fin 819: lecture 6 introduction to options some basic concepts
TRANSCRIPT
FIN 819: lecture 6
Introduction to options
Some basic concepts
FIN 819: lecture 6
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 7
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
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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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Options
Financial options Real options It depends on what is the underlying
asset the option is written in
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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.
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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.
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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.
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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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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
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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)
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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.
assetbuy toObligationasset sell Right tooptionPut
asset sell toObligationassetbuy Right tooption Call
SellerBuyer
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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
• Where S(T) is the stock price at time T
)0,)(max( KTS
)0),(max( TSK
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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
00051525Put
25155000 Call
8070605040$30PriceStock
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Option payoff at expiration
Call option value (graphic) given a $55 exercise price.
Share Price
Cal
l opt
ion
$ pa
yoff
55 75
$20
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Option payoff
Put option value (graphic) given a $55 exercise price.
Share Price
Put
opt
ion
valu
e
50 55
$5
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Option payoff
Call option payoff (to seller) given a $55 exercise price.
Share Price
Cal
l opt
ion
$ pa
yoff
55
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Option payoff
Put option payoff (to seller) given a $55 exercise price.
Share Price
Put
opt
ion
$ pa
yoff
55
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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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Option payoff
Straddle - Long call and long put
Share Price
Pos
itio
n V
alue
Straddle
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Option Value
Butterfly
Share Price
Pos
itio
n V
alue
K1 K2
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Option payoff
Protective Put - Long stock and long put
Share Price
Pos
itio
n V
alue Protective Put
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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?
Share Price
Pos
itio
n V
alue
K
K K1
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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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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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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
TfKRTKPSTKC ),(),( 0
),(),( 0 TKPSKRTKC Tf
or
ff rR 1Where
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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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Position diagram
Payoff of investing PV(K) in risk-free security and buying a call
Share Price
Pos
itio
n V
alue
K
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Position diagram
Payoff of long stock and long put
Share Price
Pos
itio
n V
alue
K
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The conclusion
Since both portfolios in the previous two slides give you exactly the same payoff, they must have the same price. That is,
),(),( 0 TKPSKRTKC Tf
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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.
TfKR
TfKRPS 0
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Portfolio (continues)
Final payoff of the portfolio
ST<K ST>KPortfolio
Stock
Borrowing
Put
Total
S0
P
ST
K - ST
ST
-K -K
0
0 ST - KTfKRPS 0
TfKR
Position
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The conclusion
Since the portfolio and a call option have exactly the same payoff, their prices should be the same. That is,
TfKRTKPSTKC ),(),( 0
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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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Applications of option concepts and put-call parity (continue)
Payoff of equity
Market value of asset
Pos
itio
n V
alue
K
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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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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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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
FIN 819: lecture 7
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 ?