1. Options

2. Options Financial Options
There are Options and Options
- Financial options
- Real options

3. Options Financial Options
A financial option gives its owner the right (but not the obligation)
to purchase or sell an asset at a fixed price at some future date.
Puts
Calls
Strike price/Exercise price
American/European

4. Table 20.1 Option Quotes for Amazon.com Stock

5. Options Financial Options
Option Pricing
Binomial
- Two state single period
- Law of one price
- Replicating portfolio
Call option, SP 50, No dividend,
Stock will either rise by 10 or fall by 10
Risk free rate is 6%

6. Options Financial Options/Pricing
Stock Bond Call
max (60-50,0) = 10
Stock 50
Bond 1
max (40 -50,0) = 0
60 = up and 40 = down S = Share price and t = number of shares and B = investment in the bond. SP = 50

7. Options Financial Options/Pricing
Value of portfolio containing the stock and the bond must = the value of the portfolio in each state.
60St B = 10
40St B = 0
So St = .5
And B =
60 x x = 10
40 x .5 – 1.06 x = 0

8. Options Financial Options/Pricing
Generalising we get
St = Cu – Cd and B = Cd – Sdt
Su – Sd rf
This gives us the replicable portfolio
The Call option price then follows
C = St + B or 50x.5 – (1) = 6.13

9. Options Financial Options/Pricing
But what about multi period models?
Strike price of 50, Rf = 6%
Periods 60 50 40 40 30 20

10. Options Financial Options/Pricing
We start at the end and work back 60
Max(60 -50,0) = 10 50 40
Max ,0) = 0
This is the same as before therefore St = .5 and B = and the call value at time 1 is 6.13

11. Options Financial Options/Pricing
What if share dropped to 30 in the next period (period 1)? 40
Max (40 – 50, 0) = 0 30
20 Max (30 – 50, 0) = 0
The option is worthless in both states so no portfolio value

12. Options Financial Options/Pricing
Now move back a period
Stock Call 40
Now work out replicating portfolio at time 0
St = Cu – Cd = – 0 =
Su – Sd – 30
B = Cd – Sdt = (0.3065) =
1 + rf

13. Options Financial Options/Pricing
So the Call value at Time 0 is
C = St + B = 40(0.3065) +(-) 8.67 = 3.59

14. Options Financial Options/Pricing
For European options if we let each period shrink to ‘zero’ and have an infinite number of periods then we may use the Black-Scholes formula to calculate the binomial pricing…………..
but we won’t
But remember the important factors in the pricing

15. Options Financial Options/Pricing
The strike price
The stock price
The exercise date
The risk free interest rate
The volatility

16. Options Real Options And there are Real Options
The right to take a particular business decision e.g. a capital investment decision.
Main distinction is that the asset is normally not traded

17. Options Real Options
Until now we have considered a stream of cash flows during the project, starting from today, to determine the NPV
But what about alternatives such as delaying the start or abandoning the project after a while?

18. Options Real Options
To analyse the alternatives we need Decision Trees
A graphical representation of future decisions and uncertainty resolution (B & DeM)

19. Options Real Options Meet (re meet) Megan Goes to markets
Sells, average profit 1,100
Costs of Booth 500, in advance
profit
1,100 – 500 = 600
Go to meet
Stay at home

20. Options Real Options Now add some uncertainty
If it rains (25% chance) she will make a loss = -100
If it is sunny her profit is higher = 1,500

21. Options Real Options 1,500 sunshine 75% Go to meet Rain 25% - 100
- 500
- 100
Stay at home
Decision node
Information node

22. Options Real Options Go to meet or not? Go to meet Stay at home 1,500
Sunshine 75%
Stay at home
Pay for booth
Rain 25%
Go to meet
-100
Don’t pay for booth
Stay at home

23. Options Real Options
So what is the ‘value’ of this real option to Megan?
Expected profit without choice i.e. go to meet regardless
= 1,500 x x .25 = 1,100
Expected profit with choice
= 1,500 x .75 = 1,125
So choice/option worth 25

24. Options Real Options Should Megan pay for the booth?
Expected profit will be = 625
So Yes

25. Options Real Options When else may they be used? Option to delay
Invest now only where NPV is substantially greater than zero
But
What are costs of delay?
What is volatility?
What are costs of investment?

26. Options Real Options Option to Grow Option to Expand Option to Abandon
Option to Prepay