A different kind of Tree Using trees to help price options. Using trees to help price options. Some of the ideas behind Black-Scholes. Some of the ideas.

Slides:

Advertisements

Similar presentations

© 2002 South-Western Publishing 1 Chapter 6 The Black-Scholes Option Pricing Model.

Advertisements

N Period Binomial Option Pricing Model Kevin Clarke.

Options Pricing Using Black Scholes Model By Christian Gabis.

Options Dr. Lynn Phillips Kugele FIN 338. OPT-2 Options Review Mechanics of Option Markets Properties of Stock Options Valuing Stock Options: –The Black-Scholes.

Valuation of real options in Corporate Finance

Valuation of Financial Options Ahmad Alanani Canadian Undergraduate Mathematics Conference 2005.

Black-Scholes Equation April 15, Contents Options Black Scholes PDE Solution Method.

Options Spring 2007 Lecture Notes Readings:Mayo 28.

Options Week 7. What is a derivative asset? Any asset that “derives” its value from another underlying asset is called a derivative asset. The underlying.

Spreads  A spread is a combination of a put and a call with different exercise prices.  Suppose that an investor buys simultaneously a 3-month put option.

Contemporary Investments: Chapter 15 Chapter 15 FUNDAMENTALS OF OPTIONS What are the basic characteristics of option contracts? What is the value of option.

1 16-Option Valuation. 2 Pricing Options Simple example of no arbitrage pricing: Stock with known price: S 0 =$3 Consider a derivative contract on S:

Mathematics in Finance Binomial model of options pricing.

© 2002 South-Western Publishing 1 Chapter 6 The Black-Scholes Option Pricing Model.

Financial options1 From financial options to real options 2. Financial options Prof. André Farber Solvay Business School ESCP March 10,2000.

FIN 685: Risk Management Topic 3: Non-Linear Hedging Larry Schrenk, Instructor.

Black-Scholes Pricing cont’d & Beginning Greeks. Black-Scholes cont’d  Through example of JDS Uniphase  Pricing  Historical Volatility  Implied Volatility.

Options An Introduction to Derivative Securities.

A Basic Options Review. Options Right to Buy/Sell a specified asset at a known price on or before a specified date. Right to Buy/Sell a specified asset.

1 OPTIONS Call Option Put Option Option premium Exercise (striking) price Expiration date In, out-of, at-the-money options American vs European Options.

1 Today Options Option pricing Applications: Currency risk and convertible bonds Reading Brealey, Myers, and Allen: Chapter 20, 21.

Pricing Cont’d & Beginning Greeks. Assumptions of the Black- Scholes Model  European exercise style  Markets are efficient  No transaction costs 

Théorie Financière Financial Options Professeur André Farber.

Corporate Finance Options Prof. André Farber SOLVAY BUSINESS SCHOOL UNIVERSITÉ LIBRE DE BRUXELLES.

Option Pricing Approaches

VIII: Options 26: Options Pricing. Chapter 26: Options Pricing © Oltheten & Waspi 2012 Options Pricing Models  Binomial Model  Black Scholes Options.

Principles of option pricing Option A contract that gives the holder the right - not the obligation - to buy (call), or to sell (put) a specified amount.

OPTION PRICING: BASICS Aswath Damodaran 1. 2 The ingredients that make an “option” Aswath Damodaran 2  An option provides the holder with the right to.

Class 5 Option Contracts. Options n A call option is a contract that gives the buyer the right, but not the obligation, to buy the underlying security.

Chapter 20 Option Valuation and Strategies. Portfolio 1 – Buy a call option – Write a put option (same x and t as the call option) n What is the potential.

Introduction to Financial Engineering Aashish Dhakal Week 5: Black Scholes Model.

Session 4– Binomial Model & Black Scholes CORP FINC Spring 2014 Shanghai.

AIM How can we use derivative investments to enhance our portfolio? DO NOW What are stock options? OPTIONS AND FUTURES.

Option Valuation. Intrinsic value - profit that could be made if the option was immediately exercised –Call: stock price - exercise price –Put: exercise.

Investment Analysis and Portfolio Management Lecture 10 Gareth Myles.

Properties of Stock Options

Ch8. Financial Options. 1. Def: a contract that gives its holder the right to buy or sell an asset at predetermined price within a specific period of.

1 Chapter 9 Financial Options and Applications in Corporate Finance.

OPTIONS MARKETS: INTRODUCTION Derivative Securities Option contracts are written on common stock, stock indexes, foreign exchange, agricultural commodities,

2007 Page 1 F. MICHAUX CORPORATE FINANCE Financial and Real Options.

Greeks of the Black Scholes Model. Black-Scholes Model The Black-Scholes formula for valuing a call option where.

© 2007 The MathWorks, Inc. ® ® Pricing Derivatives Securities using MATLAB Mayeda Reyes-Kattar March 2007.

Chapter 10: Options Markets Tuesday March 22, 2011 By Josh Pickrell.

Black Scholes Option Pricing Model Finance (Derivative Securities) 312 Tuesday, 10 October 2006 Readings: Chapter 12.

Intermediate Investments F3031 Option Pricing There are two primary methods we will examine to determine how options are priced –Binomial Option Pricing.

FUTURES AND OPTIONS Chapter 16

Lecture Presentation Software to accompany Investment Analysis and Portfolio Management Seventh Edition by Frank K. Reilly & Keith C. Brown Chapter 23.

Options An Introduction to Derivative Securities.

Option Pricing BA 543 Aoyang Long. Agenda Binomial pricing model Black—Scholes model.

Financial Risk Management of Insurance Enterprises Options.

A Cursory Introduction to Real Options Andrew Brown 5/2/02.

Introduction Finance is sometimes called “the study of arbitrage”

Lecture 15.  Option - Gives the holder the right to buy or sell a security at a specified price during a specified period of time.  Call Option -

Derivative Securities Law of One Price Payoff Diagrams for common derivatives Valuation of Derivatives Put-Call Parity.

Properties of Stock Option Prices Chapter 9. Notation c : European call option price p :European put option price S 0 :Stock price today K :Strike price.

Lecture 2.  Option - Gives the holder the right to buy or sell a security at a specified price during a specified period of time.  Call Option - The.

CAPITAL BUDGETING &FINANCIAL PLANNING. d. Now suppose this project has an investment timing option, since it can be delayed for a year. The cost will.

© 2003 The McGraw-Hill Companies, Inc. All rights reserved. Basics of Financial Options.

Class Business Upcoming Groupwork Course Evaluations.

Professor XXXXX Course Name / # © 2007 Thomson South-Western Chapter 19 Black and Scholes and Beyond.

FINANCIAL DERIVATIVES PRESENTED TO: SIR ILYAS RANA PRESENTED BY: TAQDEES TAHIR.

Class 20 Financial Management,

Covered Calls and Cash-secured Puts

An Introduction to Binomial Trees Chapter 11

An Introduction to Binomial Trees Chapter 11

Financial Market Theory

Chapter 17 Futures Options

Financial Market Theory

Presentation transcript:

A different kind of Tree Using trees to help price options. Using trees to help price options. Some of the ideas behind Black-Scholes. Some of the ideas behind Black-Scholes. Myron ScholesFischer Black

Option Basics A stock option is a derivative security, because the value of the option is “derived” from the value of the underlying common stock. A stock option is a derivative security, because the value of the option is “derived” from the value of the underlying common stock. There are two basic option types. There are two basic option types. Call options are options to buy the underlying asset. Call options are options to buy the underlying asset. Put options are options to sell an underlying asset Put options are options to sell an underlying asset

Example Suppose Aetna is selling for $30 a share. Suppose Aetna is selling for $30 a share. Suppose the option price is $1.30. Suppose the option price is $1.30. Consider the following scenarios and whether or not you would exercise your option: Consider the following scenarios and whether or not you would exercise your option: At the expiration date the stock is $28 per share. At the expiration date the stock is $28 per share. At the expiration date the stock is $30 per share. At the expiration date the stock is $30 per share. At the expiration date the stock is $32 per share. At the expiration date the stock is $32 per share. How do you know what a good price is for your option? How do you know what a good price is for your option?

$30 Price of stock = $32 Value of option = $2 Price of stock = $28 Value of option = $0 Suppose you buy x shares and sell one option. If the price goes up to $32 your portfolio is worth 32x-2. If the price goes down to $28 your portfolio is worth 28x-0.

$30 Price of stock = $32 Value of option = $2 Price of stock = $28 Value of option = $0 Suppose you buy x shares and sell one option. A risk free portfolio will have the same value regardless of what happens: 32x-2 = 28x-0. Solve for x to get x = ½. If you have ½ a share, then regardless of how the price of the stock changes (up to $32 or down to $28) the portfolio is worth 32(1/2)-2=14. So a risk free portfolio that contains x shares and sells one option has a value of 1/2x- 1 option = 14. This means an option is worth (1/2)(30) – 1 option = 14. Solve for one option to get 1 option = $1.

$30 $31 $1 $29 $0 $32 $2 $30 $0 $28 $0 $31 $1 $29 $0 $33 $3 $27 $0

The Black and Scholes Model