ction to Derivative - ets, and Risk Manage ment Robert A. Jarrow Ar k...

SOLUTIO

NS MANUAL

An Introdu ction to Derivative Securities, Financial Mark ets, and Risk Manage ment Robert A. Jarrow Ar kadev Chatterjea 1 st Edition 1 / 4

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Part I: Introduction

Chapter 1 | Derivatives and Risk Management 1 Chapter 2 | Interest Rates 11 Chapter 3 | Stocks 20 Chapter 4 | Forwards and Futures 26 Chapter 5 | Options 34 Chapter 6 | Arbitrage and Trading 41 Chapter 7 | Financial Engineering and Swaps 50

Part II: Forwards and Futures

Chapter 8 | Forwards and Futures Markets 60 Chapter 9 | Futures Trading 68 Chapter 10 | Futures Regulations 79 Chapter 11 | The Cost- of- Carry Model 89 Chapter 12 | The Extended Cost- of- Carry Model 105 Chapter 13 | Futures Hedging 119

Part III: Options

Chapter 14 | Options Markets and Trading 132 Chapter 15 | Option Trading Strategies 142 Chapter 16 | Option Relations 157 Chapter 17 | Single- Period Binomial Model 169 Chapter 18 | Multiperiod Binomial Model 180

TABLE OF CONTENTS 2 / 4

Chapter 19 | The Black– Scholes– Merton Model 194 Chapter 20 | Using the Black– Scholes– Merton Model 205

Part IV: Interest Rates Derivatives

Chapter 21 | Yields and Forward Rates 221 Chapter 22 | Interest Rate Swaps 233 Chapter 23 | Single- Period Binomial Heath–Jarrow–Morton Model 241 Chapter 24 | Multiperiod Binomial Heath–Jarrow–Morton Model 250 Chapter 25 | The Heath–Jarrow–Morton Libor Model 264 Chapter 26 | Risk Management Models 273 iv | Contents 3 / 4

1 CHAPTER 1 Derivatives and Risk Management

1.1. What is a derivative security? Give an example of a derivative and explain why it is

a derivative.

ANSWER

A derivative security is a fi nancial contract that derives its value from the price of an underlying asset such as a stock or a commodity, or from the value of an underlying notional variable such as a stock index or an interest rate (see Section 1.1).Consider a forward contract to trade 50 ounces of gold three months from today at a forward price of F = $1,500 per ounce. The spot price of the underlying commodity gold determines this derivative’s payoff. For example, if the spot price of gold is S(T) = $1,510 per ounce at time T = 3 months, then the buyer of this forward contract buys gold worth $1,510 for $1,500. Her profi t is [S(T) – F] × Number of units = (1,510 – 1,500) × 50 = $500. This is the seller’s loss because derivative trading is a zero- sum game; that is, for each buyer there is a seller.

1.2. List some major applications of derivatives.

ANSWER

Some applications of derivatives:

• They help generate a variety of future payoffs, which makes the market more “complete.” • They enable trades at lower transactions costs.• Hedgers can use them to cheaply reduce preexisting risk in their economic activities.Speculators can take leveraged positions without tying up too much capital.• They help traders overcome market restrictions. For example, an exchange may restrict traders from short- selling a stock in a falling market, but a trader can adopt a similar position by buying a put option.• They promote a more effi cient allocation of risk by allowing the risk of economic transactions to be shifted to dealers who can better manage these risks.

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