Quantitative Finance For Dummies

Steve Bell is a Quantitative Investment Researcher and Director at Research In Action. A highly experienced mathematical and statistical modeller, he is knowledgeable in energy markets and has a particular interest in systematic quantitative trading strategy development at any frequency.

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