Supplement for: Quantitative Finance With Python (Includes coding examples)

192 Pages·2022·0.933 MB·English

by  C. Kelliher

Chris Kelliher
A Practical Guide to Investment
Management, Trading and Financial
Engineering

To my amazing daughter Sloane, my light and purpose.
To my wonderful, loving wife Andrea without whom none of my
achievements would be possible.
To my incredible, supportive parents and sister and brother, Jen
and Lucas.

Contents
Author Bio vii
Foreword ix
Contributors xi
Section I Foundations of Quant Modeling
Chapter 1(cid:4) Setting the Stage: Quant Landscape 3
1.0.1 Coding Example: Option Payoff 3
1.0.2 Coding Example: Valuing a Swap Contract 3
Chapter 2(cid:4) Theoretical Underpinnings of Quant Modeling: Modeling the
Risk Neutral Measure 5
2.1 CALCULUSREVIEW 5
2.1.1 Differentiation 5
2.1.2 Derivatives of a Multivariate Function 7
2.1.3 Integration 7
2.1.4 Taylor Series 9
2.2 REVIEWOFPROBABILITYCONCEPTS 10
2.2.1 Discrete and Continuous Probability Distributions 10
2.2.2 Probability Density and Cumulative Density Functions 11
2.2.3 Expected Value, Variance and Correlation 12
2.2.4 Common Probability Distributions 15
2.2.5 Coding Example: Call Option Price via Binomial Tree 18
Chapter 3(cid:4) Theoretical Underpinnings of Quant Modeling: Modeling the
Physical Measure 21
3.0.1 Coding Example: Using OLS to Find Regression Betas 21
i
ii (cid:4) Contents
3.0.2 Coding Example: Portfolio Return and Volatility 21
3.0.3 Coding Example: Bootstrapping Synthetic Returns 22
Chapter 4(cid:4) Python Programming Environment 27
4.0.1 Plotting / Visualizations 27
4.1 WORKINGINAMULTI-PROGRAMMERENVIRONMENT 27
Chapter 5(cid:4) Programming Concepts in Python 33
5.0.1 Coding Example: Covariance Matrix Calculations 33
5.0.2 Coding Example: Working with Time Series Data 34
5.0.3 Coding Example: Working with Panel Data 34
5.0.4 CodingExample:TestingforAutocorrelationinStockReturns 34
5.0.5 Coding Example: Using Inheritance to Create a Generic
Stochastic Process Class 35
5.0.6 Abstract Base Classes 36
5.0.7 Factory Pattern 36
5.0.8 Singleton Pattern 37
5.0.9 Template Method 37
5.0.10 Binary Search Algorithm 38
5.0.11 Selection Sort 38
5.0.12 Insertion Sort 38
5.0.13 Bubble Sort 39
5.0.14 Merge Sort 39
Chapter 6(cid:4) Working with Financial Datasets 45
6.0.1 Coding Example: Downloading Data from Yahoo Finance 45
6.1 BASICSOFSQLQUERYING 45
6.1.1 Modifying Data via Insert, Update and Delete Statements 46
6.1.2 Retrieving Data via Select Statements 46
6.1.3 Retrieving Data from Multiple Tables via JOINs 47
6.1.4 Aggregating Data via a Group By Clause 49
6.1.5 Coding Example: Filling Missing Data with Python Data
Frames 49
6.1.6 Coding Example: Filling Missing ETF Data via Regression 50
Contents (cid:4) iii
6.1.7 Coding Example: Using Bootstrapping to Create Synthetic
History for a set of Indices 51
6.1.8 Coding Example: Outlier Detection 51
Chapter 7(cid:4) Model Validation 55
7.1 UNIT TESTS IN PRACTICE: VALIDATING A SIMULATION ALGO-
RITHM 55
Section II Options Modeling
Chapter 8(cid:4) Stochastic Models 61
8.0.1 Coding Example: Black-Scholes Formula 61
8.0.2 Coding Example: Bachelier Pricing Formula 61
8.0.3 Coding Example: Option Pricing under the CEV Model 61
8.0.4 Coding Example: Option Prices in the SABR Model 62
8.0.5 Coding Example: Local Volatility Model 62
Chapter 9(cid:4) Options Pricing Techniques for European Options 67
9.0.1 Coding Example: Pricing a Digital Option via Quadrature
Methods 67
9.0.2 Coding Example: FFT Option Pricing in the Heston Model 67
9.0.3 Coding Example: Extracting Implied Volatility using Root
Finding 68
9.0.4 Coding Example: Finding the Minimum Variance Portfolio
of Two Assets 68
9.0.5 Coding Example: Calibrating a Volatility Surface 69
Chapter 10(cid:4) Options Pricing Techniques for Exotic Options 75
10.0.1 Coding Example: Simulation from the Heston Model 75
10.0.2 Coding Example: Simulation from the Variance Gamma 76
10.0.3 Coding Example: American Options Pricing via the Black-
Scholes PDE 76
Chapter 11(cid:4) Greeks and Options Trading 85
11.0.1 Coding Example: Calculating Delta and Gamma 85
iv (cid:4) Contents
11.0.2 Coding Example: Black-Scholes Theta 85
11.0.3 CodingExample:EstimationofLookbackOptionGreeksvia
Finite Differences 85
11.0.4 Coding Example: Smile Adjusted Greeks 86
Chapter 12(cid:4) Extraction of Risk Neutral Densities 91
12.0.1 Breeden-Litzenberger: Python Coding Example 91
12.0.2 Coding Example: Pricing a Digital Option 92
12.0.3 Weighted Monte Carlo: Coding Example 92
Section III Quant Modelling in Different Markets
Chapter 13(cid:4) Interest Rate Markets 99
13.0.1 Coding Example: Bond Pricing, Duration & Convexity 99
13.0.2 Coding Example: Bootstrapping a Yield Curve 99
13.0.3 Coding Example: Cap Pricing via Black’s Model 100
13.0.4 Coding Example: Calibrating Swaptions via the SABR Model 101
13.0.5 Coding Example: Simulation from the Vasicek Model 102
Chapter 14(cid:4) Credit Markets 111
14.0.1 Coding Example: Pricing a Risky Bond 111
14.0.2 Coding Example: Calibrating a CDS Curve via Optimization 111
14.0.3 Coding Example: Pricing a Knock-out CDS Swaption 113
14.0.4 Coding Example: Building an Index Loss Distribution in the
Homogeneous Model 113
14.0.5 Coding Example: Merton’s Formula 114
Chapter 15(cid:4) Foreign Exchange Markets 121
15.0.1 Coding Example: Pricing FX Options via the Black-Scholes
Model 121
15.0.2 Coding Example: Calibrating an FX Vol. Surface using SABR 121
15.0.3 Coding Example: Pricing Digis and One-Touches 123
Chapter 16(cid:4) Equity & Commodity Markets 127
Contents (cid:4) v
Section IV Portfolio Construction & Risk Management
Chapter 17(cid:4) Portfolio Construction & Optimization Techniques 135
17.0.1 Coding Example: Creating an Efficient Frontier 135
17.0.2 Coding Example: Safely Inverting a Covariance Matrix 136
17.0.3 Coding Example: Finding the Tangency Portfolio 137
17.0.4 Coding Example: Resampling an Efficient Frontier 137
17.0.5 Coding Example: Risk Parity Optimization 138
Chapter 18(cid:4) Modelling Expected Returns and Covariance Matrices 145
18.0.1 Coding Example: Regularization Models 145
18.0.2 Coding Example: Calculating Rolling IC 145
18.0.3 Coding Example: Calibration of GARCH(1,1) Model 146
18.0.4 Coding Example: Shrinking a Covariance Matrix 147
Chapter 19(cid:4) Risk Management 153
19.0.1 Coding Example: Calculating Common Risk Metrics 153
19.0.2 CodingExample:CalculatingValueatRiskviaBootstrapping 153
Chapter 20(cid:4) Quantitative Trading Models 159
20.0.1 Coding Example: Pairs Trading Algorithm 159
20.0.2 Coding Example: PCA Analysis 160
20.0.3 Coding Example: Momentum Strategy 160
20.0.4 Coding Example: Covered Calls Back-test 161
Chapter 21(cid:4) Incorporating Machine Learning Techniques 167
21.0.1 Coding Example: Optimizing Model Parameters via Cross
Validation 167
21.0.2 Coding Example: Clustering 167
21.0.3 Coding Example: K-Nearest Neighbor Algorithm 168
21.0.4 Coding Example: Classification via SVM 168
21.0.5 Coding Example: Feature Importance Tools 168