▪ Credit Markets
16.1 Market Setting
16.2 Modeling Default Risk: Hazard Rate Models
16.3 Risky Bond
xxiii. 16.3.1 Modeling Risky Bonds
16.3.2 Bonds in Practice: Comparison of Risky & Risk-Free Bond Duration
16.4 Credit Default Swaps
16.4.1 Overview
16.4.2 Valuation of CDS
16.4.3 Risk Annuity vs. IR Annuity
16.4.4 Credit Triangle
16.4.5 Mark to Market of a CDS
16.4.6 Market Risks of CDS
16.5 CDS vs. Corporate Bonds
16.5.1 CDS Bond Basis
16.5.2 What Drives the CDS-Bond Basis?
16.6 Bootstrapping a Survival Curve
16.6.1 Term Structure of Hazard Rates
16.6.2 CDS Curve: Bootstrapping Procedure
16.6.3 Alternate Approach: Optimization
16.7 Indices of Credit Default Swaps
16.7.1 Credit Indices
16.7.2 Valuing Credit Indices
16.7.3 Index vs. Single Name Basis
16.7.4 Credit Indices in Practice: Extracting IG & HY Index Hazard Rates
16.8 Market Implied vs. Empirical Default Probabilities
16.9 Options on CDS & CDX Indices
16.9.1 Options on CDS
16.9.2 Options on Indices
16.10 Modeling Correlation: CDOs
16.10.1 CDO Subordination Structure
16.10.2 Mechanics of CDOs
16.10.3 Default Correlation & the Tranche Loss Distribution
16.10.4 A Simple Model for CDOs: One Factor Large Pool Homogeneous Model
16.10.5 Correlation Skew
16.10.6 CDO Correlation in Practice: Impact of Correlation on TrancValuation
16.10.7 Alternative Models for CDOs
xxiv. 16.11 Models Connecting Equity and Credit
16.11.1 Merton's Model
16.11.2 Hirsa-Madan Approach
16.12 Mortgage Backed Securities
16.12.1 Overview
16.12.2 MBS Waterfall Structure
16.12.3 Modeling Default & Delinquency Risk
16.12.4 Modeling Prepayment Risk
16.13 Investment Perspective: Traded Structures
16.13.1 Hedging Credit Risk
16.13.2 Harvesting Carry in Credit Markets
16.13.3 CDS Bond Basis
16.13.4 Trading Credit Index Calendar Spreads
16.13.5 Correlation Trade: Mezzanine vs. Equity Tranches
Chapter 17 ▪ Foreign Exchange Markets
17.1 Market Setting
17.1.1 Overview
17.1.2 G10 Major Currencies
17.1.3 EM Currencies
17.1.4 Major Players
17.1.5 Derivatives Market Structure
17.2 Modeling in a Currency Setting
17.2.1 FX Quotations
17.2.2 FX Forward Valuations
17.2.3 Carry in FX Markets: Do FX Forward Realize?
17.2.4 Deliverable vs. Non-Deliverable Forwards
17.2.5 FX Triangles
17.2.6 Black-Scholes Model in an FX Setting
17.2.7 Quoting Conventions in FX Vol. Surfaces
17.3 Volatility Smiles in Foreign Exchange Markets
17.3.1 Persistent Characteristics of FX Volatility Surfaces
17.3.2 FX Volatility Surfaces in Practice: Comparison Across Currency Pairs
17.4 Exotic Options in Foreign Exchange Markets
17.4.1 Digital Options
xxv. 17.4.2 One Touch Options
17.4.3 One-Touches vs. Digis in Practice: Ratio of Prices in EURJPY
17.4.4 Asian Options
17.4.5 Barrier Options
17.4.6 Volatility & Variance Swaps
17.4.7 Dual Digitals
17.5 Investment Perspective: Traded Structures
17.5.1 Hedging Currency Risk
17.5.2 Harvesting Carry in FX Markets
17.5.3 Trading Dispersion: Currency Triangles
17.5.4 Trading Skewness: Digital Options vs. One Touches
17.6 Case Study: CHF Peg Break in 2015
Chapter 18 ▪ Equity & Commodity Markets
18.1 Market Setting
18.2 Futures Curves in Equity & Commodity Markets
18.2.1 Determinants of Futures Valuations
18.2.2 Futures Curves of Hard to Store Assets
18.2.3 Why Are VIX & Commodity Curves Generally in Contango?
18.2.4 Futures Curves in Practice: Excess Contango in Natural Gas & VIX
18.3 Volatility Surfaces in Equity & Commodity Markets
18.3.1 Persistent Characteristics of Equity & Commodity Volatility Surfaces
18.4 Exotic Options in Equity & Commodity Markets
18.4.1 Lookback Options
18.4.2 Basket Options
18.5 Investment Perspective: Traded Structures
18.5.1 Hedging Equity Risk
18.5.2 Momentum in Single Stocks
18.5.3 Harvesting Roll Yield via Commodity Futures Curves
18.5.4 Lookback vs. European
18.5.5 Dispersion Trading: Index vs. Single Names
18.5.6 Leveraged ETF Decay
xxvi. 18.6 Case Study: Nat. Gas Short Squeeze
18.7 Case Study: Volatility ETP Apocalypse of 2018
Section V Portfolio Construction & Risk Management
Chapter 19 ▪ Portfolio Construction & Optimization Techniques
19.1 Theoretical Background
19.1.1 Physical vs. Risk-Neutral Measure
19.1.2 First- & Second-Order Conditions, Lagrange Multipliers
19.1.3 Interpretation of Lagrange Multipliers
19.2 Mean-Variance Optimization
19.2.1 Investor Utility
19.2.2 Unconstrained Mean-Variance Optimization
9.2.3 Mean-Variance Efficient Frontier
19.2.4 Mean-Variance Fully Invested Efficient Frontier
19.2.5 Mean-Variance Optimization in Practice: Efficient Frontier
19.2.6 Fully Invested Minimum Variance Portfolio
19.2.7 Mean-Variance Optimization with Inequality Constraints
19.2.8 Most Common Constraints
19.2.9 Mean-Variance Optimization: Market or Factor Exposure Constraints
19.2.10 Mean-Variance Optimization: Turnover Constraint
19.2.11 Minimizing Tracking Error to a Benchmark
19.2.12 Estimation of Portfolio Optimization Inputs
19.3 Challenges Associated with Mean-Variance Optimization
19.3.1 Estimation Error in Expected Returns
19.3.2 Mean-Variance Optimization in Practice: Impact of Estimation Error
19.3.3 Estimation Error of Variance Estimates
19.3.4 Singularity of Covariance Matrices
19.3.5 Mean-Variance Optimization in Practice: Analysis of Covariance Matrices
19.3.6 Non-Stationarity of Asset Correlations
19.4 Capital Asset Pricing Model
19.4.1 Leverage & the Tangency Portfolio
19.4.2 CAPM
xxvii. 19.4.3 Systemic vs. Idiosyncratic Risk
19.4.4 CAPM in Practice: Efficient Frontier, Tangency Portfolio and Leverage
19.4.5 Multi-Factor Models
19.4.6 Fama-French Factors
19.5 Black-Litterman
19.5.1 Market Implied Equilibrium Expected Returns
19.5.2 Bayes' Rule
19.5.3 Incorporating Subjective Views
19.5.4 The Black-Litterman Model
19.6 Resampling
19.6.1 Resampling the Efficient Frontier
19.6.2 Resampling in Practice: Comparison to a Mean-Variance Efficient Frontier
19.7 Robust Portfolio Optimization
19.8 Downside Risk Based Optimization
19.8.1 Value at Risk (VaR)
19.8.2 Conditional Value at Risk (CVaR)
19.8.3 Mean-VaR Optimal Portfolio
19.8.4 Mean-CVaR Optimal Portfolio
19.9 Risk Parity
19.9.1 Introduction
19.9.2 Inverse Volatility Weighting
19.9.3 Marginal Risk Contributions
19.9.4 Risk Parity Optimization Formulation
19.9.5 Strengths and Weaknesses of Risk Parity
19.9.6 Asset Class Risk Parity Portfolio in Practice
19.10 Comparison of Methodologies
19.11 Case Study: Risk Parity and the post-Covid Inflation Shock
Chapter 20 ▪ Modeling Expected Returns and Covariance Matrices
20.1 Single & Multi-Factor Models for Expected Returns
20.1.1 Building Expected Return Models
20.1.2 Employing Regularization Techniques
xxviii. 20.1.3 Regularization Techniques in Practice: Impact on Expected Return Model
20.1.4 Correcting for Serial Correlation
20.1.5 Isolating Signal from Noise
20.1.6 Information Coefficient
20.1.7 Information Coefficient in Practice: Rolling IC of a Short Term FX Reversal Signal
20.1.8 The Fundamental Law of Active Management: Relationship between Information Ratio & Information Coefficient
20.2 Modeling Volatility
20.2.1 Estimating Volatility
20.2.2 Rolling & Expanding Windows Volatility Estimates
20.2.3 Exponentially Weighted Moving Average Estimates
20.2.4 High Frequency & Range Based Volatility Estimators
20.2.5 Mean-Reverting Volatility Models: GARCH
20.2.6 GARCH in Practice: Estimation of GARCH(1,1) Parameters to Equity Index Returns
20.2.7 Estimation of Covariance Matrices
20.2.8 Correcting for Negative Eigenvalues
20.2.9 Shrinkage Methods for Covariance Matrices
20.2.10 Shrinkage in Practice: Impact on Structure of Principal Components
20.2.11 Random Matrix Theory
Chapter 21 ▪ Risk Management
21.1 Motivation & Setting
21.1.1 Risk Management in Practice
21.1.2 Defined vs. Undefined Risks
21.1.3 Types of Risk
21.2 Common Risk Measures
21.2.1 Portfolio Value at Risk
21.2.2 Marginal VaR Contribution
21.2.3 Portfolio Conditional Value at Risk
21.2.4 Marginal CVaR Contribution
21.2.5 Extreme Loss, Stress Tests & Scenario Analysis
21.3 Calculation of Portfolio VaR and CVaR
21.3.1 Overview
xxix. 21.3.2 Historical Simulation
21.3.3 Monte Carlo Simulation
21.3.4 Strengths and Weaknesses of Each Approach
21.3.5 Validating Our Risk Calculations Out-of-Sample
21.3.6 VaR in Practice: Out of Sample Test of Rolling VaR
21.4 Risk Management of Non-Linear Instruments
21.4.1 Non-Linear Risk
21.4.2 Hedging Portfolios via Scenarios
21.5 Risk Management in Rates & Credit Markets
21.5.1 Introduction
21.5.2 Converting from Change in Yield to Change in Price
21.5.3 DV01 and Credit Spread 01: Risk Management via Parallel Shifts
21.5.4 Partial DV01's: Risk Management via Key Rate Shifts
21.5.5 Jump to Default Risk
21.5.6 Principal Component Based Shifts
21.6 Measuring Counterparty Risk
21.6.1 Counterparty Risk: Introduction
21.6.2 Counterparty Risk: Exchange Traded vs. OTC Contracts
21.6.3 Wrong Way Counterparty Risk & CDS
21.6.4 Credit Valuation Adjustments: Definitions & Terminology
21.6.5 Credit Valuation Adjustments: Modeling
21.6.6 Credit Valuation Adjustments & Wrong Way CDS Risk
21.6.7 Other Valuation Adjustments
21.6.8 Counterparty Risk in Practice: Impact of a Credit Valuation Adjustment on a CDS Contract
Chapter 22 ▪ Quantitative Trading Models
22.1 Introduction to Quant Trading Models
22.1.1 Quant Strategies
22.1.2 What is Alpha Research?
22.1.3 Types of Quant Strategies
22.2 Back-testing
22.2.1 Parameter Estimation
22.2.2 Modeling Transactions Costs
22.2.3 Evaluating Back-Test Performance
xxx. 22.2.4 Most Common Quant Traps
22.2.5 Common Performance Metrics
22.2.6 Back-Tested Sharpe Ratios
22.2.7 In-Sample and Out-of-Sample Analysis
22.2.8 Out-of-Sample Performance & Slippage
2.3 Common Stat-Arb Strategies
22.3.1 Single Asset Momentum & Mean-Reversion Strategies
22.3.2 Cross Asset Autocorrelation Strategies
22.3.3 Pairs Trading
22.3.4 Pairs Trading in Practice: Gold vs. Gold Miners
22.3.5 Factor Models
22.3.6 PCA-Based Strategies
22.3.7 PCA Decomposition in Practice: How many Principal Components Explain the S&P 500?
22.3.8 Risk Premia Strategies
22.3.9 Momentum in Practice: Country ETFs
22.3.10 Translating Raw Signals to Positions
22.4 Systematic Options Based Strategies
22.4.1 Back-Testing Strategies Using Options
22.4.2 Common Options Trading Strategies
22.4.3 Options Strategy in Practice: Covered Calls on NASDAQ
22.5 Combining Quant Strategies
22.6 Principles of Discretionary vs. Systematic Investing
22.7 Case Study: Do trend following strategies produce convex returns?
Chapter 23 ▪ Artificial Intelligence: Incorporating Machine Learning Techniques
23.1 Artifical Intelligence & Machine Learning: Landscape
23.2 Machine Learning Framework
23.2.1 Machine Learning vs. Econometrics
23.2.2 Stages of a Machine Learning Project
23.2.3 Parameter Tuning & Cross Validation
23.2.4 Classes of Machine Learning Algorithms
23.2.5 Applications of Machine Learning in Asset Management & Trading
xxxi. 23.2.6 Challenges of Using Machine Learning in Finance
23.3 Supervised vs. Unsupervised Learning Methods
23.3.1 Supervised vs. Unsupervised Learning
23.3.2 Supervised Learning Methods
23.3.3 Regression vs. Classification Techniques
23.3.4 Unsupervised Learning Methods
23.4 Clustering
23.4.1 What is Clustering?
23.4.2 K-Means Clustering
23.4.3 Hierarchical Clustering
23.4.4 Distance Metrics
23.4.5 Optimal Number of Clusters
23.4.6 Clustering in Finance
23.4.7 Clustering in Practice: Asset Class & Risk-on Risk-off Clusters
3.5 Classification Techniques
23.5.1 What is Classification?
23.5.2 K-Nearest Neighbor
23.5.3 Probit Regression
23.5.4 Logistic Regression
23.5.5 Support Vector Machines
23.5.6 Confusion Matrices
23.5.7 Classification Problems in Finance
23.5.8 Classification in Practice: Using Classification Techniques in an Alpha Signal
23.5.9 Other uses of Classification Techniques: Credit Risk Modeling
23.6 Feature Importance & Interpretability
23.6.1 Feature Importance & Interpretability
Chapter 24 ▪ Artificial Intelligence: Incorporating Deep Learning, Large Language Models and Working with Unstructured Data
24.1 Overview
24.1.1 Artificial Intelligence and the Investment Process
24.2 Deep Learning
24.2.1 Deep Neural Networks
xxii. 24.2.3 Autoencoder in Practice: Reducing the Dimensionality of a Covariance Matrix
24.2.4 Convolutional Neural Networks
24.2.5 Recurrent Neural Networks
24.2.6 Generative Adversarial Networks
24.3 Natural Language Processing
24.3.1 Alternative Data Sources
24.3.2 Natural Language Processing Algorithms
24.3.3 Natural Language Processing in Practice: Parsing News for Trading Signal
24.4 Large Language Models
24.4.1 What are LLMs?
24.4.2 Transformer Networks
24.4.3 Prompt Engineering
24.4.4 Hallucinations
24.5 Applications of Deep Learning & Unstructured Data
24.5.1 Delta Hedging Schemes & Optimal Execution via Reinforcement Learning
24.5.2 Volatility Surface Calibration via Deep Learning
24.5.3 Credit Risk Estimation via Deep Learning
24.5.4 Leveraging GANs in Risk Modeling
24.5.5 Generating Expected Returns via Generative AI & LLMs
24.5.6 Challenges & Limitations
24.5.7 Responsible Use
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