Solution to Derivatives Markets: for Exam Fm

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Solution to Derivatives Markets: for Exam FM
Yufeng Guo June 24, 2007

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c °Yufeng Guo

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Contents
Introduction 1 Introduction to derivatives 2 Introduction to forwards and options vii 1 7 29 79 129 141

3 Insurance, collars, and other strategies 4 Introduction to risk management 5 Financial forwards and futures 8 Swaps

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CONTENTS

CONTENTS

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Preface
This is Guo’s solution to Derivatives Markets (2nd edition ISBN 0-321-28030X) for Exam FM. Unlike the official solution manual published by AddisonWesley, this solution manual provides solutions to both the even-numbered and odd-numbered problems for the chapters that are on the Exam FM syllabus. Problems that are out of the scope of the FM syllabus are excluded. Please report any errors to yufeng_guo@msn.com. This book is the exclusive property of Yufeng Guo. Redistribution of this book in any form is prohibited.

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PREFACE

PREFACE

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Introduction
Recommendations on using this solution manual: 1. Obviously, you’ll need to buy Derivatives Markets (2nd edition) to see the problems. 2. Make sure you download the textbook errata from http://www.kellogg. northwestern.edu/faculty/mcdonald/htm/typos2e_01.html

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CHAPTER 0. INTRODUCTION

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Chapter 1

Introduction to derivatives
Problem 1.1. Derivatives on weather are not as farfetched as it might appear. Visit http: //www.cme.com/trading/ and you’ll find more than a dozen weather derivatives currently traded at CME such as "CME U.S. Monthly Weather Heating Degree Day Futures" and "CME U.S. Monthly Weather Cooling Degree Day Futures." a. Soft drink sales greatly depend on weather. Generally, warm weather boosts soft drink sales and cold weather reduces sales. A soft drink producer can use weather futures contracts to reduce the revenue swing caused by weather and smooth its earnings. Shareholders of a company generally want the earnings to be steady. They don’t want the management to use weather as an excuse for poor earnings or wild fluctuations of earnings. b. The recreational skiing industry greatly dependents on weather. A ski resort can lose money due to warm temperatures, bitterly cold temperatures, no snow, too little snow, or too much snow. A resort can use weather derivatives to reduce its revenue risk. c. Extremely hot or cold weather will result in greater demand for electricity. An electric utility company faces the risk that it may have to buy electricity at a higher spot price. d. Fewer people will visit an amusement park under extreme weather conditions. An amusement park can use weather derivatives to manage its revenue risk. How can we buy or sell weather? No one can accurately predict weather. No one can deliver weather. For people to trade on weather derivatives, weather indexes need to be invented and agreed upon. Once we have weather indexes, we can link the payoff of a weather derivative to a weather index. For more information on weather derivatives, visit: • http://hometown.aol.com/gml1000/wrms.htm • http://www.investopedia.com 1

CHAPTER 1. INTRODUCTION TO DERIVATIVES Problem 1.2. • Anyone (such as speculators and investors) who wants to earn a profit can enter weather futures. If you can better predict a weather index than does the market maker, you can enter weather futures and make a profit. Of course, it’s hard to predict a weather index and hence loss may occur. • Two companies with opposite risks may enter weather futures as counter parties. For example, a soft drink company and a ski-resort operator have opposite hedging needs and can enter a futures contract. The soft drink company can have a positive payoff if the weather is too cold and a negative payoff if warm. This way, when the weather is too cold, the soft drink company can use the gain from the weather futures to offset its loss in...
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