1. Options Concepts Richard de Neufville
Professor of Engineering Systems and of
Civil and Environmental Engineering
MIT

2. Theme for Rest of Course
Flexibility Adds Value
Enables adaptation to actual future conditions
Flexibility Requires a Special Effort
Time and Effort to create flexible plans and designs
Complexity of design and management
Surprisingly, Flexibility often does not cost more:
staged development (using smaller increments, deferring additions to system) can reduce both Capital Expenditure (Capex) and Total PV of Development Costs
The Central Design issue is: How much Flexibility should we incorporate into system?
The analytic question is: How do value flexibility?

3. Outline: Options Presentations - Theory
What is an Option?
Learning Objective: Basic concept and use
Lattice Model
LO: Analysis of time evolution of uncertainty
Option Valuation by Lattice (decision analysis)
LO: How valuation proceeds through a lattice
Dynamic Programming
LO: Use of this optimization analysis
Arbitrage Pricing of Options
LO: Significance and Applicability of Concept
Black-Scholes Analysis
LO: Use in Financial Markets

4. Outline: Lessons from Options Cases
Merck and Kodak
LO: Choice of Decision or ‘Options’ Analysis
Antamina
LO: Use of Simulation for Valuation
Research Development at Ford
LO: Hybrid of Decision and ‘Options’ Analysis
Complex Engineering Systems
LO: Screening Models to Identify Good Options
Hydropower Development
LO: Path Dependency Issues

5. Objectives of this presentation
To define technical concept of “Options”
4 step ‘Mantra’
To identify types of Options: ‘calls’ and ‘puts’
Build upon their use in financial context
To present non-linear asymmetric returns
Use of diagrams
To indicate drivers of value for options
Uncertainty, Time increase value for American options
To distinguish range of applications
Financial, “ON” and “IN” systems
Examples

6. “Options” Embody Idea of Flexibility
An “Option” provides a formal way of defining flexibility
An “Option” has a specific technical definition
Semantic Caution:
The technical meaning of an “option” is… much more specific and limited than … ordinary meaning of “option” in conversation where “option” = “alternative”
Pay careful attention to definition that follows!

7. Technical definition of an Option
An Option is...
A right, but not an obligation…
“Exercise”, that is “use” only if advantageous
Asymmetric returns -- “all gain, no pain”
Usually acquired at some cost or effort
to take some action…
to grow or change system, buy or sell something, etc, etc,
now, or in the future...
May be indefinite
But can be for a limited time after which option expires
for a pre-determined price (the “strike” price).
Cost of action separate from cost of option

8. Illustration of option definition
Spare tire on a car is an “option” because it provides
right, but not an obligation…
Operator can use it or not
Acquired at some cost – price of tire, loss of storage space
to take some action…
to change the tire
now, or in the future...
In this case, whenever desired
for a pre-determined price (the “strike” price).
Time and effort of jacking up car, replacing tire, etc.

9. Types of Options Two basic types of options
CALL: right to take advantage of an opportunity (such as ability to expand garage if demand is high)
PUT: right to limit losses of a bad situation (which is what an insurance policy provides)
Options in design can be complicated
NESTED: one following another (e.g.: successful research provides option on development; successful prototyping provides option on production)
SIMULTANEOUS: (e.g.: successful research on fuel cells provides options on hybrid cars and home uses)

10. Financial Options Focus first on financial options because
Consequences easiest to present
This is where options and valuation developed
Financial Options
Are tradable assets (see quotes finance.yahoo.com)
Sold through exchanges similar to stock markets
Are on all kinds of goods (known as “underlying assets”)
Stocks, that is, shares in companies
Commodities (oil, meat, cotton, electricity...)
Foreign exchange, etc., etc.

11. Types of Financial Options
Two basic types of options
Call: right to BUY asset for a set price
Put: right to SELL asset for a set price
The set price is known as the “strike” price
Financial options can get very complicated
In addition to Nested and Simultaneous
Very exotic possibilities (“Asian”, “Bermudan”, “caput”, etc , etc. -- see en.wikipedia.org/wiki/Exotic_option)
Not in this course !

12. Standard Option Terminology
S = fluctuating market price of “underlying asset”
S* = S at the moment owner of option takes advantage of right (when option is “exercised”)
K = Strike price
PAYOFF = owner’s net from a having the option, this is consequence we need to understand
Let’s examine what payoff looks like…

13. Call Option Payoff
Call Option gives person right to buy an asset for a predetermined “strike” price, K
Only rational to exercise right when price of asset is greater than “strike” price: S > K
If exercised, option owner pays agreed price of K to get asset worth S* => Payoff = S* - K
If unexercised, Payoff = 0
Formally, payoff = Maximum of either 0 or S* K = Max [0, S* K]

14. Payoff Diagram for Call Option
($) S
Payoff of Option
Price of
Asset
S - K K
Asset Price ($)

15. Example of Current Call Option
Example: A Call Option to
buy 100 shares of Google (shares of Google constitute the “underlying asset”)
at $350 per share (this is the “strike price”)
through Jan. 20, 2006
On Oct. 26, 2005, prices were (finance.yahoo.com)
1 share of Google = $
option to buy 1 share = $
NOTE: option price> immediate value of exercise = $ 3.53
Here’s what the payoff diagram looks like…

16. Payoff Diagram for Call Option
Per
share
($) S
Payoff of Option
Price of
Google
S - K
Current
Google Price
K= $350
Price of Google share ($)

17. Put Option Payoff
Put Option gives person right to sell an asset for a predetermined “strike” price, K
Only rational to exercise right when price of asset is LOWER than “strike” price: S < K
If exercised, option owner GETS agreed price of K for asset worth S* => Payoff = K - S*
If unexercised, Payoff = 0
Net payoff for put = Max [0, K - S*]

18. Payoff Diagram for Put Option
($)
Asset
Price S K
K-S
Payoff of
Option
Asset Price ($) K

19. Example Financial Option
Example: A PUT Option to
SELL 100 shares of Google
at $350 per share (the “strike” price)
Through Jan. 20, 2006
On Oct. 26, 2005, prices were (finance.yahoo.com)
1 share of Google = $
option to sell 1 share = $
NOTE: option value > value of immediate payoff = - $3.55

20. Asymmetry of Option
For Call Option, if asset price > strike price… owner then makes profit – that could be unlimited
Owner not required to exercise option, so… Loss limited to cost of buying option ( $27.00/share in Google example)
Value of option not symmetric
For owner of call option: All gain, No pain
Note: This applies once you have option. Normally, you have to pay for option, so net value of option (after purchase price, will have possibility of loss
Asymmetry is key to option value

21. What drives option value?
How much should you pay to acquire an option?
Payoff diagrams show for a given strike price
Call payoff increases with asset price increases
Put payoff increases with asset price decreases
Payoff generally does not reflect full value of option
Why is that?
Owner exercises only when advantageous
In general, owner can wait for a higher price
Value is Max[ immediate exercise, waiting]

22. Boundaries on Price
Some logical boundaries on value of call option that can be exercised any time (American) Price > 0 Otherwise buy option immediately Price < S Option yields S*- K Option value < S Price > S - K Or buy and exercise immediately
Payoff
($)
Stock Price ($) K
Upper Bound:
Call Value Equals
Asset Price
Lower Bound: S

23. Why Payoff and Value Differ
Consider an option whose current asset price equals strike price: (S = K) (it is “at the money”) Immediate exercise payoff is zero However, if you wait: Payoff might be higher Worst is zero payoff Value of waiting not reflected in immediate exercise, to be added
Payoff ($)
EV[S]
S - K
= value of option K
Asset Price ($)

24. Value for All Stock Prices
Value exceeds immediate exercise payoff
Asymptotically nears immediate payoff for increased S
If no upside: value (expectations) = 0 = value (option)
Payoff($)
S - K
Value K
Asset Price ($)

25. Option Value Increases with Volatility
Two “at the money” options (S=K) on different assets Both have immediate payoff = 0 Asset A with greater volatility has higher P(larger net payoffs) => higher expected value Asymmetric value favors high variation (limited losses)
Payoff ($)
Asset A
Payoff ($)
Asset B
pdf
S-K
S-K
pdf K
Asset Price ($) K
Asset Price ($)

26. Impact of Time
Increasing time to expiration increases value of options you can exercise any time (“American”)
Ability to wait allows option owner to benefit from asymmetric returns
Longer- term contains shorter-term options + more time cannot be worse, can only be better
Compare a 3 and 6 month American call
Can exercise 6 month call at same time as 3 month
Can wait longer with 6 month
Which is more valuable? Must be longer one...
Time impact not obvious for options with fixed date for exercise (“European”)
Could miss out on profitable opportunities

27. Generalized Value of American Call
For a set strike price, value increases with
Stock price increases
Volatility
Time
Increased strike
price
Reduces likelihood of payoffs
Reduces call option value
Payoff
($)
Value increases with volatility and time to expiration
S - K
Asset Price ($) K

28. Real Options “Real” because they refer to project and systems
Contrast with financial options that are contracts
Real Options are focus of interest for Design
They provide flexibility for evolution of system
Projects often contain option-like flexibilities
Rights, not obligations (example: to expand garage)
Exercise only if advantageous
These flexibilities are “real” options
Let’s develop idea by looking at possibilities…

29. Real Options are Everywhere
Examples:
Lease equipment with option to buy at end of lease
Action is to buy at end of lease (or to walk away)
Lease period defined up-front (typically 2-3 years)
Purchase price defined in lease contract
Flexible manufacturing processes
Ability to select mode of operation (e.g. thermal power by burning either gas or oil)
Switching between modes is action
Continuous opportunity (can switch at any time)
Switching often entails some cost (e.g.: set-up time)

30. Generic Real Options Call-like Put-like Compound (nested) In detail…
Capture benefits from increases in project value
Exercise typically involves putting money into project
Exercise when expectations of positive return increase
Put-like
Insure against losses from decreased project value
Exercise may involve short-term costs or salvage value
Exercise when expectations of losses
Compound (nested)
Projects might contain multiple options
Exercise decisions based on overall profit maximization
In detail…

31. Call-Like Real Options
Waiting to Invest
A project might be profitable today, but better tomorrow
Leaving investment opportunity open ~ holding a call
Deciding factors: uncertainty resolution; foregone profits
Choice based on: Max [immediate investment, waiting, 0]
Expand -- Accelerate effort or level of involvement
Allows greater participation in upside
Cost of expansion is like strike price
Choice based on: Max [status quo, expanded project
Restart Temporarily Closed Operations
Similar to waiting to invest or expand (a special case)
Choice based on: Max [remain closed, re-open]

32. Put-Like Real Options Abandon
Ability to halt investment eliminates further losses
might include shut-down costs and salvage values
Choice based on: Max [continuing, abandoning]
Contract -- Decelerate or narrow involvement
Reduces participation level and exposure to losses
Often incurs short-term scale down costs
Choice based on: Max [status quo, contracted]
Temporarily Shut Down Operations
A special case of contraction
Eliminates losses, but can incur shut-down costs
Choice on: Max [status quo, temporarily shut-down]

33. Compound or Nested Options
Combinations of Options
Many real options exist simultaneously
E.g.: those to abandon, contract, or temporarily shut down
Complex problem: value of multiple options are often interdependent and in general not additive
Exercise may make others valueless (abandon ends project)
Switching Between Modes of Operation (example: dual fuel burner case)
Flexible systems contain an infinite series of options
Allow continual switching between modes of operation
If switching modes has a cost, it acts like a strike price
For compound options, must value as system

34. Real Options “IN” and “ON” projects
Those “real” because, in contrast to financial options, they concern projects, they are “ON” projects
E.g.: the option to open a mine (Antamina case)
These do not concern themselves with system design
Most common in literature
Those “real” because they concern the design elements of system, they are “IN” projects
EX: options for staging of system of communication satellites
These require detailed understanding of system
Most interesting to system designers
Financial
options
Options ON
projects
Options IN
Real Options
These need
knowledge
of system

35. Real Options “ON” projects
These are financial options, but on technical things
They treat technology as a “black box”
Example: Antamina mine (detailed discussion later)
option to open the mine after a two-year exploration period
Uncertainty concerns: amount of ore and future price =>uncertainty in revenue and thus in value of mine
Option is a Financial Call Option (on Mine as asset)
Differs from normal Financial Option because
Much longer period -- financial option usually < 2 years
Special effort needed to model future value of asset, it can’t be projected simply from past data (as otherwise typical)

36. Real Options “IN” projects
These create options by design of technical system
They require understanding of technology
Example: Communications Satellites
Designers can create options for expansion of capacity by way they configure original satellites
Technical skill needed to create and exercise option
Differ from other “real” Options because
Special effort needed to model feasible flexibility within system itself (e.g.: modeling of ‘trade space” for design of communication satellites)

37. Summary of Introduction to Options
Options embody formal concept of flexibility
Options are not “alternatives”
4 step Mantra “right, but not obligation, to act…”
“Calls” for opportunities, “puts” for downside risks
Options have asymmetric returns => source of value
Options are Financial and “Real”
Many “real” options available to system designers
“Real” Options “ON ” and “IN” systems

38. Appendix Slides Illustrating impracticality of using:
Net present value, discounted cash flows, to analyze flexibility practice
decision analysis to analyze complex problems with many possible decision points (stages)

39. Example: Project R&D Risk
Start R&D project for $100,000 (0.1M)
$1,100,000 (1.1 M) more to complete development
Commercial feasibility determined by initial R&D results
Plan to sell (license) technology to highest bidder
Revenue estimate
50% chance to sell technology for $2000,000 (2M)
50% chance to sell for $100,000 (0.1M)
Assume constant 10% discount rate applies
Fund project?

40. Traditional NPV Valuation of R&D
Year 1 2
Initial Cost
(0.1)
Develop-
(1.1)
ment
License
0.5*2
Revenues
0.5*0.1
Present
(0.1)
(1)
0.868
Value

41. Tree for NPV Valuation of R&D
Project should be rejected
Com Good (1.1/1.1)
0.5
2/1.1^2
Com Bad (1.1/1.1)
0.1/1.1^2
Fund (0.1)
Do Not Fund

42. Flexibility Perspective of R&D
Develop only if $2000 license is expected
Year 1 2
Initial Cost
(0.1)
Develop-
0.5*(1.1)
ment
License
0.5*2
Revenues
0.5*0
Present
(0.1)
(0.5)
0.826
Value

43. Tree for Flexibility View of R&D
NPV = + 226
Should accept project
Commit
(1.1/1.1)
2/1.1^2
Abandon
Good
0.5
Com (1.1/1.1)
0.1/1.1^2
Bad
Fund
(0.1)
Do Not Fund

44. Lessons from R&D Example
Ability to abandon project has significant value
Limits downside
Continue only if advantageous
Standard NPV misses option value completely
Fails to consider effect of intelligent management decisions
Standard NPV distorts value when there is risk
Assumes that: NPV with expected values = expected NPV
“Flaw of the Averages” see article by Savage cited on web
However: Consequences of scenarios have asymmetries
Example, production costs often not linear with volume
Decision analysis has the advantage of recognizing value of flexibility

45. Decision Analysis can be Impractical
Decision Analysis is computationally reasonable for a few stages.
However, when we are talking about many stages, and complicated patterns of uncertainties, the analysis may become impractical
Case for power plant burners either flexible (gas or oil) compared to Fixed (either gas or oil)

46. Example: Market Risk of Production
Case of Flexible Burner on Power Plant
Turbines for electric power generation can be powered by
Gas burners
Oil burner
Flexible, dual use burner (accepts either oil or gas)
Fixed technologies (gas or oil) cost less to acquire than more complex flexible burner
Under what conditions might flexible systems be valuable?

47. Specifics of Flexible Burner case
Based on Kulatilaka and Marcus paper
Price of gas: fixed at $1 per energy unit
Price of oil: increases over time
In Year 1 oil costs $0.75 per energy unit
Price increases 5% per year
Discount cash flows at 10%
Installation occurs in Year 0
Operations start in Year 1
Revenues are independent of technology
What is the NPV for each burner?

48. Oil burner cheaper to operate until Year 6
Base Case: Oil and Gas Prices assumed Known with Certainty
Oil burner cheaper to operate until Year 6
Oil and Gas Prices
$0.85
$0.95
$1.05
$1.15
$1.25 5 10
Year
Price
Oil
Gas
$0.75

49. Cash Flows Under Certainty

50. Results of Certainty Case
Ranking of technologies
Oil Flexible Gas
Oil burner captures early cost advantages over gas
Time value of money means early gains more significant than later losses
Oil burner also better than flexible
Both capture cost advantages early-on
Flexible advantageously switches to gas in Year
Extra cost of acquiring flexible > later gains
Critical assumption: input prices are predictable

51. What if oil could follow one of three price paths?
More Realistic Case:
Uncertainty in Oil Prices
What if oil could follow one of three price paths?
Oil Prices
$1.80
$1.40
High
Medium
Price
$1.00
Low
$0.60
$0.20 5 10
Year

52. Cash Flows with Uncertainty1 2 3 4 5 6 7 8 9 O i l P n t R v u . C o s ( H g h ) p = M d i u m ) p = . 4 2 5 7 9 8 3 1 6 C o s t ( L w A v g P V N e a h F l - . 2 9 8 6 5 4 3 N P V F l e x i b a n t R v u 1 7 C o s ( H g h ) p = M d m
0.24
1.00 1 1 . C o s t ( L w ) p = 3 9 4 5 7 2 8 6 A v g P V N e a h F l - 1 .
0.63 .

53. Results of Uncertainty Case
Rank of technologies
Flexible -- Oil Gas
Flexible technology enabled advantageous switching
For high oil price: dual technology better than oil only
For high gas price: dual better than gas alone
Benefits accrue early on when uncertainty in prices is considered
Operating cost savings outweigh additional acquisition costs

54. Lessons from Burner Example
Real Situation can be VERY complicated
Prices Change Rapidly
They may go up and down in many pathways
The switch between fuels can be exercised often
Decision Analysis can be Impractical
Simple Example Situation Already Difficult
Analysis assumed fixed Discount Rate, But
Discount rate should reflect volatility of prices
As risk changes, so should discount rate
Cannot change discount rate in decision analysis
Another Method Required!!! => Options Analysis

55. Decision Analysis May be Impractical
Analysis may be too complicated
Situation may change too often so that analysis too confused
Example: Prices for Basic Resources fluctuate rapidly up and down
Inadequate basis for Choosing discount rate
When nature of risk constantly changing,
… discount rate should also be changing
… No single discount rate adequately covers situation
See Presentation on Valuation for details