An Introduction to Equity Derivatives

Theory and Practice

Sebastien Bossu, Philippe Henrotte

• Publisher: Wiley
• Year: 2012
• Print ISBN: 9781119961857
• eBook ISBN: 9781119969037
• Edition: 2
• Topic: Business
• Subtopic: Finance
• Index: Business

Everything you need to get a grip on the complex world of derivatives

Written by the internationally respected academic/finance professional author team of Sebastien Bossu and Philipe Henrotte, An Introduction to Equity Derivatives is the fully updated and expanded second edition of the popular Finance and Derivatives. It covers all of the fundamentals of quantitative finance clearly and concisely without going into unnecessary technical detail. Designed for both new practitioners and students, it requires no prior background in finance and features twelve chapters of gradually increasing difficulty, beginning with basic principles of interest rate and discounting, and ending with advanced concepts in derivatives, volatility trading, and exotic products. Each chapter includes numerous illustrations and exercises accompanied by the relevant financial theory. Topics covered include present value, arbitrage pricing, portfolio theory, derivates pricing, delta-hedging, the Black-Scholes model, and more.

• An excellent resource for finance professionals and investors looking to acquire an understanding of financial derivatives theory and practice
• Completely revised and updated with new chapters, including coverage of cutting-edge concepts in volatility trading and exotic products

An accompanying website is available which contains additional resources including powerpoint slides and spreadsheets. Visit www.introeqd.com for details.

Part I

Building Blocks

1

Interest Rate

In this chapter we review the idea of interest rate and the closely related concepts of compounding and discounting.

1-1 Measuring Time

In finance the standard unit of time is the year. But can we safely assume that a year has 365 days? What about the 366 days of a leap year? What fraction of a year does the first six months represent: 0.5, or 181/365 (except, again, for leap years)?

Financial markets have regulations and conventions to answer these questions. The problem is that these conventions tend to vary by country. Worse still, within a given country different conventions may apply to different financial products.

We leave it to readers to become familiar with these day count conventions while in this book we will use the following rule, which professionals call 30/360 (Table 1-1 below). Note that the initial date starts at noon and the final date ends at noon; thus, there is only one whole day between 2 February 2012 and 3 February 2012.

Table 1-1 The 30/360 rule for measuring time

Rule	Result	Example: from 15 January 2012 to 13 March 2015
1. Count the number of whole years	Y	3 (from 15 January 2012 to 15 January 2015)
2. Count the number of remaining whole months and divide by 12	M/12	1/12 (from 15 January 2015 to 15 February 2015)
3. Count the number of remaining days (the last day of the month counting as the 30th unless it is the final date) and divide by 360	D/360	28/360 (under the 30/360 convention there are 16 days from 15 February 2015 to 1 March 2015 at noon and 12 days from 1 March 2015 to 13 March 2015)
TOTAL	Y + M/12 + D/360	3 + 1/12 + 28/360 = 3.161111…

From this rule we obtain the following simplified measures:

Semester (half year)	0.5 year
Quarter (three months)	0.25 year
Month	1/12 year
Week	7/360 year
Day	1/360 year

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In practice…

The Excel function DAYS360(Start_date, End_date) counts the number of days on a 30/360 basis.

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1-2 Interest Rate

In business life one can encounter two types of individuals whose interests are by definition opposed to each other:

• Investors, who have money and want to get richer while they remain idle;
• Entrepreneurs, who don't have money but want to become rich using the money of others.

Banks help to reconcile these two interests by acting as intermediaries, placing the money of the investor at the entrepreneur's disposal while taking the risk of bankruptcy (see Figure 1.1). In exchange, the bank demands that the entrepreneur pay interest at regular intervals, which serves to pay for the bank's service and the investor's capital.

Figure 1-1 Banks are intermediaries between investors and entrepreneurs

1-2.1 Gross Interest Rate

Consider an investor who deposits $100 and receives a total interest of $12 over 2 years. His gross 2-year interest rate is then 12%. Generally, if I is the total interest paid on a capital K, the gross interest rate over the period in consideration is defined as:

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Examples

• €10 of interest paid over one year on a capital of €200 corresponds to a 5% annual gross interest rate.
• $10 of interest paid every year for five years on a capital of $200 corresponds to a 25% gross interest rate over five years, which is five times the above annual rate.

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We must emphasize that an interest rate is meaningless if no time period is specified: a 5% gross interest rate every six months is far more lucrative than every year.

This rate is called ‘gross’ because it does not take int...

Table of contents

• Cover
• Title Page
• Copyright
• Foreword
• Preface
• Addendum: A Path to Economic Renaissance
• Part I: Building Blocks
• Part II: First Steps in Equity Derivatives
• Part III: Advanced Models and Techniques
• Solutions
• Appendices
• Index