Quantitative Finance For Dummies E-Book

Steve Bell

• Herausgeber: John Wiley & Sons
• Kategorie: Fachliteratur
• Sprache: Englisch

Seitenzahl: 596

Veröffentlichungsjahr: 2016

Beschreibung

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.

Leseprobe

Quantitative Finance For Dummies®

Published by: John Wiley & Sons, Ltd., The Atrium, Southern Gate, Chichester,www.wiley.com

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ISBN: 978-1-118-76946-1

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Quantitative Finance For Dummies®

To view this book's Cheat Sheet, simply go to www.dummies.com and search for “Quantitative Finance For Dummies Cheat Sheet” in the Search box.

Table of Contents

Cover

Introduction

About This Book

Foolish Assumptions

Icons Used in This Book

Where to Go from Here

Part 1: Getting Started with Quantitative Finance

Chapter 1: Quantitative Finance Unveiled

Defining Quantitative Finance

Wielding Financial Weapons of Mass Destruction

Analysing and Describing Market Behaviour

Managing Risk

Computing, Algorithms and Markets

Chapter 2: Understanding Probability and Statistics

Figuring Probability by Flipping a Coin

Defining Random Variables

Introducing Some Important Distributions

Chapter 3: Taking a Look at Random Behaviours

Setting Up a Random Walk

Averaging with the Central Limit Theorem

Moving Like the Stock Market

Generating Random Numbers on a Computer

Simulating Random Walks

Moving Up a Gear

Reverting to the Mean

Part 2: Tackling Financial Instruments

Chapter 4: Sizing Up Interest Rates, Shares and Bonds

Explaining Interest

Sharing in Profits and Growth

Taking the Pulse of World Markets

Defining Bonds and Bond Jargon

Swapping between Fixed and Floating Rates

Chapter 5: Exploring Options

Examining a Variety of Options

Reading Financial Data

Getting Paid when Your Option Expires

Using Options in Practice

Trading Options On and Off Exchanges

Relating the Price of Puts and Calls

Chapter 6: Trading Risk with Futures

Surveying Future Contracts

Seeing into the Future

Rolling a Position

Converging Futures to the Spot Price

Using Futures Creatively

Seasonality in Futures Prices

Part 3: Investigating and Describing Market Behaviour

Chapter 7: Reading the Market’s Mood: Volatility

Defining Volatility

Using Historical Data

Shrinking Time Using a Square Root

Comparing Volatility Calculations

Estimating Volatility by Statistical Means

Going Beyond Simple Volatility Models

Estimating Future Volatility with Term Structures

Chapter 8: Analysing All the Data

Data Smoothing

Estimating More Distributions

Modelling Non-Normal Returns

Chapter 9: Analysing Data Matrices: Principal Components

Reducing the Amount of Data

Applying PCA to Yield Curves

Using PCA to Build Models

Part 4: Option Pricing

Chapter 10: Examining the Binomial and Black-Scholes Pricing Models

Looking at a Simple Portfolio with No Arbitrage

Pricing in a Single Step

Branching Out in Pricing an Option

Making Assumptions about Option Pricing

Introducing Black-Scholes – The Most Famous Equation in Quantitative Finance

Solving the Black-Scholes Equation

Properties of the Black-Scholes Solutions

Generalising to Dividend-Paying Stocks

Defining other Options

Valuing Options Using Simulations

Chapter 11: Using the Greeks in the Black-Scholes Model

Using the Black-Scholes Formulae

Hedging Class

That’s Greek to Me: Explaining the Greek Maths Symbols

Rebalancing a Portfolio

Troubleshooting Model Risk

Chapter 12: Gauging Interest-Rate Derivatives

Looking at the Yield Curve and Forward Rates

Modelling the Interest-Rate

Part 5: Risk and Portfolio Management

Chapter 13: Managing Market Risk

Investing in Risky Assets

Stopping Losses and other Good Ideas

Hedging Schemes

Betting without Losing Your Shirt

Evaluating Outcomes with Utility Functions

Using the Covariance Matrix to Measure Market Risk

Chapter 14: Comprehending Portfolio Theory

Diversifying Portfolios

Minimising Portfolio Variance

Capital Asset Pricing Model

Assessing Portfolio Performance

Chapter 15: Measuring Potential Losses: Value at Risk (VaR)

Controlling Risk in Your Portfolio

Defining Volatility and the VaR Measure

Constructing VaR using the Covariance Matrix

Estimating Volatilities and Correlations

Simulating the VaR

Validating Your Model

Including the Average VaR

Estimating Tail Risk with Extreme Value Theory

Part 6: Market Trading and Strategy

Chapter 16: Forecasting Markets

Measuring with Technical Analysis

Making Predictions Using Market Variables

Predicting from Past Values

Chapter 17: Fitting Models to Data

Maximising the Likelihood

Fitting and Overfitting

Applying Occam’s Razor

Detecting Outliers

The Curse of Dimensionality

Seeing into the Future

Chapter 18: Markets in Practice

Auctioning Assets

Looking at the Price Impact of a Trade

Being a Market Maker and Coping with Bid-Ask Spreads

Trading Factors and Distributions

Part 7: The Part of Tens

Chapter 19: Ten Key Ideas of Quantitative Finance

If Markets Were Truly Efficient Nobody Would Research Them

The Gaussian Distribution is Very Helpful but Doesn’t Always Apply

Don’t Ignore Trading Costs

Know Your Contract

Understanding Volatility is Key

You Can Price Options by Building Them from Cash and Stock

Finance Isn’t Like Physics

Diversification is the One True Free Lunch

Find Tools to Help Manage All the Data

Don’t Get Fooled by Complex Models

Chapter 20: Ten Ways to Ace Your Career in Quantitative Finance

Follow Financial Markets

Read Some Classic Technical Textbooks

Read Some Non-technical Books

Take a Professional Course

Attend Networking Meetings and Conferences

Participate in Online Communities

Study a Programming Language

Go Back to School

Apply for that Hedge Fund or Bank Job

Take Time to Rest Up and Give Back

Glossary

About the Author

Advertisement Page

Connect with Dummies

End User License Agreement

Guide

Cover

Table of Contents

Begin Reading

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Introduction

Quantitative finance is about applying mathematics and statistics to finance. For maths lovers that’s exciting, but for the rest of us it may sound scary and off-putting. But I guide you step by step, so no need to worry. Quantitative finance helps you to price contracts such as options, manage the risk of investment portfolios and improve trade management.

I show you how banks price derivatives contracts based on the statistics of stock and bond price movements and some simple rules of probability. Similar maths help you understand how to manage the risk of investment portfolios. Quantitative tools help you understand and manage these systems, and this book introduces you to many of the most important ones.

About This Book

This book should be helpful for professionals working in the financial sector – especially in banking. It won’t take you to the level of doing the maths for pricing the latest derivative contract, but it can help you to contribute, perhaps as a programmer, data scientist or accountant. It should also be helpful for those taking a masters course in finance or financial analysis and who want help in a module on quantitative finance. Enough detail is included to really help in understanding key topics such as the Black-Scholes equation. The book also has breadth so you can discover a range of key financial instruments and how they’re used as well as techniques used by traders and hedge fund managers. Whether you plan a career as a corporate treasurer, risk analyst, investment manager or master of the universe at an investment bank, this book should give you a boost.

This book isn’t a traditional textbook and isn’t a traditional book on quantitative finance. It is significantly different from either in the following ways:

The book is designed as a reference so that you can dive into the section of most importance to you. I include lots of cross references to clearly point you to other sections and chapters that may have additional or complementary information.

The maths is at the minimum level required to explain the subjects. I made no attempt to impress with fancy mathematical jargon, lengthy proofs or references to obscure theorems.

It’s about applying mathematics and probability to finance. That includes derivatives but also includes tools to help you with trading and risk management. Finance is a subject centred on numbers, so maths is a natural way to help you get to grips with it.

It includes real-world examples so you can relate quantitative finance to your day-to-day job.

If you haven’t done any algebra for a while, remember that mathematicians like to write products without multiplication signs. So P(H)P(H) is shorthand for the probability of heads multiplied by the probability of heads. For maths with actual numbers, I use the symbol * to indicate multiplication. This avoids any confusion with the variable x, which is a favourite of mathematicians to signify an unknown quantity.

Within this book, web addresses may break across two lines of text. If you’re reading this book in print and want to visit one of these web pages, simply key in the web address exactly as noted in the text, pretending the line break doesn’t exist. If you’re reading this as an e-book, you’ve got it easy — just click the web address to be taken directly to the website.

Foolish Assumptions

I don’t assume that you have any previous experience of quantitative finance. I don’t even assume that you’re familiar with the world of finance except for the apocalyptic stories you read in the press about crises, greed, bonuses and debt. However, I’m assuming that you’re reading this book because you’re working in a financial institution such as a bank or a hedge fund and want to know what those clever quants (quantitative finance professionals) are doing. Alternatively, you may be studying for a Masters in Finance and looking for help with those quantitative modules.

I assume that you’re familiar with mathematics such as logarithms, exponentials and basic algebra. In some parts of the book, I also assume some knowledge of calculus both differentiation and integration. The online Cheat Sheet at www.dummies.com/cheatsheet/quantitativefinance is a good place to visit if you need to brush up on some of this maths. Some of the sections with the heaviest maths have Technical Stuff icons, which means that you can skip them if you wish.

Where I use algebra, I try to take you through it step by step and introduce all the symbols before the equations so that you know what they’re about. I also include a few example calculations to help you become familiar with them and see how to use the equations in practice.

Quantitative finance is what it says it is and involves numbers and maths but you don’t need to become bogged down by it. Only then will you see that the numbers are useful in real life in your job.

Icons Used in This Book

Icons are used in this book to draw your attention to certain features that occur on a regular basis. Here’s what they mean:

This icon is to give those grey cells a little jolt. It’s so easy to forget what you learned in school.

This icon points to helpful ideas that can save you time and maybe even money.

Skip paragraphs marked with this icon if you don’t want to go into the gory mathematical details. But if you do manage them, you’ll really glow with achievement.

Sometimes things can go badly wrong. Follow these sections to avoid disasters.

Where to Go from Here

The obvious answer is to start with Chapter 1. In fact, that’s a good idea if you’re not too familiar with quantitative finance as Chapter 1 is a bit like the book in miniature. I hope it will fire you up ready to read the rest of the book. Another obvious answer is to go to the table of contents. Just find the topic you’d like to know about and go straight there – no messing about. The book is designed to be used like that. Check out the topics you want to know about and skip what you’re not interested in. A third obvious answer is to use the index, which has been conveniently arranged in alphabetical order for you. If some quantitative finance jargon is bugging you, go to the Glossary at the back. Finally, if you’re really in a hurry, try Chapters 19 and 20. They give quantitative finance to you in ten bite-sized sections.

And you can use some free online material to help. The Cheat Sheet is a goldmine of handy formulae used in quantitative finance. To view this book’s Cheat Sheet, go to www.dummies.com and search for “Quantitative Finance For Dummies Cheat Sheet” for additional bits of information that you can refer to whenever you need it.

Part 1

Getting Started with Quantitative Finance

IN THIS PART …

Realise that the chart of a stock price can look jumpy and rather random because market prices are indeed very close to being random.

Get to grips with the mathematics of random numbers and brush up on probability and statistics.

Enter the strange and fascinating world of random walks. Find out how you can use them as models for the price movement of financial assets such as stocks.

Use calculus to analyse random walks so that you can get going on the classic maths for option pricing.

Chapter 1

Quantitative Finance Unveiled

IN THIS CHAPTER

Using probability and statistics in finance

Finding alternatives for cash

Looking at efficient (and not-so-efficient) markets

Tackling options, futures and derivatives

Managing risk

Doing the maths (and the machines that can help)

Quantitative finance is the application of probability and statistics to finance. You can use it to work out the price of financial contracts. You can use it to manage the risk of trading and investing in these contracts. It helps you develop the skill to protect yourself against the turbulence of financial markets. Quantitative finance is important for all these reasons.

If you’ve ever looked at charts of exchange rates, stock prices or interest rates, you know that they can look a bit like the zigzag motion of a spider crossing the page. However, major decisions have to be made based on the information in these charts. If your bank account is in dollars but your business costs are in euros, you want to make sure that, despite fluctuations in the exchange rate, you can still pay your bills. If you’re managing a portfolio of stocks for investors and you want to achieve the best return for them at minimum risk, then you need to learn how to balance risk with reward. Quantitative finance is for banks, businesses and investors who want better control over their finances despite the random movement of the assets they trade or manage. It involves understanding the statistics of asset price movements and working out what the consequences of these fluctuations are.

However, finance, even quantitative finance, isn’t just about maths and statistics. Finance is about the behaviour of the participants and the financial instruments they use. You need to know what they’re up to and the techniques they use. This is heady stuff, but this book guides you through.

Defining Quantitative Finance

My guess is that if you’ve picked up a book with a title like this one, you want to know what you’re going to get for your money. Definitions can be a bit dry and rob a subject of its richness but I’m going to give it a go.

Quantitative finance is the application of mathematics – especially probability theory – to financial markets. It’s used most effectively to focus on the most frequently traded contracts. What this definition means is that quantitative finance is much more about stocks and bonds (both heavily traded) than real estate or life insurance policies. The basis of quantitative finance is an empirical observation of prices, exchange rates and interest rates rather than economic theory.

Quantitative finance gets straight to the point by answering key questions such as, ‘How much is a contract worth?’ It gets to the point by using many ideas from probability theory, which are laid out in and . In addition, sometimes quantitative finance uses a lot of mathematics. Maths is really unavoidable because the subject is about answering questions about price and quantity. You need numbers for that. However, if you use too much mathematics, you can lose sight of the context of borrowing and lending money, the motivation of traders and making secure investments. covers subjects such as attitudes to risk and prospect theory while looks in more detail at the way markets function and dysfunction.