2. How is a fund manager motivated to behave with this type of renumeration package?

Save this PDF as:
Size: px
Start display at page:

Download "2. How is a fund manager motivated to behave with this type of renumeration package?"

Transcription

1 MØA 155 PROBLEM SET: Options Exercise 1. Arbitrage [2] In the discussions of some of the models in this course, we relied on the following type of argument: If two investment strategies have the same payoff tomorrow, they must have the same price today. (Which we also called an no arbitrage argument.) Which of the following theories relied explicitly on these kinds of no-arbitrage arguments? (a) (b) (c) The Put Call parity of option pricing. The Miller Modigliani theorems for capital structure. The CAPM. Exercise 2. Mutual Fund Manager [2] A mutual fund announces that the salaries of its fund managers will depend on the performance of the fund. If the fund loses money, the salaries will be zero. If the fund makes a profit, the salaries will be proportional to the profit. 1. Describe the salary of a fund manager as an option. 2. How is a fund manager motivated to behave with this type of renumeration package? Exercise 3. Pricing factors [1] Which of the following are always positively related to the price of a European call option on a stock? (Hint: There is more than one) 1. The stock price. 2. The strike price. 3. The time to expiration. 4. The volatility 5. The risk-free rate 6. The magnitude of dividends anticipated during the life of the option. Exercise 4. Product [3] A bank has sold a product that offers investors the total return (excluding dividends) on the Oslo OBX index over a one year period. The return is capped at 2%. If the index goes down the original investment of the investor is returned. 1. What option position is equivalent to the product? Exercise 5. Put [2] Suppose that a European put option to sell a share for $6 costs $4 and is held until maturity. 1. Under what circumstances will the seller of the option(i. e. the party with the short position) make a profit? 2. Under what circumstances will the option be exercised? 1

2 3. Draw a diagram illustrating how the profit from a short position in the option depends on the stock price at the maturity of the option. Exercise 6. Straddles and Butterflies [3] Option traders often refer to straddles and butterflies. Here is an example of each: Straddle Buy call with exercise price of $1 and simultaneously buy put with exercise price of $1. Butterfly Simultaneously buy one call with exercise price of $1, sell two calls with exercise price of $11, and buy one call with exercise price of $ Draw position diagrams for the straddle and butterfly, showing the payoffs from the investor s net position. 2. Each strategy is a bet on variability. Explain briefly the nature of this bet. Exercise 7. Bank [3] You are working for an investment bank in South East Asia, and have sold a large number of straddles on the Japanese stock market index, with exercise price 18,5. 1. Give two ways to achieve this straddle position. 2. What does the profit structure of your position look like? 3. What are the conditions that make this a profitable transaction? 4. How much can you lose? Exercise 8. Breakeven [1] A one year call option on a stock with a strike price of $3 costs $3. A one year put option on the stock with a strike price of $3 costs $4. Suppose that a trader buys two call options and one put option. 1. What is the breakeven stock price above which the traders makes a profit? 2. What is the breakeven stock price below which the traders makes a profit? Exercise 9. [2] A default-free zero-coupon bond costs $91 and will pay $1 at maturity in 1 year. What is the effective annual interest rate? What is the payoff diagram for the bond? What is the profit diagram for the bond? Exercise 1. Put Call Parity [3] You can currently purchase a share of stock for $25, purchase a put option on the stock for $3, and write a call option against the stock for $4. Suppose that holding these three positions guarantees a payoff of $3 one year from today. 1. If the risk free rate (with discrete, annual compounding), is 2%, does put-call parity hold? If not, then what new price of the put option would allow put-call parity to hold? Exercise 11. Arbitrage? [4] For the following cases, determine whether these data define an arbitrage opportunity. If it does involve an arbitrage opportunity, describe the transactions that can be used to exploit it. The price of an ABC call with exercise price 4, expiring at the end of six months, is currently 1.5. ABC stock is at 4, and the annual rate on a risk free security is 6%. 2

3 A September ABC 4 European call is trading at $3 and a September ABC 5 European call is trading at $4. Exercise 12. [2] A Canadian company wants to purchase GBP 6 months from now. The current forward rate is F = 1.6. They enter into a range forward contract, which can simplest be described in terms of the payoffs: Spot rate Contract rate S > 1.61 Purchase GBP at > S > 1.59 Purchase GBP at S 1.59 > S Purchase GBP at 1.59 or as graph illustrating the contract price as a function of the exchange rate contract rate spot 1. Discuss how such a contract can be constructed from more simple building blocks, specifically put and call options. Exercise 13. [2] A call option is at expiration with an exercise price of 15 on a stock trading for 1. What is the value of the option? Impossible to determine without knowing the standard deviation of the stock. 5. I choose not to answer. Exercise 14. A stock is selling for $31. There is a call option on the stock with an exercise price of $27. Which of the below is an appropriate minimum value of the call option today? (a) $ (b) $4 (c) $27 (d) Cannot be determined without knowing the time to expiration. (e) I choose not to answer 3

4 Exercise 15. Options [4] A put is worth $1 and matures in one year. A call on the same stock is worth $15 and matures in one year also. Both options are European. The put and call have the same exercise price of $4. The stock price is $5. The current price of a (risk free) discount bond (zero coupon bond) paying $1 that matures in one year is $.9. How do you make risk free profits given these prices? Exercise 16. Put Upper bound [5] Show that the following is an upper bound for the price of a put option P t (1 + r) (T t) where P t is the current put price, is the exercise price, r is the risk free interest rate and (T t) is the time to maturity of the option. 4

5 Empirical Solutions MØA 155 PROBLEM SET: Options Exercise 1. Arbitrage [2] (a) and (b). Exercise 2. Mutual Fund Manager [2] 1. Salary behaves like a call option. 2. Go for broke (high volatility) Exercise 3. Pricing factors [1] 1, 4 og 5: S, volatility, risk free rate Exercise 4. Product [3] 1. Suppose that S is invested in the product where S is the index level today. The value of the investment in one year is S plus the payoff from a bull spread. The bull spread is created from a long call option with strike price S and a short call option with strike price 1.2S. The payoffs (in terms of returns) from the product can be summarized as 2% Percentage return S 1.2S S T Exercise 5. Put [2] Short put Exercised if S T <. Profit if or p = 4 = 6 Payoff = max(, S T ) Profit = p max(, S T ) p ( S T ) > S T > p 5

6 Profit p = 4 = 6 S T Exercise 6. Straddles and Butterflies [3] Profit Buying a straddle. 1 S T 6

7 Profit Buying a butterfly. 11 S T A straddle is a gamble that the stock price will have a large movement either up or down. A butterfly is a gamble on the price staying close to the exercise price. Exercise 7. Bank [3] 1. Some ways to get a short straddle: Sell a put and a call. Buy the underlying, and sell two call options. Short the underlying, sell two put options. 2. Profit structure Profit Selling a straddle. S T 3. If the price stays around 18,5 you make a profit. However, you risk large losses if the price moves far away from 18,5. 4. The bank. 7

8 Exercise 8. Breakeven [1] +2 call +1 put Cost: = 1. Payoff: 2 max(, S T 3) + max(, 3 S T ). 1. $35 2. $2 Exercise 9. [2] With continous compounding: 91 = e r 1 r = ln(91/1) = 9.43%. With discrete, annual compounding 91 = 1 1+r r = = 9.89%. Payoff 91 Profit 9 Exercise 1. Put Call Parity [3] This can be solved several ways. One is to observe that for put call parity to hold, arbitrage opportunities must not be present. The return on a risk free payoff should equal the risk free rate. Investment is $25 + $3 - $4 = $24, Guaranteed payoff = $3, Guaranteed return = = 25%. Put call parity does not hold, since the annually compounded risk free rate is 2%. Alternatively we can use the put call relation directly. C P = S 1 + r 8

9 Then have to argue that the exercise price equals 3, from the fact that this portfolio is known to equal 3 at maturity: 3 = S T max(, S T ) + max(, S T ) = Put call parity does not hold. Exercise 11. Arbitrage? [4] Both cases involve arbitrage opportunity C P = 4 3 = 1 S 3 = r = 1. The first violates the inequality c max(, S e r(t t) ). To exploit this arbitrage opportunity, can for example use the following strategy. time t time T S 4 S > 4 Buy Call 1.5 S 4 Short stock 4 S S Invest risk free = e = Sum S >.136 > 2. Here there is a mispricing, the option with the higher exercise price should have a lower price. Buy the 5 option, sell the 4 option, receive 4 3 = 1 today, and max(, S 5) max(, S 4) > at option expiry. Exercise 12. [2] The following figure translates this into payoff space. payoff spot From which we realize that it is really a combination of two options: payoff spot Sell 1 put with = 1.59, and buy 1 call with = Exercise 13. [2] 9

10 Th option is not in the money, the value is zero, (a) is correct. Exercise 14. (b) is correct Exercise 15. Options [4] Put call parity is violated. C > S P V (X) S X = = 4 C P = 15 1 = 5 S P V (X) = 5 P V (4) 1 No need to calculate PV(4), since it must be less than or equal 4, but can do it using To make money, buy sheep and sell deer. Exercise 16. Put Upper bound [5] r = = 11.11% S P V (X) = 5 The most you can get at exercise is (if stock price is zero). The value today is less than the present value of this, or 1 p (1 + r) (T t) = 14 Put 1 (1+r)(T t) 1 (1+r)(T t) S T 1

Factors Affecting Option Prices

Factors Affecting Option Prices Factors Affecting Option Prices 1. The current stock price S 0. 2. The option strike price K. 3. The time to expiration T. 4. The volatility of the stock price σ. 5. The risk-free interest rate r. 6. The

More information

Lecture 7: Bounds on Options Prices Steven Skiena. http://www.cs.sunysb.edu/ skiena

Lecture 7: Bounds on Options Prices Steven Skiena. http://www.cs.sunysb.edu/ skiena Lecture 7: Bounds on Options Prices Steven Skiena Department of Computer Science State University of New York Stony Brook, NY 11794 4400 http://www.cs.sunysb.edu/ skiena Option Price Quotes Reading the

More information

Finance 436 Futures and Options Review Notes for Final Exam. Chapter 9

Finance 436 Futures and Options Review Notes for Final Exam. Chapter 9 Finance 436 Futures and Options Review Notes for Final Exam Chapter 9 1. Options: call options vs. put options, American options vs. European options 2. Characteristics: option premium, option type, underlying

More information

Trading Strategies Involving Options. Chapter 11

Trading Strategies Involving Options. Chapter 11 Trading Strategies Involving Options Chapter 11 1 Strategies to be Considered A risk-free bond and an option to create a principal-protected note A stock and an option Two or more options of the same type

More information

Figure S9.1 Profit from long position in Problem 9.9

Figure S9.1 Profit from long position in Problem 9.9 Problem 9.9 Suppose that a European call option to buy a share for $100.00 costs $5.00 and is held until maturity. Under what circumstances will the holder of the option make a profit? Under what circumstances

More information

FIN-40008 FINANCIAL INSTRUMENTS SPRING 2008

FIN-40008 FINANCIAL INSTRUMENTS SPRING 2008 FIN-40008 FINANCIAL INSTRUMENTS SPRING 2008 Options These notes consider the way put and call options and the underlying can be combined to create hedges, spreads and combinations. We will consider the

More information

11 Option. Payoffs and Option Strategies. Answers to Questions and Problems

11 Option. Payoffs and Option Strategies. Answers to Questions and Problems 11 Option Payoffs and Option Strategies Answers to Questions and Problems 1. Consider a call option with an exercise price of $80 and a cost of $5. Graph the profits and losses at expiration for various

More information

Option Properties. Liuren Wu. Zicklin School of Business, Baruch College. Options Markets. (Hull chapter: 9)

Option Properties. Liuren Wu. Zicklin School of Business, Baruch College. Options Markets. (Hull chapter: 9) Option Properties Liuren Wu Zicklin School of Business, Baruch College Options Markets (Hull chapter: 9) Liuren Wu (Baruch) Option Properties Options Markets 1 / 17 Notation c: European call option price.

More information

Option Premium = Intrinsic. Speculative Value. Value

Option Premium = Intrinsic. Speculative Value. Value Chapters 4/ Part Options: Basic Concepts Options Call Options Put Options Selling Options Reading The Wall Street Journal Combinations of Options Valuing Options An Option-Pricing Formula Investment in

More information

Lecture 12. Options Strategies

Lecture 12. Options Strategies Lecture 12. Options Strategies Introduction to Options Strategies Options, Futures, Derivatives 10/15/07 back to start 1 Solutions Problem 6:23: Assume that a bank can borrow or lend money at the same

More information

Underlying (S) The asset, which the option buyer has the right to buy or sell. Notation: S or S t = S(t)

Underlying (S) The asset, which the option buyer has the right to buy or sell. Notation: S or S t = S(t) INTRODUCTION TO OPTIONS Readings: Hull, Chapters 8, 9, and 10 Part I. Options Basics Options Lexicon Options Payoffs (Payoff diagrams) Calls and Puts as two halves of a forward contract: the Put-Call-Forward

More information

K 1 < K 2 = P (K 1 ) P (K 2 ) (6) This holds for both American and European Options.

K 1 < K 2 = P (K 1 ) P (K 2 ) (6) This holds for both American and European Options. Slope and Convexity Restrictions and How to implement Arbitrage Opportunities 1 These notes will show how to implement arbitrage opportunities when either the slope or the convexity restriction is violated.

More information

Use the option quote information shown below to answer the following questions. The underlying stock is currently selling for $83.

Use the option quote information shown below to answer the following questions. The underlying stock is currently selling for $83. Problems on the Basics of Options used in Finance 2. Understanding Option Quotes Use the option quote information shown below to answer the following questions. The underlying stock is currently selling

More information

Chapter 1: Financial Markets and Financial Derivatives

Chapter 1: Financial Markets and Financial Derivatives Chapter 1: Financial Markets and Financial Derivatives 1.1 Financial Markets Financial markets are markets for financial instruments, in which buyers and sellers find each other and create or exchange

More information

Introduction to Options. Derivatives

Introduction to Options. Derivatives Introduction to Options Econ 422: Investment, Capital & Finance University of Washington Summer 2010 August 18, 2010 Derivatives A derivative is a security whose payoff or value depends on (is derived

More information

American Options. An Undergraduate Introduction to Financial Mathematics. J. Robert Buchanan. J. Robert Buchanan American Options

American Options. An Undergraduate Introduction to Financial Mathematics. J. Robert Buchanan. J. Robert Buchanan American Options American Options An Undergraduate Introduction to Financial Mathematics J. Robert Buchanan 2010 Early Exercise Since American style options give the holder the same rights as European style options plus

More information

CHAPTER 20. Financial Options. Chapter Synopsis

CHAPTER 20. Financial Options. Chapter Synopsis CHAPTER 20 Financial Options Chapter Synopsis 20.1 Option Basics A financial option gives its owner the right, but not the obligation, to buy or sell a financial asset at a fixed price on or until a specified

More information

CHAPTER 20: OPTIONS MARKETS: INTRODUCTION

CHAPTER 20: OPTIONS MARKETS: INTRODUCTION CHAPTER 20: OPTIONS MARKETS: INTRODUCTION PROBLEM SETS 1. Options provide numerous opportunities to modify the risk profile of a portfolio. The simplest example of an option strategy that increases risk

More information

Chapter 11 Options. Main Issues. Introduction to Options. Use of Options. Properties of Option Prices. Valuation Models of Options.

Chapter 11 Options. Main Issues. Introduction to Options. Use of Options. Properties of Option Prices. Valuation Models of Options. Chapter 11 Options Road Map Part A Introduction to finance. Part B Valuation of assets, given discount rates. Part C Determination of risk-adjusted discount rate. Part D Introduction to derivatives. Forwards

More information

9 Basics of options, including trading strategies

9 Basics of options, including trading strategies ECG590I Asset Pricing. Lecture 9: Basics of options, including trading strategies 1 9 Basics of options, including trading strategies Option: The option of buying (call) or selling (put) an asset. European

More information

Options Markets: Introduction

Options Markets: Introduction Options Markets: Introduction Chapter 20 Option Contracts call option = contract that gives the holder the right to purchase an asset at a specified price, on or before a certain date put option = contract

More information

Options. Moty Katzman. September 19, 2014

Options. Moty Katzman. September 19, 2014 Options Moty Katzman September 19, 2014 What are options? Options are contracts conferring certain rights regarding the buying or selling of assets. A European call option gives the owner the right to

More information

Lecture 4: Properties of stock options

Lecture 4: Properties of stock options Lecture 4: Properties of stock options Reading: J.C.Hull, Chapter 9 An European call option is an agreement between two parties giving the holder the right to buy a certain asset (e.g. one stock unit)

More information

Chapter 21: Options and Corporate Finance

Chapter 21: Options and Corporate Finance Chapter 21: Options and Corporate Finance 21.1 a. An option is a contract which gives its owner the right to buy or sell an underlying asset at a fixed price on or before a given date. b. Exercise is the

More information

INTRODUCTION TO OPTIONS MARKETS QUESTIONS

INTRODUCTION TO OPTIONS MARKETS QUESTIONS INTRODUCTION TO OPTIONS MARKETS QUESTIONS 1. What is the difference between a put option and a call option? 2. What is the difference between an American option and a European option? 3. Why does an option

More information

CHAPTER 7: PROPERTIES OF STOCK OPTION PRICES

CHAPTER 7: PROPERTIES OF STOCK OPTION PRICES CHAPER 7: PROPERIES OF SOCK OPION PRICES 7.1 Factors Affecting Option Prices able 7.1 Summary of the Effect on the Price of a Stock Option of Increasing One Variable While Keeping All Other Fixed Variable

More information

Lecture 5: Put - Call Parity

Lecture 5: Put - Call Parity Lecture 5: Put - Call Parity Reading: J.C.Hull, Chapter 9 Reminder: basic assumptions 1. There are no arbitrage opportunities, i.e. no party can get a riskless profit. 2. Borrowing and lending are possible

More information

Option Valuation. Chapter 21

Option Valuation. Chapter 21 Option Valuation Chapter 21 Intrinsic and Time Value intrinsic value of in-the-money options = the payoff that could be obtained from the immediate exercise of the option for a call option: stock price

More information

Chapter 2 An Introduction to Forwards and Options

Chapter 2 An Introduction to Forwards and Options Chapter 2 An Introduction to Forwards and Options Question 2.1. The payoff diagram of the stock is just a graph of the stock price as a function of the stock price: In order to obtain the profit diagram

More information

Name Graph Description Payoff Profit Comments. commodity at some point in the future at a prespecified. commodity at some point

Name Graph Description Payoff Profit Comments. commodity at some point in the future at a prespecified. commodity at some point Name Graph Description Payoff Profit Comments Long Commitment to purchase commodity at some point in the future at a prespecified price S T - F S T F No premium Asset price contingency: Always Maximum

More information

Lecture Notes: Basic Concepts in Option Pricing - The Black and Scholes Model

Lecture Notes: Basic Concepts in Option Pricing - The Black and Scholes Model Brunel University Msc., EC5504, Financial Engineering Prof Menelaos Karanasos Lecture Notes: Basic Concepts in Option Pricing - The Black and Scholes Model Recall that the price of an option is equal to

More information

EC372 Bond and Derivatives Markets Topic #5: Options Markets I: fundamentals

EC372 Bond and Derivatives Markets Topic #5: Options Markets I: fundamentals EC372 Bond and Derivatives Markets Topic #5: Options Markets I: fundamentals R. E. Bailey Department of Economics University of Essex Outline Contents 1 Call options and put options 1 2 Payoffs on options

More information

CHAPTER 20 Understanding Options

CHAPTER 20 Understanding Options CHAPTER 20 Understanding Options Answers to Practice Questions 1. a. The put places a floor on value of investment, i.e., less risky than buying stock. The risk reduction comes at the cost of the option

More information

Call and Put. Options. American and European Options. Option Terminology. Payoffs of European Options. Different Types of Options

Call and Put. Options. American and European Options. Option Terminology. Payoffs of European Options. Different Types of Options Call and Put Options A call option gives its holder the right to purchase an asset for a specified price, called the strike price, on or before some specified expiration date. A put option gives its holder

More information

Copyright 2009 by National Stock Exchange of India Ltd. (NSE) Exchange Plaza, Bandra Kurla Complex, Bandra (East), Mumbai 400 051 INDIA

Copyright 2009 by National Stock Exchange of India Ltd. (NSE) Exchange Plaza, Bandra Kurla Complex, Bandra (East), Mumbai 400 051 INDIA Copyright 2009 by National Stock Exchange of India Ltd. (NSE) Exchange Plaza, Bandra Kurla Complex, Bandra (East), Mumbai 400 051 INDIA All content included in this book, such as text, graphics, logos,

More information

Chapter 20 Understanding Options

Chapter 20 Understanding Options Chapter 20 Understanding Options Multiple Choice Questions 1. Firms regularly use the following to reduce risk: (I) Currency options (II) Interest-rate options (III) Commodity options D) I, II, and III

More information

Institutional Finance 08: Dynamic Arbitrage to Replicate Non-linear Payoffs. Binomial Option Pricing: Basics (Chapter 10 of McDonald)

Institutional Finance 08: Dynamic Arbitrage to Replicate Non-linear Payoffs. Binomial Option Pricing: Basics (Chapter 10 of McDonald) Copyright 2003 Pearson Education, Inc. Slide 08-1 Institutional Finance 08: Dynamic Arbitrage to Replicate Non-linear Payoffs Binomial Option Pricing: Basics (Chapter 10 of McDonald) Originally prepared

More information

Introduction to Options

Introduction to Options Introduction to Options By: Peter Findley and Sreesha Vaman Investment Analysis Group What Is An Option? One contract is the right to buy or sell 100 shares The price of the option depends on the price

More information

Lecture 6: Portfolios with Stock Options Steven Skiena. http://www.cs.sunysb.edu/ skiena

Lecture 6: Portfolios with Stock Options Steven Skiena. http://www.cs.sunysb.edu/ skiena Lecture 6: Portfolios with Stock Options Steven Skiena Department of Computer Science State University of New York Stony Brook, NY 11794 4400 http://www.cs.sunysb.edu/ skiena Portfolios with Options The

More information

Options Pricing. This is sometimes referred to as the intrinsic value of the option.

Options Pricing. This is sometimes referred to as the intrinsic value of the option. Options Pricing We will use the example of a call option in discussing the pricing issue. Later, we will turn our attention to the Put-Call Parity Relationship. I. Preliminary Material Recall the payoff

More information

Finance 400 A. Penati - G. Pennacchi. Option Pricing

Finance 400 A. Penati - G. Pennacchi. Option Pricing Finance 400 A. Penati - G. Pennacchi Option Pricing Earlier we derived general pricing relationships for contingent claims in terms of an equilibrium stochastic discount factor or in terms of elementary

More information

CHAPTER 8: TRADING STRATEGES INVOLVING OPTIONS

CHAPTER 8: TRADING STRATEGES INVOLVING OPTIONS CHAPTER 8: TRADING STRATEGES INVOLVING OPTIONS Unless otherwise stated the options we consider are all European. Toward the end of this chapter, we will argue that if European options were available with

More information

Lecture 4: Derivatives

Lecture 4: Derivatives Lecture 4: Derivatives School of Mathematics Introduction to Financial Mathematics, 2015 Lecture 4 1 Financial Derivatives 2 uropean Call and Put Options 3 Payoff Diagrams, Short Selling and Profit Derivatives

More information

Manual for SOA Exam FM/CAS Exam 2.

Manual for SOA Exam FM/CAS Exam 2. Manual for SOA Exam FM/CAS Exam 2. Chapter 7. Derivatives markets. c 2009. Miguel A. Arcones. All rights reserved. Extract from: Arcones Manual for the SOA Exam FM/CAS Exam 2, Financial Mathematics. Fall

More information

t = 1 2 3 1. Calculate the implied interest rates and graph the term structure of interest rates. t = 1 2 3 X t = 100 100 100 t = 1 2 3

t = 1 2 3 1. Calculate the implied interest rates and graph the term structure of interest rates. t = 1 2 3 X t = 100 100 100 t = 1 2 3 MØA 155 PROBLEM SET: Summarizing Exercise 1. Present Value [3] You are given the following prices P t today for receiving risk free payments t periods from now. t = 1 2 3 P t = 0.95 0.9 0.85 1. Calculate

More information

EXERCISES FROM HULL S BOOK

EXERCISES FROM HULL S BOOK EXERCISES FROM HULL S BOOK 1. Three put options on a stock have the same expiration date, and strike prices of $55, $60, and $65. The market price are $3, $5, and $8, respectively. Explain how a butter

More information

Chapter 21 Valuing Options

Chapter 21 Valuing Options Chapter 21 Valuing Options Multiple Choice Questions 1. Relative to the underlying stock, a call option always has: A) A higher beta and a higher standard deviation of return B) A lower beta and a higher

More information

FIN-40008 FINANCIAL INSTRUMENTS SPRING 2008. Options

FIN-40008 FINANCIAL INSTRUMENTS SPRING 2008. Options FIN-40008 FINANCIAL INSTRUMENTS SPRING 2008 Options These notes describe the payoffs to European and American put and call options the so-called plain vanilla options. We consider the payoffs to these

More information

Overview. Option Basics. Options and Derivatives. Professor Lasse H. Pedersen. Option basics and option strategies

Overview. Option Basics. Options and Derivatives. Professor Lasse H. Pedersen. Option basics and option strategies Options and Derivatives Professor Lasse H. Pedersen Prof. Lasse H. Pedersen 1 Overview Option basics and option strategies No-arbitrage bounds on option prices Binomial option pricing Black-Scholes-Merton

More information

CHAPTER 22 Options and Corporate Finance

CHAPTER 22 Options and Corporate Finance CHAPTER 22 Options and Corporate Finance Multiple Choice Questions: I. DEFINITIONS OPTIONS a 1. A financial contract that gives its owner the right, but not the obligation, to buy or sell a specified asset

More information

CHAPTER 20: OPTIONS MARKETS: INTRODUCTION

CHAPTER 20: OPTIONS MARKETS: INTRODUCTION CHAPTER 20: OPTIONS MARKETS: INTRODUCTION 1. Cost Profit Call option, X = 95 12.20 10 2.20 Put option, X = 95 1.65 0 1.65 Call option, X = 105 4.70 0 4.70 Put option, X = 105 4.40 0 4.40 Call option, X

More information

University of Texas at Austin. HW Assignment 7. Butterfly spreads. Convexity. Collars. Ratio spreads.

University of Texas at Austin. HW Assignment 7. Butterfly spreads. Convexity. Collars. Ratio spreads. HW: 7 Course: M339D/M389D - Intro to Financial Math Page: 1 of 5 University of Texas at Austin HW Assignment 7 Butterfly spreads. Convexity. Collars. Ratio spreads. 7.1. Butterfly spreads and convexity.

More information

Note: There are fewer problems in the actual Final Exam!

Note: There are fewer problems in the actual Final Exam! HEC Paris Practice Final Exam Questions Version with Solutions Financial Markets Fall 2013 Note: There are fewer problems in the actual Final Exam! Problem 1. Are the following statements True, False or

More information

SOCIETY OF ACTUARIES FINANCIAL MATHEMATICS. EXAM FM SAMPLE QUESTIONS Financial Economics

SOCIETY OF ACTUARIES FINANCIAL MATHEMATICS. EXAM FM SAMPLE QUESTIONS Financial Economics SOCIETY OF ACTUARIES EXAM FM FINANCIAL MATHEMATICS EXAM FM SAMPLE QUESTIONS Financial Economics June 2014 changes Questions 1-30 are from the prior version of this document. They have been edited to conform

More information

Caput Derivatives: October 30, 2003

Caput Derivatives: October 30, 2003 Caput Derivatives: October 30, 2003 Exam + Answers Total time: 2 hours and 30 minutes. Note 1: You are allowed to use books, course notes, and a calculator. Question 1. [20 points] Consider an investor

More information

Derivatives: Options

Derivatives: Options Derivatives: Options Call Option: The right, but not the obligation, to buy an asset at a specified exercise (or, strike) price on or before a specified date. Put Option: The right, but not the obligation,

More information

Chapter 8 Financial Options and Applications in Corporate Finance ANSWERS TO END-OF-CHAPTER QUESTIONS

Chapter 8 Financial Options and Applications in Corporate Finance ANSWERS TO END-OF-CHAPTER QUESTIONS Chapter 8 Financial Options and Applications in Corporate Finance ANSWERS TO END-OF-CHAPTER QUESTIONS 8-1 a. An option is a contract which gives its holder the right to buy or sell an asset at some predetermined

More information

Lecture 3: Put Options and Distribution-Free Results

Lecture 3: Put Options and Distribution-Free Results OPTIONS and FUTURES Lecture 3: Put Options and Distribution-Free Results Philip H. Dybvig Washington University in Saint Louis put options binomial valuation what are distribution-free results? option

More information

CHAPTER 22: FUTURES MARKETS

CHAPTER 22: FUTURES MARKETS CHAPTER 22: FUTURES MARKETS PROBLEM SETS 1. There is little hedging or speculative demand for cement futures, since cement prices are fairly stable and predictable. The trading activity necessary to support

More information

Fundamentals of Futures and Options (a summary)

Fundamentals of Futures and Options (a summary) Fundamentals of Futures and Options (a summary) Roger G. Clarke, Harindra de Silva, CFA, and Steven Thorley, CFA Published 2013 by the Research Foundation of CFA Institute Summary prepared by Roger G.

More information

Part V: Option Pricing Basics

Part V: Option Pricing Basics erivatives & Risk Management First Week: Part A: Option Fundamentals payoffs market microstructure Next 2 Weeks: Part B: Option Pricing fundamentals: intrinsic vs. time value, put-call parity introduction

More information

Options: Valuation and (No) Arbitrage

Options: Valuation and (No) Arbitrage Prof. Alex Shapiro Lecture Notes 15 Options: Valuation and (No) Arbitrage I. Readings and Suggested Practice Problems II. Introduction: Objectives and Notation III. No Arbitrage Pricing Bound IV. The Binomial

More information

Session IX: Lecturer: Dr. Jose Olmo. Module: Economics of Financial Markets. MSc. Financial Economics

Session IX: Lecturer: Dr. Jose Olmo. Module: Economics of Financial Markets. MSc. Financial Economics Session IX: Stock Options: Properties, Mechanics and Valuation Lecturer: Dr. Jose Olmo Module: Economics of Financial Markets MSc. Financial Economics Department of Economics, City University, London Stock

More information

Mid-Term Spring 2003

Mid-Term Spring 2003 Mid-Term Spring 2003 1. (1 point) You want to purchase XYZ stock at $60 from your broker using as little of your own money as possible. If initial margin is 50% and you have $3000 to invest, how many shares

More information

Options: Definitions, Payoffs, & Replications

Options: Definitions, Payoffs, & Replications Options: Definitions, s, & Replications Liuren Wu Zicklin School of Business, Baruch College Options Markets Liuren Wu (Baruch) s Options Markets 1 / 34 Definitions and terminologies An option gives the

More information

ECMC49F Options Practice Questions Suggested Solution Date: Nov 14, 2005

ECMC49F Options Practice Questions Suggested Solution Date: Nov 14, 2005 ECMC49F Options Practice Questions Suggested Solution Date: Nov 14, 2005 Options: General [1] Define the following terms associated with options: a. Option An option is a contract which gives the holder

More information

Options/1. Prof. Ian Giddy

Options/1. Prof. Ian Giddy Options/1 New York University Stern School of Business Options Prof. Ian Giddy New York University Options Puts and Calls Put-Call Parity Combinations and Trading Strategies Valuation Hedging Options2

More information

Option pricing. Vinod Kothari

Option pricing. Vinod Kothari Option pricing Vinod Kothari Notation we use this Chapter will be as follows: S o : Price of the share at time 0 S T : Price of the share at time T T : time to maturity of the option r : risk free rate

More information

Introduction, Forwards and Futures

Introduction, Forwards and Futures Introduction, Forwards and Futures Liuren Wu Zicklin School of Business, Baruch College Fall, 2007 (Hull chapters: 1,2,3,5) Liuren Wu Introduction, Forwards & Futures Option Pricing, Fall, 2007 1 / 35

More information

TPPE17 Corporate Finance 1(5) SOLUTIONS RE-EXAMS 2014 II + III

TPPE17 Corporate Finance 1(5) SOLUTIONS RE-EXAMS 2014 II + III TPPE17 Corporate Finance 1(5) SOLUTIONS RE-EXAMS 2014 II III Instructions 1. Only one problem should be treated on each sheet of paper and only one side of the sheet should be used. 2. The solutions folder

More information

n(n + 1) 2 1 + 2 + + n = 1 r (iii) infinite geometric series: if r < 1 then 1 + 2r + 3r 2 1 e x = 1 + x + x2 3! + for x < 1 ln(1 + x) = x x2 2 + x3 3

n(n + 1) 2 1 + 2 + + n = 1 r (iii) infinite geometric series: if r < 1 then 1 + 2r + 3r 2 1 e x = 1 + x + x2 3! + for x < 1 ln(1 + x) = x x2 2 + x3 3 ACTS 4308 FORMULA SUMMARY Section 1: Calculus review and effective rates of interest and discount 1 Some useful finite and infinite series: (i) sum of the first n positive integers: (ii) finite geometric

More information

CHAPTER 21: OPTION VALUATION

CHAPTER 21: OPTION VALUATION CHAPTER 21: OPTION VALUATION 1. Put values also must increase as the volatility of the underlying stock increases. We see this from the parity relation as follows: P = C + PV(X) S 0 + PV(Dividends). Given

More information

A) 1.8% B) 1.9% C) 2.0% D) 2.1% E) 2.2%

A) 1.8% B) 1.9% C) 2.0% D) 2.1% E) 2.2% 1 Exam FM Questions Practice Exam 1 1. Consider the following yield curve: Year Spot Rate 1 5.5% 2 5.0% 3 5.0% 4 4.5% 5 4.0% Find the four year forward rate. A) 1.8% B) 1.9% C) 2.0% D) 2.1% E) 2.2% 2.

More information

2 Stock Price. Figure S1.1 Profit from long position in Problem 1.13

2 Stock Price. Figure S1.1 Profit from long position in Problem 1.13 Problem 1.11. A cattle farmer expects to have 12, pounds of live cattle to sell in three months. The livecattle futures contract on the Chicago Mercantile Exchange is for the delivery of 4, pounds of cattle.

More information

Futures Price d,f $ 0.65 = (1.05) (1.04)

Futures Price d,f $ 0.65 = (1.05) (1.04) 24 e. Currency Futures In a currency futures contract, you enter into a contract to buy a foreign currency at a price fixed today. To see how spot and futures currency prices are related, note that holding

More information

Option Values. Determinants of Call Option Values. CHAPTER 16 Option Valuation. Figure 16.1 Call Option Value Before Expiration

Option Values. Determinants of Call Option Values. CHAPTER 16 Option Valuation. Figure 16.1 Call Option Value Before Expiration CHAPTER 16 Option Valuation 16.1 OPTION VALUATION: INTRODUCTION Option Values Intrinsic value - profit that could be made if the option was immediately exercised Call: stock price - exercise price Put:

More information

Derivative Users Traders of derivatives can be categorized as hedgers, speculators, or arbitrageurs.

Derivative Users Traders of derivatives can be categorized as hedgers, speculators, or arbitrageurs. OPTIONS THEORY Introduction The Financial Manager must be knowledgeable about derivatives in order to manage the price risk inherent in financial transactions. Price risk refers to the possibility of loss

More information

2. Exercising the option - buying or selling asset by using option. 3. Strike (or exercise) price - price at which asset may be bought or sold

2. Exercising the option - buying or selling asset by using option. 3. Strike (or exercise) price - price at which asset may be bought or sold Chapter 21 : Options-1 CHAPTER 21. OPTIONS Contents I. INTRODUCTION BASIC TERMS II. VALUATION OF OPTIONS A. Minimum Values of Options B. Maximum Values of Options C. Determinants of Call Value D. Black-Scholes

More information

CHAPTER 11 INTRODUCTION TO SECURITY VALUATION TRUE/FALSE QUESTIONS

CHAPTER 11 INTRODUCTION TO SECURITY VALUATION TRUE/FALSE QUESTIONS 1 CHAPTER 11 INTRODUCTION TO SECURITY VALUATION TRUE/FALSE QUESTIONS (f) 1 The three step valuation process consists of 1) analysis of alternative economies and markets, 2) analysis of alternative industries

More information

Solutions to Lectures on Corporate Finance, Second Edition. Peter Bossaerts and Bernt Arne Ødegaard

Solutions to Lectures on Corporate Finance, Second Edition. Peter Bossaerts and Bernt Arne Ødegaard Solutions to Lectures on Corporate Finance, Second Edition Peter Bossaerts and Bernt Arne Ødegaard 2006 Contents 1 Finance 1 2 Axioms of modern corporate finance 2 3 On Value Additivity 3 4 On the Efficient

More information

Options, Derivatives, Risk Management

Options, Derivatives, Risk Management 1/1 Options, Derivatives, Risk Management (Welch, Chapter 27) Ivo Welch UCLA Anderson School, Corporate Finance, Winter 2014 January 13, 2015 Did you bring your calculator? Did you read these notes and

More information

6. Foreign Currency Options

6. Foreign Currency Options 6. Foreign Currency Options So far, we have studied contracts whose payoffs are contingent on the spot rate (foreign currency forward and foreign currency futures). he payoffs from these instruments are

More information

Hedging. An Undergraduate Introduction to Financial Mathematics. J. Robert Buchanan. J. Robert Buchanan Hedging

Hedging. An Undergraduate Introduction to Financial Mathematics. J. Robert Buchanan. J. Robert Buchanan Hedging Hedging An Undergraduate Introduction to Financial Mathematics J. Robert Buchanan 2010 Introduction Definition Hedging is the practice of making a portfolio of investments less sensitive to changes in

More information

Example 1. Consider the following two portfolios: 2. Buy one c(s(t), 20, τ, r) and sell one c(s(t), 10, τ, r).

Example 1. Consider the following two portfolios: 2. Buy one c(s(t), 20, τ, r) and sell one c(s(t), 10, τ, r). Chapter 4 Put-Call Parity 1 Bull and Bear Financial analysts use words such as bull and bear to describe the trend in stock markets. Generally speaking, a bull market is characterized by rising prices.

More information

Chapter 6 APPENDIX B. The Yield Curve and the Law of One Price. Valuing a Coupon Bond with Zero-Coupon Prices

Chapter 6 APPENDIX B. The Yield Curve and the Law of One Price. Valuing a Coupon Bond with Zero-Coupon Prices 196 Part Interest Rates and Valuing Cash Flows Chapter 6 APPENDIX B The Yield Curve and the Law of One Price Thus far, we have focused on the relationship between the price of an individual bond and its

More information

Options Trading Strategies

Options Trading Strategies Options Trading Strategies Liuren Wu Zicklin School of Business, Baruch College Options Markets (Hull chapter: ) Liuren Wu (Baruch) Options Trading Strategies Options Markets 1 / 18 Objectives A strategy

More information

Chapter 1 - Introduction

Chapter 1 - Introduction Chapter 1 - Introduction Derivative securities Futures contracts Forward contracts Futures and forward markets Comparison of futures and forward contracts Options contracts Options markets Comparison of

More information

Practice Questions for Midterm II

Practice Questions for Midterm II Finance 333 Investments Practice Questions for Midterm II Winter 2004 Professor Yan 1. The market portfolio has a beta of a. 0. *b. 1. c. -1. d. 0.5. By definition, the beta of the market portfolio is

More information

CHAPTER 8 SUGGESTED ANSWERS TO CHAPTER 8 QUESTIONS

CHAPTER 8 SUGGESTED ANSWERS TO CHAPTER 8 QUESTIONS INSTRUCTOR S MANUAL: MULTINATIONAL FINANCIAL MANAGEMENT, 9 TH ED. CHAPTER 8 SUGGESTED ANSWERS TO CHAPTER 8 QUESTIONS. On April, the spot price of the British pound was $.86 and the price of the June futures

More information

Fin 3710 Investment Analysis Professor Rui Yao CHAPTER 14: OPTIONS MARKETS

Fin 3710 Investment Analysis Professor Rui Yao CHAPTER 14: OPTIONS MARKETS HW 6 Fin 3710 Investment Analysis Professor Rui Yao CHAPTER 14: OPTIONS MARKETS 4. Cost Payoff Profit Call option, X = 85 3.82 5.00 +1.18 Put option, X = 85 0.15 0.00-0.15 Call option, X = 90 0.40 0.00-0.40

More information

FINANCIAL ENGINEERING CLUB TRADING 101

FINANCIAL ENGINEERING CLUB TRADING 101 FINANCIAL ENGINEERING CLUB TRADING 101 WHAT IS TRADING TRADING/INVESTING is the act of putting capital to use, by either buying or selling securities, for the purpose of gaining profits. Buy low, sell

More information

Option Payoffs. Problems 11 through 16: Describe (as I have in 1-10) the strategy depicted by each payoff diagram. #11 #12 #13 #14 #15 #16

Option Payoffs. Problems 11 through 16: Describe (as I have in 1-10) the strategy depicted by each payoff diagram. #11 #12 #13 #14 #15 #16 Option s Problems 1 through 1: Assume that the stock is currently trading at $2 per share and options and bonds have the prices given in the table below. Depending on the strike price (X) of the option

More information

Hedging Strategies Using

Hedging Strategies Using Chapter 4 Hedging Strategies Using Futures and Options 4.1 Basic Strategies Using Futures While the use of short and long hedges can reduce (or eliminate in some cases - as below) both downside and upside

More information

FINANCIAL ECONOMICS OPTION PRICING

FINANCIAL ECONOMICS OPTION PRICING OPTION PRICING Options are contingency contracts that specify payoffs if stock prices reach specified levels. A call option is the right to buy a stock at a specified price, X, called the strike price.

More information

The Intuition Behind Option Valuation: A Teaching Note

The Intuition Behind Option Valuation: A Teaching Note The Intuition Behind Option Valuation: A Teaching Note Thomas Grossman Haskayne School of Business University of Calgary Steve Powell Tuck School of Business Dartmouth College Kent L Womack Tuck School

More information

Answers to Concepts in Review

Answers to Concepts in Review Answers to Concepts in Review 1. Puts and calls are negotiable options issued in bearer form that allow the holder to sell (put) or buy (call) a stipulated amount of a specific security/financial asset,

More information

Determination of Forward and Futures Prices. Chapter 5

Determination of Forward and Futures Prices. Chapter 5 Determination of Forward and Futures Prices Chapter 5 Fundamentals of Futures and Options Markets, 8th Ed, Ch 5, Copyright John C. Hull 2013 1 Consumption vs Investment Assets Investment assets are assets

More information

Investment Finance 421-002 Prototype Midterm I

Investment Finance 421-002 Prototype Midterm I Investment Finance 421-002 Prototype Midterm I The correct answer is highlighted by a *. Also, a concise reasoning is provided in Italics. 1. are an indirect way U. S. investor can invest in foreign companies.

More information

Name: 1 (5) a b c d e TRUE/FALSE 1 (2) TRUE FALSE. 2 (5) a b c d e. 3 (5) a b c d e 2 (2) TRUE FALSE. 4 (5) a b c d e.

Name: 1 (5) a b c d e TRUE/FALSE 1 (2) TRUE FALSE. 2 (5) a b c d e. 3 (5) a b c d e 2 (2) TRUE FALSE. 4 (5) a b c d e. Name: Thursday, February 28 th M375T=M396C Introduction to Actuarial Financial Mathematics Spring 2013, The University of Texas at Austin In-Term Exam I Instructor: Milica Čudina Notes: This is a closed

More information

University of Texas at Austin. HW Assignment 4

University of Texas at Austin. HW Assignment 4 HW: 4 Course: M339D/M389D - Intro to Financial Math Page: 1 of 6 University of Texas at Austin HW Assignment 4 Arbitrage. Put options. Parallels between put options and homeowner s insurance. Digital options.

More information