Transcript Real Option-Chapter 4 - Iowa State University

Real Option-Chapter 4
Wang YU
Feb 14, 2002
NPV vs. DTA vs. ROA
• NPV(Net Present Value): Implicitly assume on flexibility
in decision making. You only can do mutually exclusive
scenarios analysis.
• DTA( Decision Tree Analysis): Allow for flexibility but
use a constant discount rate for different scenarios with
different risk and payoff
• ROA(Real Option Analysis): Allow for flexibility and use
different discount rate for different scenarios.
Review of NPV
• PV of Expected Cash Flow: We use Expected Cash Flow +
Risk –adjusted Discount Rate to get PV.
• We use CAPM( Capital Asset Pricing Model) to find the
Risk-adjusted Rate. ( Find the comparable marketed
security to get the Beta of a project.)
• PV of Investment: Amount for Investment + Risk-free
Discount Rate ( Assume the amount for investment is
known for sure)
• NPV= PV of Expected Cash Flow- PV of Investment.
Review of DTA
• DTA gives you the flexibility to make your decision, but
the PVs of defer point, commitment point are using the
same discount rate
Payoff of Upper Case:
55
Defer
Payoff of Lower
Case:0
Start
Payoff of Upper
Case:170
Commitment
Payoff of Lower
Case:65
Review of ROA
• Two approaches to implement ROA:
• Replicating Portfolio Approach: Discounting expected
cash flow at a risk-adjusted rate.
• Risk-Neutral Probability Approach: Discounting certaintyequivalent cash flow at a risk-free rate.
Replicating Portfolio Approach
• The idea is to find a portfolio composed by a risk-free bound and a
market-priced underlying risky asset, whose cash flow and risk are
perfectly correlated with our subject. Because the portfolio has the
same payoff with our option, their value or price should be the same.
• The idea is based on the theory of one price. If there are two
commodities, which are perfect substitutes for each other, their price
should be equal to eliminate arbitrage.
• MAD(Marketed Asset Disclaimer): It’s hard to find a a market-priced
underlying risky asset, whose cash flow and risk are perfectly
correlated with our subject, so MAS suggests that we use the project
itself as the underlying asset and regard it’s PV as the marketed price.
Risk-Neutral Probability Approach
• The idea is that you are hedge against your risk by holding
the underlying asset and options written on it. If you hold
the right amounts of options, your expected payoff will be
constant in any cases. The conclusion is that the PV of
our option equals to the discounted weighted sum of values
of options in each possible outcomes. The weights are
risk-neutral probabilities instead of objective probabilities.
• The results given by the two approaches are the same, but
the processes are different. The risk-neutral probability
approach will be easy to compute sometimes, because the
risk-neutral probability maybe same across all the decision.
ROA vs. Black-Scholes Approach
• The assumptions embedded in the black-scholes models
restricts its usage in real option analysis.
• European Option vs. American Option
• Single source of uncertainty vs. Rainbow option
• Single underlying asset vs. Compounded option
• Observable marketed price vs. No comparables.
• Constant variance vs. Incoming information
• Certainty and constant exercise price vs. Uncertainties in
exercise prices
• Underlying assets pays no dividends vs. Dividends
Financial Option vs. Real Option
• Underlying financial asset vs. Physical assets
• Observable information( statistical/historical data)
vs. MAD ( simulations)
• Side bets vs. Involvers (control and influence on
the underlying assets)
• Source of risk, both are assumed to be exogenous.
But the holder of a real option may interact with
its competitor and the uncertainty will change.
Suggestions
• Read the examples, they will make it easier
to understand the ideas.
• If you don’t understand the examples, find a
financial book.