Table of Contents
Introduction 1 About This Book 1
Foolish Assumptions 2
Icons Used in This Book 3
Where to Go from Here 3
Part 1: Getting Started With Quantitative Finance 5
Chapter 1: Quantitative Finance Unveiled 7
Defining Quantitative Finance 8
Summarising the mathematics 8
Pricing, managing and trading 9
Meeting the market participants 9
Walking like a drunkard 10
Knowing that almost nothing isn’t completely nothing 11
Recognising irrational exuberance 14
Wielding Financial Weapons of Mass Destruction 15
Going beyond cash 17
Inventing new contracts 18
Analysing and Describing Market Behaviour 20
Measuring jumpy prices 20
Keeping your head while using lots of data 21
Valuing your options 21
Managing Risk 22
Hedging and speculating 22
Generating income 23
Building portfolios and reducing risk 23
Computing, Algorithms and Markets 24
Seeing the signal in the noise 24
Keeping it simple 25
Looking at the finer details of markets 25
Trading at higher frequency 26
Chapter 2: Understanding Probability and Statistics 27
Figuring Probability by Flipping a Coin 28
Playing a game 31
Flipping more coins 32
Defining Random Variables 33
Using random variables 34
Building distributions with random variables 35
Introducing Some Important Distributions 38
Working with a binomial distribution 39
Recognising the Gaussian, or normal, distribution 40
Describing real distributions 41
Chapter 3: Taking a Look at Random Behaviours 45
Setting Up a Random Walk 45
Stepping in just two directions 47
Getting somewhere on your walk 48
Taking smaller and smaller steps 49
Averaging with the Central Limit Theorem 50
Moving Like the Stock Market 53
Generating Random Numbers on a Computer 54
Getting random with Excel 55
Using the central limit theorem again 58
Simulating Random Walks 58
Moving Up a Gear 60
Working a stochastic differential equation 60
Expanding from the origin 61
Reverting to the Mean 62
Part 2: Tackling Financial Instruments 65
Chapter 4: Sizing Up Interest Rates, Shares and Bonds 67
Explaining Interest 68
Compounding your interest 68
Compounding continuously 69
Sharing in Profits and Growth 71
Taking the Pulse of World Markets 72
Defining Bonds and Bond Jargon 74
Coupon-bearing bonds 75
Zeroing in on yield 76
Cleaning up prices 78
Learning to like LIBOR 79
Plotting the yield curve 80
Swapping between Fixed and Floating Rates 81
Chapter 5: Exploring Options 85
Examining a Variety of Options 86
Starting with plain vanilla options 86
Aiming for a simple, binary option 87
Branching out with more exotic options 87
Reading Financial Data 88
Seeing your strike price 88
Abbreviating trading information 89
Valuing time 89
Getting Paid when Your Option Expires 90
Using Options in Practice 92
Hedging your risk 92
Placing bets on markets 93
Writing options 94
Earning income from options 94
Distinguishing European, American and other options 95
Trading Options On and Off Exchanges 96
Relating the Price of Puts and Calls 96
Chapter 6: Trading Risk with Futures 99
Surveying Future Contracts 99
Trading the futures market 101
Marking to market and margin accounts 101
Dealing in commodity futures 102
Index futures 105
Interest rate futures 106
Seeing into the Future 107
Paying in cash now 108
Connecting futures and spot prices 109
Checking trading volume 110
Looking along the forward curve 110
Rolling a Position 112
Keeping a consistent position 113
Adjusting backwards 113
Converging Futures to the Spot Price 114
Using Futures Creatively 115
Calendar spreads 116
Commodity spreads 116
Seasonality in Futures Prices 117
Part 3: Investigating and Describing Market Behaviour 119
Chapter 7: Reading The Market’s Mood: Volatility 121
Defining Volatility 122
Using Historical Data 124
Weighting the data equally 124
Weighting returns 125
Shrinking Time Using a Square Root 127
Comparing Volatility Calculations 128
Estimating Volatility by Statistical Means 132
The symmetric GARCH model 132
The leverage effect 134
Going Beyond Simple Volatility Models 135
Stochastic volatility 135
Regime switching 136
Estimating Future Volatility with Term Structures 137
Chapter 8: Analysing All the Data 139
Data Smoothing 139
Putting data in bins 140
Smoothing data with kernels 143
Using moving averages as filters 147
Estimating More Distributions 149
Mixing Gaussian distributions 149
Going beyond one dimension 150
Modelling Non-Normal Returns 151
Testing and visualising non-normality 151
Maximising expectations 153
Chapter 9: Analysing Data Matrices: Principal Components 159
Reducing the Amount of Data 160
Understanding collinearity 163
Standardising data 166
Brushing up some maths 167
Decomposing data matrices into principal components 170
Calculating principal components 173
Checking your model with cross- validation 174
Applying PCA to Yield Curves 177
Using PCA to Build Models 180
Identifying clusters of data 180
Principal components regression 181
Part 4: Option Pricing 183
Chapter 10: Examining the Binomial and Black-Scholes Pricing Models 185
Looking at a Simple Portfolio with No Arbitrage 186
Pricing in a Single Step 187
Entering the world of risk neutral 188
Calculating the parameters 191
Branching Out in Pricing an Option 192
Building a tree of asset prices 192
Building a tree of option prices by working backwards 192
Pricing an American option 194
Making Assumptions about Option Pricing 195
Introducing Black-Scholes – The Most Famous Equation in Quantitative Finance 196
Solving the Black-Scholes Equation 199
Properties of the Black-Scholes Solutions 202
Generalising to Dividend-Paying Stocks 204
Defining other Options 205
Valuing Options Using Simulations 206
Chapter 11: Using the Greeks in the Black-Scholes Model 209
Using the Black-Scholes Formulae 210
Hedging Class 211
That’s Greek to Me: Explaining the Greek Maths Symbols 213
Delta 213
Dynamic hedging and gamma 216
Theta 218
Rho 219
Vega 219
Relating the Greeks 220
Rebalancing a Portfolio 220
Troubleshooting Model Risk 221
Chapter 12: Gauging Interest-Rate Derivatives 223
Looking at the Yield Curve and Forward Rates 224
Forward rate agreements 227
Interest-rate derivatives 228
Black 76 model 230
Bond pricing equations 232
The market price of risk 234
Modelling the Interest-Rate 234
The Ho Lee model 234
The one-factor Vasicek model 235
Arbitrage free models 237
Part 5: Risk and Portfolio Management 239
Chapter 13: Managing Market Risk 241
Investing in Risky Assets 241
Stopping Losses and other Good Ideas 244
Hedging Schemes 245
Betting without Losing Your Shirt 247
Evaluating Outcomes with Utility Functions 249
Seeking certainty 250
Modelling attitudes to risk 251
Using the Covariance Matrix to Measure Market Risk 253
Estimating parameters 254
Shrinking the covariance matrix 254
Chapter 14: Comprehending Portfolio Theory 257
Diversifying Portfolios 258
Minimising Portfolio Variance 259
Using portfolio budget constraints 260
Doing the maths for returns and correlations 262
Building an efficient frontier 266
Dealing with poor estimates 267
Capital Asset Pricing Model 268
Assessing Portfolio Performance 270
Sharpe ratio 270
Drawdowns 272
Going for risk parity 273
Chapter 15: Measuring Potential Losses: Value at Risk (VaR) 275
Controlling Risk in Your Portfolio 276
Defining Volatility and the VaR Measure 277
Constructing VaR using the Covariance Matrix 279
Calculating a simple cash portfolio 280
Using the covariance matrix 281
Estimating Volatilities and Correlations 282
Simulating the VaR 283
Using historical data 283
Spinning a Monte Carlo simulation 284
Validating Your Model 285
Backtesting 285
Stress testing and the Basel Accord 286
Including the Average VaR 286
Estimating Tail Risk with Extreme Value Theory 289
Part 6: Market Trading and Strategy 291
Chapter 16: Forecasting Markets 293
Measuring with Technical Analysis 294
Constructing candlesticks 294
Relying on relative strength 295
Checking momentum indicators 298
Blending the stochastic indicator 299
Breaking out of channels 300
Making Predictions Using Market Variables 301
Understanding regression models 302
Forecasting with regression models 304
Predicting from Past Values 306
Defining and calculating autocorrelation 306
Getting to know autocorrelation models 308
Moving average models 309
Mentioning kernel regression 311
Chapter 17: Fitting Models to Data 313
Maximising the Likelihood 314
Minimising least squares 316
Using chi-squared 318
Comparing models with Akaike 318
Fitting and Overfitting 319
Applying Occam’s Razor 322
Detecting Outliers 322
The Curse of Dimensionality 324
Seeing into the Future 325
Backtesting 325
Out-of-sample validation 327
Chapter 18: Markets in Practice 329
Auctioning Assets 330
Selling on eBay 331
Auctioning debt by the US Treasury 332
Balancing supply and demand with double-sided auctions 333
Looking at the Price Impact of a Trade 336
Being a Market Maker and Coping with Bid-Ask Spreads 337
Exploring the meaning of liquidity 338
Making use of information 339
Calculating the bid-ask spread 342
Trading Factors and Distributions 343
Part 7: The Part Of Tens 345
Chapter 19: Ten Key Ideas of Quantitative Finance 347
If Markets Were Truly Efficient Nobody Would Research Them 347
The Gaussian Distribution is Very Helpful but Doesn’t Always Apply 348
Don’t Ignore Trading Costs 349
Know Your Contract 349
Understanding Volatility is Key 350
You Can Price Options by Building Them from Cash and Stock 350
Finance Isn’t Like Physics 351
Diversification is the One True Free Lunch 351
Find Tools to Help Manage All the Data 352
Don’t Get Fooled by Complex Models 353
Chapter 20: Ten Ways to Ace Your Career in Quantitative
Finance 355
Follow Financial Markets 355
Read Some Classic Technical Textbooks 356
Read Some Non-technical Books 356
Take a Professional Course 357
Attend Networking Meetings and Conferences 357
Participate in Online Communities 358
Study a Programming Language 358
Go Back to School 359
Apply for that Hedge Fund or Bank Job 359
Take Time to Rest Up and Give Back 359
Glossary 361
Index 369
