Solutions Manual - Part One Insurance, Hedging, and Simple Strategies

Solutions Manual

For Derivatives Markets Third Edition Robert L. McDonald 1 / 4

Contents Chapter 1 Introduction to Derivatives .................................................................................................. 1 Part One Insurance, Hedging, and Simple Strategies Chapter 2 An Introduction to Forwards and Options ........................................................................... 8 Chapter 3 Insurance, Collars, and Other Strategies ........................................................................... 22 Chapter 4 Introduction to Risk Management ..................................................................................... 44 Part Two Forwards, Futures, and Swaps Chapter 5 Financial Forwards and Futures ........................................................................................ 69 Chapter 6 Commodity Forwards and Futures .................................................................................... 83 Chapter 7 Interest Rate Forwards and Futures ................................................................................... 92 Chapter 8 Swaps .............................................................................................................................. 107 Part Three Options Chapter 9 Parity and Other Option Relationships ............................................................................ 116 Chapter 10 Binomial Option Pricing: Basic Concepts ....................................................................... 128 Chapter 11 Binomial Option Pricing: Selected Topics ...................................................................... 147 Chapter 12 The Black-Scholes Formula ............................................................................................ 170 Chapter 13 Market-Making and Delta-Hedging ................................................................................ 193 Chapter 14 Exotic Options: I ............................................................................................................. 209 Part Four Financial Engineering and Applications Chapter 15 Financial Engineering and Security Design .................................................................... 219 Chapter 16 Corporate Applications ................................................................................................... 230 Chapter 17 Real Options .................................................................................................................... 242 Part Five Advanced Pricing Theory Chapter 18 The Lognormal Distribution ............................................................................................ 254 Chapter 19 Monte Carlo Valuation .................................................................................................... 260 Chapter 20 Brownian Motion and Ito’s Lemma ................................................................................ 270 Chapter 21 The Black-Scholes-Merton Equation .............................................................................. 277 Chapter 22 Risk-Neutral and Martingale Pricing .............................................................................. 285 Chapter 23 Exotic Options: II ............................................................................................................ 295

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Chapter 24 Volatility.......................................................................................................................... 307 Chapter 25 Interest Rate and Bond Derivatives ................................................................................. 328 Chapter 26 Value at Risk ................................................................................................................... 342 Chapter 27 Credit Risk....................................................................................................................... 350

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Chapter 1 Introduction to Derivatives Question 1.1 This problem offers different scenarios in which some companies may have an interest to hedge their exposure to temperatures that are detrimental to their business. In answering the problem, it is useful to ask the question: Which scenario hurts the company, and how can it protect itself?a) A soft drink manufacturer probably sells more drinks when it is abnormally hot. She dislikes days at which it is abnormally cold because people are likely to drink less, and her business suffers. She will be interested in a cooling-degree-day futures contract because it will make payments when her usual business is slow. She hedges her business risk.b) A ski-resort operator may fear large losses if it is warmer than usual. It is detrimental to her business if it does not snow in the beginning of the season or if the snow is melting too fast at the end of the season. She will be interested in a heating-degree-day futures contract because it will make payments when her usual business suffers, thus compensating the losses.c) During the summer months, an electric utility company, such as one in the south of the United States, will sell a lot of energy during days of excessive heat because people will use their air conditioners, refrigerators, and fans more often, thus consuming a lot of energy and increasing profits for the utility company. In this scenario, the utility company will have less business during relatively colder days, and the cooling-degree-day futures offers a possibility to hedge such risk.Alternatively, we may think of a utility provider in the northeast during the winter months, a region where people use many additional electric heaters. This utility provider will make more money during unusually cold days and may be interested in a heating-degree-day contract because that contract pays off if the primary business suffers.d) An amusement park operator fears bad weather and cold days because people will abstain from going to the amusement park during cold days. She will buy a cooling-degree-day future to offset her losses from ticket sales with gains from the futures contract.Question 1.2 A variety of counterparties are imaginable. For one, we could think about speculators who have differences in opinion and who do not believe that we will have excessive temperature variations during the life of the futures contracts. Thus, they are willing to take the opposing side, receiving a payoff if the weather is stable.Alternatively, there may be opposing hedging needs: Compare the ski-resort operator and the soft drink manufacturer. The cooling-degree-day futures contract will pay off if the weather is relatively mild, and we saw that the resort operator will buy the futures contract. The buyer of 1 .

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