Part A: The put call parity relation is: call + present value of exercise price = put + stock price.


 Debra Merritt
 5 years ago
 Views:
Transcription
1 Corporate Finance Mod 20: Options, put call parity relation, Practice Problem s ** Exercise 20.1: Put Call Parity Relation! One year European put and call options trade on a stock with strike prices of $85.! The riskfree rate is 11.9% per annum.! The value of the put option is $1 more than the value of the call option. A. Using the put call parity relation, what is the value of the put option minus the value of the call option? B. W hat is the stock price in this exercise? Part A: The put call parity relation is: call + present value of exercise price = put + stock price. This gives: put call = present value of exercise price stock price Part B: Rewriting the expression above gives stock price = present value of exercise price (put call) The put value the call value = $1, so the stock price = $85 / = $74.96 $75.
2 ** Exercise 20.2: Stock Price On January 1, at 10:00 am, the stock price is $68. Three month European call and put options on ABC stock sell at an exercise price of $65. (The exercise price is the strike price.)! At 10:00 am, the call option is worth $10 and the put option is worth $2.! At 11:00 am, the call option is worth $8 and the put option is worth $4. Assume that the riskfree interest rate does not change between 10:00 am and 11:00 am. A. Express the present value of the exercise price as a function of the call value, put value, and stock price. B. Express the stock price as a function of the call value, put value, and exercise price. C. W hat is the stock price at 11:00 am? Part A: The put call parity relation is: call + present value of exercise price = put + stock price, so present value of exercise price = stock price + put call Part B: The put call parity relation is: call + present value of exercise price = put + stock price, so stock price = present value of exercise price + call put Part C: The present value of the exercise price does not change in one hour if the riskfree rate does not change, so the change in call put is the change in the stock price. The change in call put is $4, so the new stock price is $68 $4 = $64.
3 ** Question 20.3: Put Call Parity Relation A stock trades for $80, and the riskfree interest rate is 15%. A European call option that expires in six months and has a strike price of $90 is valued at $12. W hat is the value to the nearest dollar of a European put option that expires in six months and has a strike price of $90? A. $8 B. $10 C. $12 D. $14 E. $16 Answer 20.3: E Solution 20.3: W e use the put call parity relation: c + PV(X) = p + S: put + $80 = $12 + $ ½ ½ or put = $ $68 = $15.93 Jacob: Can you explain the put call parity relation intuitively? Rachel: Suppose an investor buys and a put option with a strike price of $90, and sells a call option with a strike price of $90. At the expiration date, the stock price is either above or below $90. ~ If the stock price is above $90, the person who bought the call option exercises it, and the investor gets $90 but must give up the stock. ~ If the stock price is below $90, the investor exercises the put option and gives up the stock for $90. Either way, the investor has $90 and no stock. This means that the investor s portfolio is now worth the present value of $90, or stock + put call = present value ($90). The $90 is the strike price. Substituting X for the $90 gives the put call parity relation.
4 ** Question 20.4: Strike Price One year European call and put options are trading on the ABC stock at the values shown below. Strike Price $110 $115 call $10.00 $7.50 put $10.00 Z The riskfree interest rate is 11% per annum. Find Z. A. $12.00 B. $12.25 C. $12.50 D. $12.75 E. $13.00 Answer 20.4: A Let the stock price be S. By the put call parity relation: call + present value of exercise price = put + stock price, so 1 put minus 1 call = the present value of the exercise price the stock price. For an exercise price (strike price) of $110, put call = $0 = $110 / 1.11 S S = $110 / 1.11 = $ For an exercise price (strike price) of $115, put call = put $7.50 = $115 / 1.11 $99.10 put = $115 / 1.11 $ $7.50 = $ W e can simplify the solution as follows:! The change in the exercise price is +$5.00.! The change in the present value of the exercise price is $5.00 / 1.11 = $4.50.! The change in the value of 1 put minus 1 call is $4.50.! The call value decreases by $2.50, so the put value increases by $2 to $ The following explanation is another perspective: The difference between the call and put prices at the two exercise prices is the difference in the present value of the exercise prices. This is the present value of ($115 $110) = $5, for one year at an 11% discount rate: $5 / 1.11 = $4.50. The change in(put call) between the two exercise prices is $4.50 and the change in the call option price is $2.50, so the change in the put option price is $4.50 $2.50 = $2. The put option price with a $115 exercise price is $ $2 = $12.00.
5
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 informationTwoState Model of Option Pricing
Rendleman and Bartter [1] put forward a simple twostate model of option pricing. As in the BlackScholes model, to buy the stock and to sell the call in the hedge ratio obtains a riskfree portfolio.
More informationdebt_wbn_pv_st01 Title page Debt» What's Behind the Numbers?» Scenic Video www.navigatingaccounting.com
Title page Debt» What's Behind the Numbers?» Scenic Video www.navigatingaccounting.com Agenda Introduction Single cash flow Future value formula Present value formula Tables Multiple cash flows Present
More informationFin 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 0.000.15 Call option, X = 90 0.40 0.000.40
More informationLecture 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 informationFactors 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 riskfree interest rate r. 6. The
More informationOne Period Binomial Model
FIN40008 FINANCIAL INSTRUMENTS SPRING 2008 One Period Binomial Model These notes consider the one period binomial model to exactly price an option. We will consider three different methods of pricing
More informationTrading Strategies Involving Options. Chapter 11
Trading Strategies Involving Options Chapter 11 1 Strategies to be Considered A riskfree bond and an option to create a principalprotected note A stock and an option Two or more options of the same type
More informationTwoState Option Pricing
Rendleman and Bartter [1] present a simple twostate model of option pricing. The states of the world evolve like the branches of a tree. Given the current state, there are two possible states next period.
More informationPRACTICE EXAM QUESTIONS ON OPTIONS
PRACTICE EXAM QUESTIONS ON OPTIONS 1. An American put option allows the holder to: A) buy the underlying asset at the strike price on or before the expiration date. B) sell the underlying asset at the
More informationOptions 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 PutCall Parity Relationship. I. Preliminary Material Recall the payoff
More informationFigure 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 informationCHAPTER 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 informationOption 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 OptionPricing Formula Investment in
More informationDerivatives: 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 informationCHAPTER 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 informationOn BlackScholes Equation, Black Scholes Formula and Binary Option Price
On BlackScholes Equation, Black Scholes Formula and Binary Option Price Abstract: Chi Gao 12/15/2013 I. BlackScholes Equation is derived using two methods: (1) riskneutral measure; (2)  hedge. II.
More informationCall Price as a Function of the Stock Price
Call Price as a Function of the Stock Price Intuitively, the call price should be an increasing function of the stock price. This relationship allows one to develop a theory of option pricing, derived
More informationLecture 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 informationOptions (1) Class 19 Financial Management, 15.414
Options (1) Class 19 Financial Management, 15.414 Today Options Risk management: Why, how, and what? Option payoffs Reading Brealey and Myers, Chapter 2, 21 Sally Jameson 2 Types of questions Your company,
More information2. 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 : Options1 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. BlackScholes
More information2. How is a fund manager motivated to behave with this type of renumeration package?
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
More informationOptions. 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 informationFUNDING INVESTMENTS FINANCE 238/738, Spring 2008, Prof. Musto Class 6 Introduction to Corporate Bonds
FUNDING INVESTMENTS FINANCE 238/738, Spring 2008, Prof. Musto Class 6 Introduction to Corporate Bonds Today: I. Equity is a call on firm value II. Senior Debt III. Junior Debt IV. Convertible Debt V. Variance
More informationOptions 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 informationDetermination 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 informationLecture 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 informationOption Valuation. Chapter 21
Option Valuation Chapter 21 Intrinsic and Time Value intrinsic value of inthemoney options = the payoff that could be obtained from the immediate exercise of the option for a call option: stock price
More information1 The BlackScholes Formula
1 The BlackScholes Formula In 1973 Fischer Black and Myron Scholes published a formula  the BlackScholes formula  for computing the theoretical price of a European call option on a stock. Their paper,
More informationa. What is the portfolio of the stock and the bond that replicates the option?
Practice problems for Lecture 2. Answers. 1. A Simple Option Pricing Problem in One Period Riskless bond (interest rate is 5%): 1 15 Stock: 5 125 5 Derivative security (call option with a strike of 8):?
More informationInvestments, Chapter 4
Investments, Chapter 4 Answers to Selected Problems 2. An openend fund has a net asset value of $10.70 per share. It is sold with a frontend load of 6 percent. What is the offering price? Answer: When
More informationTest 4 Created: 3:05:28 PM CDT 1. The buyer of a call option has the choice to exercise, but the writer of the call option has: A.
Test 4 Created: 3:05:28 PM CDT 1. The buyer of a call option has the choice to exercise, but the writer of the call option has: A. The choice to offset with a put option B. The obligation to deliver the
More informationChapter 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 informationGAMMA.0279 THETA 8.9173 VEGA 9.9144 RHO 3.5985
14 Option Sensitivities and Option Hedging Answers to Questions and Problems 1. Consider Call A, with: X $70; r 0.06; T t 90 days; 0.4; and S $60. Compute the price, DELTA, GAMMA, THETA, VEGA, and RHO
More informationFIN40008 FINANCIAL INSTRUMENTS SPRING 2008
FIN40008 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 informationConvenient Conventions
C: call value. P : put value. X: strike price. S: stock price. D: dividend. Convenient Conventions c 2015 Prof. YuhDauh Lyuu, National Taiwan University Page 168 Payoff, Mathematically Speaking The payoff
More informationCHAPTER 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 informationECMC49F 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 informationCHAPTER 21: OPTION VALUATION
CHAPTER 21: OPTION VALUATION PROBLEM SETS 1. The value of a put option also increases with the volatility of the stock. We see this from the putcall parity theorem as follows: P = C S + PV(X) + PV(Dividends)
More informationIntroduction to Binomial Trees
11 C H A P T E R Introduction to Binomial Trees A useful and very popular technique for pricing an option involves constructing a binomial tree. This is a diagram that represents di erent possible paths
More informationExample 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 PutCall 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 informationCall 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 information10 Binomial Trees. 10.1 Onestep model. 1. Model structure. ECG590I Asset Pricing. Lecture 10: Binomial Trees 1
ECG590I Asset Pricing. Lecture 10: Binomial Trees 1 10 Binomial Trees 10.1 Onestep model 1. Model structure ECG590I Asset Pricing. Lecture 10: Binomial Trees 2 There is only one time interval (t 0, t
More informationCHAPTER 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 informationCaput 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 informationHigher National Diploma in Business Administration Second Year, First Semester Examination 2014 BA 2113  Business Finance
[All Rights Reserved] SLIATE SRI LANKA INSTITUTE OF ADVANCED TECHNOLOGICAL EDUCATION (Established in the Ministry of Higher Education, vide in Act No. 29 of 1995) Higher National Diploma in Business Administration
More informationUse 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 informationFIN 3710. Final (Practice) Exam 05/23/06
FIN 3710 Investment Analysis Spring 2006 Zicklin School of Business Baruch College Professor Rui Yao FIN 3710 Final (Practice) Exam 05/23/06 NAME: (Please print your name here) PLEDGE: (Sign your name
More informationSession X: Lecturer: Dr. Jose Olmo. Module: Economics of Financial Markets. MSc. Financial Economics. Department of Economics, City University, London
Session X: Options: Hedging, Insurance and Trading Strategies Lecturer: Dr. Jose Olmo Module: Economics of Financial Markets MSc. Financial Economics Department of Economics, City University, London Option
More information1 Further Pricing Relationships on Options
1 Further Pricing Relationships on Options 1.1 The Put Option with a Higher Strike must be more expensive Consider two put options on the same stock with the same expiration date. Put option #1 has a strike
More informationForward exchange rates
Forward exchange rates The forex market consists of two distinct markets  the spot foreign exchange market (in which currencies are bought and sold for delivery within two working days) and the forward
More informationFinance 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 informationChapter 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 riskadjusted discount rate. Part D Introduction to derivatives. Forwards
More information9 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 informationSAMPLE FACT EXAM (You must score 70% to successfully clear FACT)
SAMPLE FACT EXAM (You must score 70% to successfully clear FACT) 1. What is the present value (PV) of $100,000 received five years from now, assuming the interest rate is 8% per year? a. $600,000.00 b.
More informationInstitutional Finance 08: Dynamic Arbitrage to Replicate Nonlinear Payoffs. Binomial Option Pricing: Basics (Chapter 10 of McDonald)
Copyright 2003 Pearson Education, Inc. Slide 081 Institutional Finance 08: Dynamic Arbitrage to Replicate Nonlinear Payoffs Binomial Option Pricing: Basics (Chapter 10 of McDonald) Originally prepared
More informationChapter 20 Understanding Options
Chapter 20 Understanding Options Multiple Choice Questions 1. Firms regularly use the following to reduce risk: (I) Currency options (II) Interestrate options (III) Commodity options D) I, II, and III
More informationAmerican 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 informationChapter 8 Financial Options and Applications in Corporate Finance ANSWERS TO ENDOFCHAPTER QUESTIONS
Chapter 8 Financial Options and Applications in Corporate Finance ANSWERS TO ENDOFCHAPTER QUESTIONS 81 a. An option is a contract which gives its holder the right to buy or sell an asset at some predetermined
More informationIntroduction 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 informationFinal Exam Practice Set and Solutions
FIN469 Investments Analysis Professor Michel A. Robe Final Exam Practice Set and Solutions What to do with this practice set? To help students prepare for the final exam, three practice sets with solutions
More informationK 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 informationHedging. 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 informationLecture 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 informationOption 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 informationCHAPTER 23: FUTURES, SWAPS, AND RISK MANAGEMENT
CHAPTER 23: FUTURES, SWAPS, AND RISK MANAGEMENT PROBLEM SETS 1. In formulating a hedge position, a stock s beta and a bond s duration are used similarly to determine the expected percentage gain or loss
More informationChapter 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 informationLecture 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 informationOPTIONS PRICING EXERCISE
William L. Silber Foundations of Finance (B01.2311) OPTIONS PRICING EXERCISE Minnesota Mining and Manufacturing (3M) is awarding a yearend bonus to its Senior VicePresident of Marketing in the form of
More informationOption Values. Option Valuation. Call Option Value before Expiration. Determinants of Call Option Values
Option Values Option Valuation Intrinsic value profit that could be made if the option was immediately exercised Call: stock price exercise price : S T X i i k i X S Put: exercise price stock price : X
More informationInvestments 320 Dr. Ahmed Y. Dashti Chapter 3 Interactive Qustions
Investments 320 Dr. Ahmed Y. Dashti Chapter 3 Interactive Qustions 31. A primary asset is an initial offering sold by a business, or government, to raise funds. A) True B) False 32. Money market instruments
More informationSolving systems by elimination
December 1, 2008 Solving systems by elimination page 1 Solving systems by elimination Here is another method for solving a system of two equations. Sometimes this method is easier than either the graphing
More informationInvestors G u i d e 201 0 1 Investors Guide 2011
2011 Investors 2011 Guide 1. 2. 3. 01 Investors Guide 2011 1 2 5 3 4 6 Investors Guide 2011 02 03 Investors Guide 2011 1 2 3 4 5 Investors Guide 2011 04 1 2 2 2 05 Investors Guide 2011 3 3 3 4 5 5 5 Investors
More informationUnderstanding Options: Calls and Puts
2 Understanding Options: Calls and Puts Important: in their simplest forms, options trades sound like, and are, very high risk investments. If reading about options makes you think they are too risky for
More informationEXP 481  Capital Markets Option Pricing. Options: Definitions. Arbitrage Restrictions on Call Prices. Arbitrage Restrictions on Call Prices 1) C > 0
EXP 481  Capital Markets Option Pricing imple arbitrage relations Payoffs to call options Blackcholes model PutCall Parity Implied Volatility Options: Definitions A call option gives the buyer the
More informationAdvanced Futures Strategies
Advanced Futures Strategies 1. Suppose IBC stock is selling at $80 per share. Also, the Tbill rate with 180 days to maturity is 5%. Construct a synthetic futures contract with maturity in 180 days and
More informationChapter 9. The Valuation of Common Stock. 1.The Expected Return (Copied from Unit02, slide 36)
Readings Chapters 9 and 10 Chapter 9. The Valuation of Common Stock 1. The investor s expected return 2. Valuation as the Present Value (PV) of dividends and the growth of dividends 3. The investor s required
More informationBinomial lattice model for stock prices
Copyright c 2007 by Karl Sigman Binomial lattice model for stock prices Here we model the price of a stock in discrete time by a Markov chain of the recursive form S n+ S n Y n+, n 0, where the {Y i }
More informationThe Term Structure of Interest Rates, Spot Rates, and Yield to Maturity
Chapter 5 How to Value Bonds and Stocks 5A1 Appendix 5A The Term Structure of Interest Rates, Spot Rates, and Yield to Maturity In the main body of this chapter, we have assumed that the interest rate
More informationOption Basics. c 2012 Prof. YuhDauh Lyuu, National Taiwan University Page 153
Option Basics c 2012 Prof. YuhDauh Lyuu, National Taiwan University Page 153 The shift toward options as the center of gravity of finance [... ] Merton H. Miller (1923 2000) c 2012 Prof. YuhDauh Lyuu,
More informationCHAPTER 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 informationFIN 411  Investments Option Pricing. Options: Definitions. Arbitrage Restrictions on Call Prices. Arbitrage Restrictions on Call Prices
FIN 411  Investments Option Pricing imple arbitrage relations s to call options Blackcholes model PutCall Parity Implied Volatility Options: Definitions A call option gives the buyer the right, but
More informationOptions. + Concepts and Buzzwords. Readings. PutCall Parity Volatility Effects
+ Options + Concepts and Buzzwords PutCall Parity Volatility Effects Call, put, European, American, underlying asset, strike price, expiration date Readings Tuckman, Chapter 19 Veronesi, Chapter 6 Options
More informationHow To Value Options In BlackScholes Model
Option Pricing Basics Aswath Damodaran Aswath Damodaran 1 What is an option? An option provides the holder with the right to buy or sell a specified quantity of an underlying asset at a fixed price (called
More information, plus the present value of the $1,000 received in 15 years, which is 1, 000(1 + i) 30. Hence the present value of the bond is = 1000 ;
2 Bond Prices A bond is a security which offers semiannual* interest payments, at a rate r, for a fixed period of time, followed by a return of capital Suppose you purchase a $,000 utility bond, freshly
More informationThe BlackScholes Formula
FIN40008 FINANCIAL INSTRUMENTS SPRING 2008 The BlackScholes Formula These notes examine the BlackScholes formula for European options. The BlackScholes formula are complex as they are based on the
More informationAn Introduction to Exotic Options
An Introduction to Exotic Options Jeff Casey Jeff Casey is entering his final semester of undergraduate studies at Ball State University. He is majoring in Financial Mathematics and has been a math tutor
More informationOverview. 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 Noarbitrage bounds on option prices Binomial option pricing BlackScholesMerton
More information11 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 informationManual 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 informationBINOMIAL OPTION PRICING
Darden Graduate School of Business Administration University of Virginia BINOMIAL OPTION PRICING Binomial option pricing is a simple but powerful technique that can be used to solve many complex optionpricing
More informationCHAPTER 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 informationt = 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 informationLecture 17/18/19 Options II
1 Lecture 17/18/19 Options II Alexander K. Koch Department of Economics, Royal Holloway, University of London February 25, February 29, and March 10 2008 In addition to learning the material covered in
More informationPractice 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 informationChapter 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 informationGetting Started with the Marketing Kickstarter Kit THE PAPERLESS AGENT
Getting Started with the Marketing Kickstarter Kit THE PAPERLESS AGENT This guide provides an overview of everything included in your Marketing Kickstarter Kit along with an explanation of what each resources
More informationFinal Exam MØA 155 Financial Economics Fall 2009 Permitted Material: Calculator
University of Stavanger (UiS) Stavanger Masters Program Final Exam MØA 155 Financial Economics Fall 2009 Permitted Material: Calculator The number in brackets is the weight for each problem. The weights
More informationEXERCISES 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