1. Introduction to options
Some basic concepts
FIN 819: lecture 6

2. Today’s plan Briefly review the case discussed last week.
Review what we have learned so far
Introduction of options
Definition of options
Position diagrams
No arbitrage argument
Put-call parity
Application of put-call parity
How does stock return volatility affect option values?
FIN 819: lecture 6

3. What have we learned so far?
So far we have discussed or reviewed some fundamental concepts and ideas about valuation
Present value concept
Discounted cash flow approach and the NPV rule
Free-cash flow calculation
Cost of capital (WACC)
CAPM
Levered and unlevered betas
Two cases related to these concepts
FIN 819: lecture 7

4. Introduction to options
What is an option in Finance?
An option is a right or opportunity to do something at a specified price or cost on or before some specified date.
An option, is a contract
Options are everywhere.
IBM offers its CEO a bonus that is related to the stock price (stock options)
IBM postpones investment in a positive-NPV project, even if IBM has capital for taking this investment.
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5. Options Financial options Real options
It depends on what is the underlying asset the option is written in
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6. Options in financial assets
What is an option written in financial assets?
A financial option is a right to sell or buy some financial asset at a specified price or cost on or before some specified date.
(ex: option written on IBM or Dell)
A financial option can be regarded as a contract between sellers and buyers
The financial asset specified in the financial option contract is often called the underlying financial asset.
FIN 819: lecture 7

7. Real Options Real options
Options that are written on real assets are called real options
For example, the option to set up a factory is called a real option
In the next two lectures, we focus on financial options, since it is easier to price them.
FIN 819: lecture 7

8. Now we focus on (financial) options…
Suppose the financial asset is common stock or stock
There are two basic types of options,
Call option
the right to buy a share of stock at a specified price before or on some date.
Put option
the right to sell a share of stock at a specified price before or on some date.
FIN 819: lecture 7

9. Strike Price, Expiration Date
The specified price is called the strike price or exercise price. (the price you would like to buy/sell the underlying stock)
The specified date is called the maturity date or expiration date. (the date by which you want to buy/sell the stock)
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10. Exercising an Option
An option is exercised when the buyer of the option decides to buy or sell the stock at the specified price, at which time the seller must sell or buy the stock at the specified price
Oh yes, according to expiration terms
FIN 819: lecture 7

11. American vs. European Option
Call options
European call option
Buy the stock on the specified date
American call option
Buy the stock on or before the specified date
Put options
European put option
Sell the stock on the specified date
American put option
Sell the stock on or before the specified date
Key Difference?
European (1 date),
American (many dates up until expiration date)
FIN 819: lecture 7

12. Option Obligations
Options are rights (to the buyer), and are obligations (to the seller)
This means that:
the buyer of an option may or may not exercise the option.
However, the seller of the option must sell or buy the underlying assets if the buyer decides to exercise the option.
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13. Payoff or cash flows from options at expiration date
The payoff of a call option with a strike price K at the expiration date T is
Where S(T) is the stock price at time T
The payoff of a put option with a strike price K at the expiration date T is
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14. Example on payoffs
Suppose that you have bought one European put and a European call on stock ABC with the same strike price of $55. The payoffs of your options certainly depend on the price of ABC on expiration
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15. Option payoff at expiration
Call option value (graphic) given a $55 exercise price.
Call option $ payoff
$20
Share Price
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16. Option payoff Put option value (graphic) given a $55 exercise price.
50 55
Share Price
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17. Option payoff
Call option payoff (to seller) given a $55 exercise price.
Call option $ payoff 55
Share Price
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18. Option payoff
Put option payoff (to seller) given a $55 exercise price.
Put option $ payoff 55
Share Price
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19. Some examples
Please draw position diagrams for the following investment:
Buy a call and put with the same strike price and maturity (straddle)
Buy two calls with different strike prices (K1 and K2) and sell two calls with a strike price that equals the average strike price of the two calls you bought. (butterfly)
Buy a stock and a put (protective put)
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20. Option payoff Straddle - Long call and long put Position Value
Share Price
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21. Option Value Butterfly Position Value Share Price K1 K2
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22. Option payoff Protective Put - Long stock and long put Protective Put
Position Value
Share Price
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23. Form your desired portfolios
Suppose you have access to risk-free securities, stocks, calls and puts. Can you form a portfolio now to have the following payoffs at time T?
Position Value K K K1
Share Price
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24. No arbitrage concept or one price rule
If two securities have the exactly the same payoff or cash flows in every state of future, these two securities should have the same price; otherwise there is an arbitrage opportunity or money making opportunity.
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25. Example
Two treasury bonds A and B both have the maturity of 10 years and coupon rate of 6%. Certainly, they should have the same price; otherwise suppose that A is more expensive than B. You can make money by buying B and short selling A. You can make money PA-PB.
Do you like this beautiful idea?
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26. Put-Call Parity
Let P(K,T) and C(K,T) be the prices of a European put and a call with strike prices of K and maturity of T. Then we have or
Where
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27. Let’s show put-call parity
We can first use position diagrams to show put-call parity
We can also simply use the payoffs in the future to show put-call parity
This exercise is a good way of getting used to the ideas of the single price rule or no arbitrage argument.
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28. Position diagram
Payoff of investing PV(K) in risk-free security and buying a call
Position Value K
Share Price
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29. Position diagram Payoff of long stock and long put Position Value
Share Price
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30. The conclusion
Since both portfolios in the previous two slides give you exactly the same payoff, they must have the same price. That is,
FIN 819: lecture 7

31. Another way of showing put-call parity
Consider the following portfolio:
Buy the stock
Buy a European put option
Borrow the present value of the strike price
Where Rf= 1+ rf
The cost of this portfolio is
The payoff of this portfolio
If ST >= K, the payoff is ST-K
If ST < K, the payoff is 0.
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32. Portfolio (continues)
Final payoff of the portfolio
Portfolio
Position
ST<K
ST>K
Stock S0 ST ST -K
Borrowing -K
Put P
K - ST
Total
ST - K
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33. The conclusion
Since the portfolio and a call option have exactly the same payoff, their prices should be the same. That is,
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34. Applications of option concepts and put-call parity
One important application of option concepts and put-call parity is the valuation of corporate bonds.
For example, suppose that a firm has issued $K million zero-coupon bonds maturing at time T. Let the market value of the firm asset at time t be V(t).
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35. Applications of option concepts and put-call parity (continue)
Payoff of equity
Position Value K
Market value of asset
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36. Applications of option concepts and put-call parity (continue)
So based on the position payoff diagram in the previous slide, we can see that the value of equity is just the value of a call option with strike price K.
Then bond value =Asset value –equity value (value of call: C(K,T)
Using the put-call parity, we have
Bond value=PV(K)- P(K,T) (value of put )
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37. Applications of option concepts and put-call parity (continue)
Who will bear the default cost: equity holders or debt holders?
The value of risky corporate bonds is equal to the value of the safe corporate bonds minus the cost of default.
When will the firm default?
At time T, if the value of asset is less than K, the firm will default. P(K,T) is the cost of this default to bond holders.
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38. The value of option
Since an option is a right to buy or sell securities, its price is non-negative.
If the option price is negative, what will happen?
If the option value must be non-negative, can you use what you have learned to value a call option or put option by considering the following two things
Expected cash flows
The risk of options
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39. Volatility and option value
For options, the larger the volatility of the underlying asset, the larger the value of the option
For stocks, the larger the volatility of the underlying asset, the smaller the value of stocks
Why ?
FIN 819: lecture 7