Chap 8 A Four-Step Process for Valuing Real Options.

Slides:



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

A Multi-Phase, Flexible, and Accurate Lattice for Pricing Complex Derivatives with Multiple Market Variables.
Asset Pricing. Pricing Determining a fair value (price) for an investment is an important task. At the beginning of the semester, we dealt with the pricing.
The Arbitrage Pricing Theory (Chapter 10)  Single-Factor APT Model  Multi-Factor APT Models  Arbitrage Opportunities  Disequilibrium in APT  Is APT.
Applications of Stochastic Processes in Asset Price Modeling Preetam D’Souza.
Chap 10 Keeping uncertainties separate.  The way to do this is to keep the major uncertainties separate and to model their interaction and effect on.
Valuing Stock Options: The Black-Scholes-Merton Model.
Incremental Cash Flows
An Introduction to Asset Pricing Models
© 2004 South-Western Publishing 1 Chapter 6 The Black-Scholes Option Pricing Model.
© 2002 South-Western Publishing 1 Chapter 6 The Black-Scholes Option Pricing Model.
Options and Speculative Markets Introduction to option pricing André Farber Solvay Business School University of Brussels.
Chapter 6.
Mutual Investment Club of Cornell Week 8: Portfolio Theory April 7 th, 2011.
Lecture: 4 - Measuring Risk (Return Volatility) I.Uncertain Cash Flows - Risk Adjustment II.We Want a Measure of Risk With the Following Features a. Easy.
Option Basics - Part II. Call Values When Future Stock Prices Are Certain to Be Above the Exercise Price Suppose the value of a stock one year from today.
1 Limits to Diversification Assume w i =1/N,  i 2 =  2 and  ij = C  p 2 =N(1/N) 2  2 + (1/N) 2 C(N 2 - N)  p 2 =(1/N)  2 + C - (1/N)C as N  
1 Chapter 09 Characterizing Risk and Return McGraw-Hill/Irwin Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.
Derivatives Introduction to option pricing André Farber Solvay Business School University of Brussels.
Chapter 14 Risk and Uncertainty Managerial Economics: Economic Tools for Today’s Decision Makers, 4/e By Paul Keat and Philip Young.
Steve Paulone Facilitator Standard Deviation in Risk Measurement  Expected returns on investments are derived from various numerical results from a.
5- 1 Outline 5: Stock & Bond Valuation  Bond Characteristics  Bond Prices and Yields  Stocks and the Stock Market  Book Values, Liquidation Values.
Dr. Hassan Mounir El-SadyChapter 6 1 Black-Scholes Option Pricing Model (BSOPM)
Capital budgeting and the capital asset pricing model “Less is more.” – Mies can der Rohe, Architect.
© 2004 South-Western Publishing 1 Chapter 6 The Black-Scholes Option Pricing Model.
Valuing Stock Options:The Black-Scholes Model
Ewa Lukasik - Jakub Lawik - Juan Mojica - Xiaodong Xu.
Bonds Are Safe They come with two promises: The income stream they provide is usually fixed and relatively certain. They will not mature at less than.
Portfolio Management Lecture: 26 Course Code: MBF702.
1 MBF 2263 Portfolio Management & Security Analysis Lecture 2 Risk and Return.
Portfolio Management-Learning Objective
II: Portfolio Theory I 2: Measuring Portfolio Return 3: Measuring Portfolio Risk 4: Diversification.
Copyright: M. S. Humayun1 Financial Management Lecture No. 26 SML Graph & CAPM Closing Notes on Risk & Return.
Chap 9 Estimating Volatility : Consolidated Approach.
Wiener Processes and Itô’s Lemma Chapter 12 1 Options, Futures, and Other Derivatives, 7th Edition, Copyright © John C. Hull 2008.
Chapter 13 Wiener Processes and Itô’s Lemma
Chapter 08 Risk and Rate of Return
10.1 Options, Futures, and Other Derivatives, 4th edition © 1999 by John C. Hull Model of the Behavior of Stock Prices Chapter 10.
Valuing Stock Options: The Black- Scholes Model Chapter 11.
Security Analysis & Portfolio Management “RISK & RETURN” By B.Pani M.Com,LLB,FCA,FICWA,ACS,DISA,MBA
Value at Risk Chapter 16. The Question Being Asked in VaR “What loss level is such that we are X % confident it will not be exceeded in N business days?”
Risk and Capital Budgeting 13 Chapter Copyright © 2011 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin.
CHAPTER SEVEN Risk, Return, and Portfolio Theory J.D. Han.
A Cursory Introduction to Real Options Andrew Brown 5/2/02.
Chapter McGraw-Hill/Irwin Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved. Risk and Capital Budgeting 13.
Real Options Chapter 8 A 4-Step Process for Valuing Real Options.
Monte Carlo: Option Pricing
Chap 4 Comparing Net Present Value, Decision Trees, and Real Options.
1 Wiener Processes and Itô’s Lemma MGT 821/ECON 873 Wiener Processes and Itô’s Lemma.
Boundless Lecture Slides Free to share, print, make copies and changes. Get yours at Available on the Boundless Teaching Platform.
Copyright © 2011 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin 24-1 Portfolio Performance Evaluation.
Risk and Return: Portfolio Theory and Assets Pricing Models
1 Estimating Return and Risk Chapter 7 Jones, Investments: Analysis and Management.
1 Ch 7: Project Analysis Under Risk Incorporating Risk Into Project Analysis Through Adjustments To The Discount Rate, and By The Certainty Equivalent.
1 Ch 15: Forecasting and Analyzing Risks in Property Investments Applying Quantitative and Qualitative Forecasting Methods,Together With Risk Analysis,
Applications of Stochastic Processes in Asset Price Modeling Preetam D’Souza.
Chapter 13 Risk and Capital Budgeting. McGraw-Hill/Irwin © 2005 The McGraw-Hill Companies, Inc., All Rights Reserved. PPT 13-1 FIGURE 13-1 Variability.
Risk and Return An Overview
Wiener Processes and Itô’s Lemma
Capital Market Theory: An Overview
Decisions Under Risk and Uncertainty
Portfolio Risk Management : A Primer
TOPIC 3.1 CAPITAL MARKET THEORY
Techniques for Data Analysis Event Study
Chapter 3 Statistical Concepts.
Risk and Capital Budgeting
Estimating Volatility : Consolidated Approach
Valuing Stock Options:The Black-Scholes Model
Presentation transcript:

Chap 8 A Four-Step Process for Valuing Real Options

 To avoid this complexity, we use two assumptions.  The first is the MAD (marketed asset disclaimer) that uses the present value of the underlying risky asset without flexibility as if it were a marketed security.  The second, is that properly anticipated prices (or cash flows) fluctuate randomly.

A four-step process  Step 1 is a standard net present value analysis of the project using traditional techniques.  We forecast the entity-free cash flows over the life of the project; or if the investment is an acquisition, we value the target company whose cash flows are expected to last indefinitely.

 The second step is to build an event tree, based on the set of combined uncertainties that drive the volatility of the project.  An event tree does not have any decisions built into it.  We assume that in most cases, the multiple uncertainties that drive the value of a project can be combined, via a Monte Carlo analysis, into a single uncertainty.  When we combine all uncertainties into the single uncertainty of the value of the project, we call this the consolidated approach for dealing with uncertainty.

Samuelson’s proof that properly anticipated prices fluctuate randomly  If the cycle evolves as expected, investors receive their required return – exactly.  Only deviations from the expected cycle will keep the stock price from changing as expected.  But these deviations are caused by random events.  Consequently, deviations from the expected rate of return are also random.

 Samuelson starts his proof by assuming that the spot price of an asset, S t+1, follows a stationary autoregressive scheme, assuming that the coefficient of adjustment, a, is less than one and that the error term is distributed normally with mean zero and standard deviation sigma (σ).

 Covariance between error terms of adjacent time periods is zero  (i.e., E(ε t,ε t-1 ) = COV(ε t, ε t-1 ) = 0)  Also, the squared error terms from one time period are equal to those of the next period, therefore, E(ε t ) 2 = E(ε t+1 ) 2 =

 The expected change in the futures price, evaluated at time t is zero because

 Note that with a < 1, the variance increases as one gets closer to maturity.  But if a = 1, the futures price is a random walk with zero drift and with a standard deviation of a, constant across time.

Numerical examples to demonstrate Samuelson’s proof

Empirical evidence in support of Samuelson’s proof  The form of the equation was  Mean reversion :