Session X: Lecturer: Dr. Jose Olmo. Module: Economics of Financial Markets. MSc. Financial Economics. Department of Economics, City University, London


 Daniela Malone
 2 years ago
 Views:
Transcription
1 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 contracts can be used for many different purposes. There are three main objectives pursued by investors using these derivatives: hedging, insurance and speculation. Options are attractive to investors because permit them to get free of downside risk. Options used for hedging arguments allow investors to minimize the variation in portfolio s value. The use of options for insurance purposes is an attempt to obtain the impossible. To benefit from rises in stock markets but limiting losses derived from downfall markets. Finally the mechanics and design of these financial instruments permits to devise complicated instruments tailored for specific objectives that search to exploit investor s beliefs (speculation) about stock price fluctuations but without taking exaggerated amounts of risk. Hedging with options In order to diversify risk an investment portfolio usually consists on assets, bonds, and derivatives. Within the class of derivative instruments, options are widely employed due 1
2 2 to their capacity to provide coverage against negative fluctuations of the underlying asset. Alternatively stock options can also provide coverage against upwards movements of the underlying stock yielding adverse results for investor s portfolio. Consider a portfolio consisting on w 1 units of a stock and w 2 European call options on the same underlying stock. The value of the portfolio P at date t is expressed as P t = w 1 S t + w 2 c t, with c t and S t the prices of the option and the stock respectively. The variation in the value of the portfolio between two periods is P t+1 = w 1 S t+1 + w 2 c t+1, with representing the change in the variable s value. The sensitivity of the change in portfolio s value to changes in the asset is given by P t+1 S t+1 = w 1 + w 2 c t+1 S t+1. This result provides a way to choose w 1 and w 2 such that changes in the underlying stock are offset by changes in the option price. This is w 2 w 1 = S t+1 c t+1. If the price of the underlying stock is assumed to follow a geometric brownian motion the value of an option is given by the BlackScholes formula: c t = Φ(x 1 )S t + Φ(x 2 )K exp R 0(T t), with x 1 and x 2 constants satisfying x 1 = log( K S t )+(R σ2 )(T t) σ T t, and x 2 = x 1 σ T t,
3 3 and Φ denoting a normal distribution function. be In order to have full coverage against fluctuations of the stock price the ratio w 1 w 2 should w 1 w 2 = 1 Φ(x 1 ). Suppose we add a put option to the portfolio to hedge against possible falls in the stock price. The variation in the value of the portfolio between two periods is P t+1 = w 1 S t+1 + w 2 c t+1 + w 3 p t+1, with p t the put option price. The sensitivity of the put price to changes in the stock price is derived from the Black Scholes model and the putcall parity relationship. Then p t+1 S t+1 = Φ(x 1 ) 1. Hence the sensitivity of the portfolio to changes in the stock price is P t+1 S t+1 = w 1 + w 2 Φ(x 1 ) + w 3 (Φ(x 1 ) 1). This portfolio is fully hedged under variations of the price of the underlying asset if the weights corresponding to the different components satisfy the following expression. (w 1 w 3 ) + (w 2 + w 3 )Φ(x 1 ) = 0. If it is possible to construct a portfolio satisfying these restrictions and the stock options are well modelled by the BlackScholes pricing formula the variations in stock price in both directions are offset by the option contracts.
4 4 Portfolio Insurance Portfolio insurance consists on combining the upside potential of increasing prices in stock markets with the limited downside potential provided by trading on options for declining markets. The goal is to construct portfolios that fully benefit from bull stock markets, in contrast to hedging strategies, but imposing a floor to the losses incurred by the portfolio in bear markets. Portfolio insurance is also distinguished from diversification in what the latter is an effort to minimize risk by finding portfolios consisting on independent assets. In this sense well diversified portfolios are free from idiosyncratic risk derived from negative assetspecific shocks but not from negative shocks affecting the market as a whole. These portfolios are affected by market risk. In fact the risk premium required by an investor is given by the relation between the portfolio and the market. Portfolio insurance pursues a more ambitious goal. To benefit from positive returns when asset prices increase without incurring large losses when they fall. There are different strategies for portfolio insurance involving options. Stoploss selling and buying. The purchase of put options. Lending and the purchase of call options. The creation of synthetic put options. Stoploss selling and buying In this strategy assets are sold when prices start falling and are bought when prices start increasing. This strategy is implemented by setting threshold levels such that in case these are exceeded the sellingbuying mechanism is triggered. This strategy for portfolio
5 5 insurance works when the sequence of upturns or downturns in stock prices is continuous. Increases are followed by increases, or alternatively, decreases are followed by decreases. Portfolio insurance with put options An investor holding an stock can obtain insurance against downfalls of the stock by buying put options on the underlying stock. This strategy allows one to fully benefit from stock value increases but at the same time setting a floor for possible declines in the asset. The put option price is the price of the insurance. The value of an insured portfolio consisting on two assets (S t, p t ) is S T + max(0, K S T ) = max(s T, K). The net payoffs of the portfolio after considering the price of the insurance are max(s T, K) p t. Portfolio insurance with call options This strategy is used by investors interested in having insurance against rises in stock prices. Instead of buying the stock at a low price and waiting until the price rises, if this eventually occurs, or buying the stock when it has reached a high price and it is uncertain whether prices are going to increase more, investors can borrow money or invest in a bond at the riskfree interest rate, and lock in a long position in a call option. If K is the strike price of a call option on the underlying stock S t, borrowing K exp R 0(T t) permits one to obtain the stock at the expiration date when it is likely to rise but paying the strike price for it. The insurance premium is the price of the call option. The value of the portfolio is K + max(0, S T K) = max(s T, K).
6 6 The net payoffs of the portfolio are max(s T, K) c t. These strategies are useful for portfolios involving one single stock. In general portfolios consist on many more assets and these insurance strategies can be of limited use due to transactions costs derived from buying large numbers of options. These portfolios also incur in transaction costs derived from continuous changes in portfolio composition in order to maintain the level of insurance. This is due to the differences between options expiration dates and investors horizons for holding the portfolio. Synthetic put options. The idea is to replicate the payoffs of a put option on the portfolio, and in turn benefit of the insurance this derivative provides. This is implemented when trading in put options is not available, or the expiration dates of the available options do not suit the time horizon of investors s portfolio. Combinations and spreads Along with hedging and insurance strategies options can be also devised with the intention of matching specific investment objectives. Versions of these derivatives tailored to achieve these objectives are designed by using combinations of different options, combinations of options with different maturities, or combinations of long and short positions in different call and put options on the same underlying stock. These strategies are usually implemented for speculation purposes. These are further classified as combinations and spreads.
7 7 Combinations These portfolios combine bundles, either all of long positions or all of short positions in call and put options on the same asset. This class of portfolios can be further classified as Straddles. A long straddle (bottom straddle) consists of a long position in a call and a put option with the same strike price and expiration date. The reverse position is denoted top straddle. Strips. A long strip consists of buying one call and two puts with the same strike price and expiration date. Investors obtain profits from large variations in the stock price paying attention to negative departures. Straps. A long strap consists of buying two calls and one put with the same strike price and expiration date. Investors obtain profits from large variations of the stock price but considering more likely positive departures. Strangles (bottom vertical combinations). A long strangle consists on a long position in a call and a put option with the same expiration date but different strike prices. The strike price of the put option is lower than the strike corresponding to the call option. This trading strategy is used for large expected movements in the stock price. The coverage against slight variations of the stock price is higher than with a straddle position though depends on the spread between the strike prices. This also has an effect on the profit of the strangle strategy. Spreads This strategy involves trading on long and short positions in two or more options of the same type. That is, either a bundle of two or more call options based on the same underlying stock, or a bundle of two or more put options in the same stock. These trading strategies can be divided in two classes.
8 8 Horizontal (or calendar) spreads. A bundle of options in the same underlying stock with the same strike price but different expiration dates. An example of this spread is a short position on a call option with maturity t 1 and a long position on a call option with the same strike price and later expiration date t 2. The option with later expiration is sold when the first option matures. Vertical (or cylinder) spreads. These options involve trading on options with the same expiration date and different strike prices. Within this class we can distinguish the following. Bull spreads. It involves buying a call option with strike K 1 and selling a call with the same expiration date but higher strike price, K 1 < K 2. It is immediate to see the call option with lower strike price is always the most expensive. Bull spreads in put options are created by using the same strategy; buying a put with a low strike price and selling a put with a high strike price. We distinguish three types of spreads. Both calls are initially out of the money. One call is initially in the money and the other is initially out of the money. Both calls are initially in the money. These strategies are devised for scenarios where the stock is expected to rise. Alternatively, if the investor expects a decline in the stock price an appropriate strategy is bear spreads. Bear spreads. It involves buying a call with strike price K 1 and selling a call with the same expiration date but lower strike price, K 2 < K 1. Bear spreads constructed on put options consist on selling the put with maturity K 2 and buying the expensive put option. Box spreads. This strategy is a combination of a bull call spread with strike prices K 1 and K 2 and a bear put spread with the same strike prices.
9 REFERENCES 9 Butterfly spreads. It involves taking positions in options with three different strike prices. The strategy consists on a long position in a call option with low strike price K 1, and a call option with high strike price K 3, and short positions in two call options with strike price K 2 halfway between the other two strike prices. This strategy provides limited losses for departures of S T from the strike k 2 and profit when the stock price is close to the strike. Diagonal spreads. The options involved in this strategy may have different strike prices and expiration dates. This alternative provides higher freedom to benefit from the properties of trading in stock options. References [1] Bailey, R.E., (2005). The Economics of Financial Markets. Ed. Cambridge University Press, New York (Chapter 20). [2] Hull, J.C., (2006). Options, Futures and Other Derivatives. Ed. Prentice Hall (6th ed.), New Jersey (Chapter 10).
Lecture 17. Options trading strategies
Lecture 17 Options trading strategies Agenda: I. Basics II. III. IV. Single option and a stock Two options Bull spreads Bear spreads Three options Butterfly spreads V. Calendar Spreads VI. Combinations:
More informationChapter 9 Trading Strategies Involving Options
Chapter 9 Trading Strategies Involving Options Introduction Options can be used to create a wide range of different payoff functions Why? /loss lines involving just underlying assets (forward) and money
More informationSession 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 informationLecture 4 Options & Option trading strategies
Lecture 4 Options & Option trading strategies * Option strategies can be divided into three main categories: Taking a position in an option and the underlying asset; A spread which involved taking a position
More informationCHAPTER 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 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 informationLecture 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 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 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 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 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 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 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 informationFinance 350: Problem Set 8 Alternative Solutions
Finance 35: Problem Set 8 Alternative Solutions Note: Where appropriate, the final answer for each problem is given in bold italics for those not interested in the discussion of the solution. All payoff
More informationArbitrage spreads. Arbitrage spreads refer to standard option strategies like vanilla spreads to
Arbitrage spreads Arbitrage spreads refer to standard option strategies like vanilla spreads to lock up some arbitrage in case of mispricing of options. Although arbitrage used to exist in the early days
More informationOption strategies. Stock Price Payoff Profit. The butterfly spread leads to a loss when the final stock price is greater than $64 or less than $56.
Option strategies Problem 11.20. Three put options on a stock have the same expiration date and strike prices of $55, $60, and $65. The market prices are $3, $5, and $8, respectively. Explain how a butterfly
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 informationOptions. The Option Contract: Puts. The Option Contract: Calls. Options Markets: Introduction. A put option gives its holder the right to sell
Options Options Markets: Introduction Derivatives are securities that get their value from the price of other securities. Derivatives are contingent claims (A claim that can be made when certain specified
More informationSolutions to practice questions Study Session 11
BPP Professional Education Solutions to practice questions Study Session 11 Solution 11.1 A mandatory convertible bond has a payoff structure that resembles a written collar, so its price can be determined
More information1 Strategies Involving A Single Option and A Stock
Chapter 5 Trading Strategies 1 Strategies Involving A Single Option and A Stock One of the attractions of options is that they can be used to create a very wide range of payoff patterns. In the following
More informationThis question is a direct application of the PutCallParity [equation (3.1)] of the textbook. Mimicking Table 3.1., we have:
Chapter 3 Insurance, Collars, and Other Strategies Question 3.1 This question is a direct application of the PutCallParity [equation (3.1)] of the textbook. Mimicking Table 3.1., we have: S&R Index S&R
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 informationCall Option: An option, but not an obligation, to buy at a specified price. o European: Can be exercised only at expiration.
I. Introduction: A derivative is a financial instrument that has a value determined by an underlying asset. Uses of derivatives: o Risk management o Speculation on prices o Reducing transaction costs o
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 informationChapter 9 Parity and Other Option Relationships
Chapter 9 Parity and Other Option Relationships Question 9.1. This problem requires the application of putcallparity. We have: Question 9.2. P (35, 0.5) C (35, 0.5) e δt S 0 + e rt 35 P (35, 0.5) $2.27
More informationReading 28 Risk Management Applications of Option Strategies
Reading 28 Risk Management Applications of Option Strategies A Compare the use of covered calls and protective puts to manage risk exposure to individual securities. Covered calls 1. Covered Call = Long
More informationIntroduction 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 informationHedging 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 informationExamination Study Guide Futures and Options (Module 14) [Applicable to Examination Study Guide Module 14 First Edition, 2013] UPDATES
Examination Study Guide Futures and Options (Module 14) [Applicable to Examination Study Guide Module 14 First Edition, 2013] UPDATES (As at July 2014) Copyright 2014 Securities Industry Development Corporation
More informationName 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 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 informationSolution Guide to Exercises for Chapter 20 Option markets III: applications
THE ECONOMIC OF FINANCIAL MARKET R. E. BAILEY olution Guide to Exercises for Chapter 20 Option markets III: applications 1. uppose that the futures price of a contract to deliver 1 kilogram of tin twelve
More informationOption Strategies. Probability distributions. Performance
Option Strategies. Probability distributions. Performance 1.1 Market scenario undecided. Volatility undecided 1.1.1 Complete hedge using options The payoff of the underlying asset (long share) can be completely
More informationThis page intentionally left blank
This page intentionally left blank Trading Strategies Involving Options 239 Table 11.1 ST^K^ K\ < ST < K2 S T ^ K 2 a bull spread created using calls. long call option &T ^ 1 &T ^ 1 short call option
More informationIntroduction to Mathematical Finance 2015/16. List of Exercises. Master in Matemática e Aplicações
Introduction to Mathematical Finance 2015/16 List of Exercises Master in Matemática e Aplicações 1 Chapter 1 Basic Concepts Exercise 1.1 Let B(t, T ) denote the cost at time t of a riskfree 1 euro bond,
More informationSOCIETY OF ACTUARIES/CASUALTY ACTUARIAL SOCIETY FINANCIAL MATHEMATICS SAMPLE QUESTIONS AND SOLUTIONS FOR DERIVATIVES MARKETS
SOCIETY OF ACTUARIES/CASUALTY ACTUARIAL SOCIETY EXAM FM FINANCIAL MATHEMATICS SAMPLE QUESTIONS AND SOLUTIONS FOR DERIVATIVES MARKETS Copyright 2007 by the Society of Actuaries and the Casualty Actuarial
More informationChapter 3 Insurance, Collars, and Other Strategies
Chapter 3 Insurance, Collars, and Other Strategies Question 3.1. This question is a direct application of the PutCallParity (equation (3.1)) of the textbook. Mimicking Table 3.1., we have: S&R Index
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 informationFIN40008 FINANCIAL INSTRUMENTS SPRING 2008. Options
FIN40008 FINANCIAL INSTRUMENTS SPRING 2008 Options These notes describe the payoffs to European and American put and call options the socalled plain vanilla options. We consider the payoffs to these
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 informationLecture 7. Option strategies and derivatives mishaps
Lecture 7 Option strategies and derivatives mishaps Option strategies Three alternative option strategies Take a position in an option and a position in an underlying asset Take a position in two or more
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 informationUCLA Anderson School of Management Daniel Andrei, Option Markets 232D, Fall MBA Final Exam. December 2012
UCLA Anderson School of Management Daniel Andrei, Option Markets 232D, Fall 2012 MBA Final Exam December 2012 Your Name: Your Equiz.me email address: Your Signature: 1 This exam is open book, open notes.
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 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 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 informationStochastic Processes and Advanced Mathematical Finance. Options and Derivatives
Steven R. Dunbar Department of Mathematics 203 Avery Hall University of NebraskaLincoln Lincoln, NE 685880130 http://www.math.unl.edu Voice: 4024723731 Fax: 4024728466 Stochastic Processes and Advanced
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 informationOPTION TRADING STRATEGIES IN INDIAN STOCK MARKET
OPTION TRADING STRATEGIES IN INDIAN STOCK MARKET Dr. Rashmi Rathi Assistant Professor Onkarmal Somani College of Commerce, Jodhpur ABSTRACT Options are important derivative securities trading all over
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 informationChapter 5 Option Strategies
Chapter 5 Option Strategies Chapter 4 was concerned with the basic terminology and properties of options. This chapter discusses categorizing and analyzing investment positions constructed by meshing puts
More informationPutCall Parity. chris bemis
PutCall Parity chris bemis May 22, 2006 Recall that a replicating portfolio of a contingent claim determines the claim s price. This was justified by the no arbitrage principle. Using this idea, we obtain
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 informationFundamentals 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 informationTable of Contents. Bullish Strategies
Table of Contents Bullish Strategies 1. Long Call 03 2. Synthetic Long Call 04 3. Short Put 06 4. Covered Call 07 5. Long Combo 08 6. The Collar 09 7. Bull Call Spread 10 8. Bull Put Spread 11 9. Call
More informationA Report On Pricing and Technical Analysis of Derivatives
A Report On Pricing and Technical Analysis of Derivatives THE INDIAN INSTITUTE OF PLANNING AND MANAGEMENT EXECUTIVE SUMMARY The emergence of Derivatives market especially Futures and Options can be traced
More informationOPTIONS TRADING (ADVANCED) MODULE
OPTIONS TRADING (ADVANCED) MODULE PRACTICE QUESTIONS 1. Which of the following is a contract where both parties are committed? Forward Future Option 2. Swaps can be based on Interest Principal and Interest
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 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 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 informationOption 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 informationDerivative strategies using
FP CLASSROOM Derivative strategies using options Derivatives are becoming increasingly important in the world of finance. A Financial Planner can use the strategies to increase profitability, hedge portfolio
More informationChapter 2 Questions Sample Comparing Options
Chapter 2 Questions Sample Comparing Options Questions 2.16 through 2.21 from Chapter 2 are provided below as a Sample of our Questions, followed by the corresponding full Solutions. At the beginning of
More informationContents. iii. MFE/3F Study Manual 9th edition Copyright 2011 ASM
Contents 1 PutCall Parity 1 1.1 Review of derivative instruments................................................ 1 1.1.1 Forwards............................................................ 1 1.1.2 Call
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 informationOptions and Derivative Pricing. U. NaikNimbalkar, Department of Statistics, Savitribai Phule Pune University.
Options and Derivative Pricing U. NaikNimbalkar, Department of Statistics, Savitribai Phule Pune University. email: uvnaik@gmail.com The slides are based on the following: References 1. J. Hull. Options,
More informationCHAPTER 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 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 informationUnderlying (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 PutCallForward
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 informationWeek 1: Futures, Forwards and Options derivative three Hedge: Speculation: Futures Contract: buy or sell
Week 1: Futures, Forwards and Options  A derivative is a financial instrument which has a value which is determined by the price of something else (or an underlying instrument) E.g. energy like coal/electricity
More informationIntroduction. Derivatives & Risk Management. The Nature of Derivatives. Main themes Options. This & next weeks lectures. Definition.
Derivatives & Risk Management Main themes Options option pricing (microstructure & investments) hedging & real options (corporate) This & next weeks lectures Part IV: Option Fundamentals» payoffs & trading»
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 informationSOCIETY 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 130 are from the prior version of this document. They have been edited to conform
More informationDerivatives & Risk Management. option pricing (microstructure & investments) hedging & real options (corporate) Part IV: Option Fundamentals
Derivatives & Risk Management Main themes Options option pricing (microstructure & investments) hedging & real options (corporate) This & next weeks lectures Part IV: Option Fundamentals» payoffs & trading»
More informationOptions Strategies Theory & Application. By By Abukar M Ali March 2004
Options Strategies Theory & Application By By Abukar M Ali March 2004 Option Strategies Overview Options strategies are applicable to various asset classes and for OTC as well as traded Options. The main
More informationRisk / Reward Maximum Loss: Limited to the premium paid up front for the option. Maximum Gain: Unlimited as the market rallies.
Bullish Strategies Bullish options strategies are employed when the options trader expects the underlying stock price to move upwards. It is necessary to assess how high the stock price can go and 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 informationFINANCIAL ENGINEERING CLUB TRADING 201
FINANCIAL ENGINEERING CLUB TRADING 201 GREG PASTOREK OPTIONS REVIEW A call (put) option with strike K expiring on date T gives the owner the right to buy (sell) the underlying security for price K until
More informationCA Final Strategic Financial Management, Paper 2, Chapter 5. CA.Tarun Mahajan,
CA Final Strategic Financial Management, Paper 2, Chapter 5 CA.Tarun Mahajan, Options Types of options Speculation using options Valuation of options In futures both parties have right as well as duty
More informationContents. iii. MFE/3F Study Manual 9 th edition 10 th printing Copyright 2015 ASM
Contents 1 PutCall Parity 1 1.1 Review of derivative instruments................................. 1 1.1.1 Forwards........................................... 1 1.1.2 Call and put options....................................
More informationFinance 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 informationBuying Call or Long Call. Unlimited Profit Potential
Options Basis 1 An Investor can use options to achieve a number of different things depending on the strategy the investor employs. Novice option traders will be allowed to buy calls and puts, to anticipate
More informationS&P 500 Options Strategies
Options Strategies 1 About NSE National Stock Exchange of India Limited (NSE) is an electronic exchange with a nationwide presence. It offers trading facility through its fully automated, screen based
More informationProtective Put Strategy Profits
Chapter Part Options and Corporate Finance: Basic Concepts Combinations of Options Options Call Options Put Options Selling Options Reading The Wall Street Journal Combinations of Options Valuing Options
More informationOption Pricing Basics
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 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 informationIntroduction. Part IV: Option Fundamentals. Derivatives & Risk Management. The Nature of Derivatives. Definitions. Options. Main themes Options
Derivatives & Risk Management Main themes Options option pricing (microstructure & investments) hedging & real options (corporate) This & next weeks lectures Introduction Part IV: Option Fundamentals»
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 informationFUNDING INVESTMENTS FINANCE 238/738, Spring 2008, Prof. Musto Class 5 Review of Option Pricing
FUNDING INVESTMENTS FINANCE 238/738, Spring 2008, Prof. Musto Class 5 Review of Option Pricing I. PutCall Parity II. OnePeriod Binomial Option Pricing III. Adding Periods to the Binomial Model IV. BlackScholes
More informationBasics of Spreading: Butterflies and Condors
1 of 31 Basics of Spreading: Butterflies and Condors What is a Spread? Review the links below for detailed information. Terms and Characterizations: Part 1 Download What is a Spread? Download: Butterflies
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 informationb. June expiration: 9523 = 95 + 23/32 % = 95.71875% or.9571875.9571875 X $100,000 = $95,718.75.
ANSWERS FOR FINANCIAL RISK MANAGEMENT A. 24 Value of Tbond Futures Contracts a. March expiration: The settle price is stated as a percentage of the face value of the bond with the final "27" being read
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 informationCourse Outline. FNCE Derivative Securities (3,0,0)
Course Outline Department of Accounting and Finance School of Business and Economics FNCE 31803 Derivative Securities (3,0,0) Calendar Description Students learn to value the main types of derivative
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 informationCHAPTER 22: FUTURES MARKETS
CHAPTER 22: FUTURES MARKETS 1. a. The closing price for the spot index was 1329.78. The dollar value of stocks is thus $250 1329.78 = $332,445. The closing futures price for the March contract was 1364.00,
More informationBUSM 411: Derivatives and Fixed Income
BUSM 411: Derivatives and Fixed Income 2. Forwards, Options, and Hedging This lecture covers the basic derivatives contracts: forwards (and futures), and call and put options. These basic contracts are
More informationSection 4. Complex strategies
Section 4. Complex strategies This section will discuss the more complex option strategies and will present examples of these strategies. The previous section covered the simpler option trading strategies,
More informationCommodity Pricing Software
Commodity Pricing Software The main objective of this software is to provide farmers with an objective viewpoint of their potential risk and returns from selling or buying commodities while hedging their
More information