Quantitative Finance For Dummies

An accessible introduction to quantitative finance by the numbers--for students, professionals, and personal investors

The world of quantitative finance is complex, and sometimes even high-level financial experts have difficulty grasping it. Quantitative Finance For Dummies offers plain-English guidance on making sense of applying mathematics to investing decisions. With this complete guide, you'll gain a solid understanding of futures, options and risk, and become familiar with the most popular equations, methods, formulas, and models (such as the Black-Scholes model) that are applied in quantitative finance.

Also known as mathematical finance, quantitative finance is about applying mathematics and probability to financial markets, and involves using mathematical models to help make investing decisions. It's a highly technical discipline--but almost all investment companies and hedge funds use quantitative methods.

The book breaks down the subject of quantitative finance into easily digestible parts, making it approachable for personal investors, finance students, and professionals working in the financial sector--especially in banking or hedge funds who are interested in what their quant (quantitative finance professional) colleagues are up to. This user-friendly guide will help you even if you have no previous experience of quantitative finance or even of the world of finance itself.

With the help of Quantitative Finance For Dummies, you'll learn the mathematical skills necessary for success with quantitative finance and tips for enhancing your career in quantitative finance.

Get your own copy of this handy reference guide and discover:

• An easy-to-follow introduction to the complex world of quantitative finance
• The core models, formulas, and methods used in quantitative finance
• Exercises to help augment your understanding of QF
• How QF methods are used to define the current market value of a derivative security
• Real-world examples that relate quantitative finance to your day-to-day job
• Mathematics necessary for success in investment and quantitative finance
• Portfolio and risk management applications
• Basic derivatives pricing

Whether you're an aspiring quant, a top-tier personal investor, or a student, Quantitative Finance For Dummies is your go-to guide for coming to grips with QF/risk management.

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

Primary market: The high level personal investor wanting an introduction to QF/risk management.

Secondary market: Those studying finance and aspiring to a career as a quant (there even some Masters degrees in the UK focusing on QF).

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.