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

Learn the tools for investment success Use portfolio and risk management applications Sharpen your skills with useful exercises Get acquainted with Quantitative Finance Whether you're an aspiring quant or a hands-on high-level investor, this book makes quantitative finance make sense. It demystifies futures, options, and risk; explains the core models, formulas, and methods; and provides essential mathematical tools. Accessible information and practical exercises prepare you for a successful role in finance! Inside.... Get a handle on QF modelsWork with random behavioursGrasp bond jargonLearn how to estimate probabilityModel interest ratesControl riskForecast like a proPerfect your portfolio