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FINC4101 Investment Analysis
Instructor: Dr. Leng LingTopic: Introduction to options
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Learning objectives1. Define call and put options.
2. Understand the various features of options: exercise price, option premium, option exercise, American vs. European.
3. Describe how options trading is organized.
4. List the various types of option contracts.
5. Compute the payoff and profit of call option holder, call option writer, put option holder and put option writer.
6. Describe the composition of various option strategies.
7. Compute the payoff and profit of various option strategies.
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Concept Map
Foreign Exchange
Derivatives
Market Efficiency
Fixed Income
Equity
Asset Pricing
Portfolio Theory
FI400
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Derivative security A derivative transaction involves no actual transfer of ownership of the underlying assets at the time the contract is initiated. A derivative represents an agreement to transfer ownership of underlying assets at a specific place, price, and time specified in the contract. Its value (or price) depends on the value of the underlying assets.
The underlying assets: stocks, bonds, interest rates, foreign exchanges, index, commodities, some derivatives, etc.
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What is an option?
A derivative security that gives the
holder the right to buy / sell
an asset (the “underlying”)
at a specified price (“exercise price”)
on or before the option expiration date.
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Two types of options:Call vs. Put options
Call option Gives holder the right to buy an asset at
a specified exercise price on or before a specified expiration date.
Put option Gives holder the right to sell an asset at a
specified exercise price on or before a specified expiration date.
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Exercise price Exercise price
For a call option, it is the price set for buying the underlying asset.
For a put option it is the price set for selling the underlying asset.
Exercise price is also called the strike price.
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Option premium Options are financial assets. If you want an option, you
have to buy it from an option seller (counterparty). The purchase price or cost of an option is the option
premium. The option seller earns the option premium. The option premium is an immediate expense for the
buyer and an immediate return for the seller, whether or not the owner (buyer) ever exercises the option.
In option markets, to sell an option is to “write” an option. An option seller is also called an “option writer”.
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Examples At March 1, XYZ stock’s spot price = $110. A
trader buys a call option on XYZ at strike (exercise) price = $100/share. The right lasts until August 15, and the price (option premium) of this call option is $15/share.
At March 1, ABC stock’s spot price = $100. A trader buys a put option to on ABC at strike (exercise) price = $120/share. The right lasts until August 15, and the price (option premium) of this put option is $22/share.
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The long and short of it…
If you buy an option, then you are “long the option” or “long option” or you have a
“long position”.
If you sell an option, then you are “short the option” or “short option” or you have
a “short position”.
Example: if you buy a call option, you are “long call”.
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Buyer (Long) Seller (Short)
Call- Right to buy the underlying
(i.e. to exercise the option)- Pays the premium
- Obligation to sell the underlying, if buyer exercises the option
- Receives the premium
Put- Right to sell the underlying
(i.e. to exercise the option)- Pays the premium
- Obligation to buy the underlying, if buyer exercises the option
- Receives the premium
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Options trading (1) Option contracts are traded in two types
of markets:
1. Over-the-counter (OTC) markets
2. Exchanges, such as: Chicago Board Options Exchange (CBOE) Chicago Mercantile Exchange (CME) International Securities Exchange Option Clearing Corporation (OCC)
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Options trading (2)
OTC
1. Option contract can be customized to needs of trader.
2. Difficult to trade. Secondary market illiquid.
Exchanges
1. Option contracts are standardized by maturity dates and exercise price.
2. Easy to trade. Secondary market is liquid.
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Options on IBM June 7, 2004Source: Wall Street Journal Online Edition, June 8, 2004.
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Underlying asset Individual stocks Stock market indexes
S&P 100, S&P 500, DJIA, Nikkei 225, FTSE 100 etc.
Futures Foreign currency Treasury bonds, Treasury notes
And many others.
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Option exercise (1)
To “exercise a call option” means to use the option to buy the underlying asset at the exercise price.
To “exercise a put option” means to use the option to sell the underlying asset at the exercise price.
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Option exercise (2)Question: When do you exercise an option?
Answer: Simple. Only when it’s optimal to do so. That is, when you are better off exercising the option.
“Buy low, sell high”
Question: What if exercising the option does not make me better off?
Answer: Simple. Don’t exercise. After all, it’s just an option.
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American vs. European options American option: Holder has the right to exercise
the option on or before the expiration date.
European option: Holder has the right to exercise the option only on the expiration date.
Most traded options in the US are American-style. Exceptions: foreign currency options, some stock index options.
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Payoff of Long Bond Position at Expiration
-30
-25
-20
-15
-10
-5
0
5
10
15
20
25
30
0 5 10 15 20 25 30 35 40
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Payoffs of a Call OptionLong Call at $20 Short Call at $20
-30
-25
-20
-15
-10
-5
0
5
10
15
20
25
30
0 5 10 15 20 25 30 35 40
-30
-25
-20
-15
-10
-5
0
5
10
15
20
25
30
0 5 10 15 20 25 30 35 40
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Profit/Loss of a Call OptionLong Call at $20 Short Call at $20
-30
-25
-20
-15
-10
-5
0
5
10
15
20
25
30
0 5 10 15 20 25 30 35 40
-30
-25
-20
-15
-10
-5
0
5
10
15
20
25
30
0 5 10 15 20 25 30 35 40
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Profit/Loss of Long and Short on Call Option
-30
-25
-20
-15
-10
-5
0
5
10
15
20
25
30
0 5 10 15 20 25 30 35 40
-30
-25
-20
-15
-10
-5
0
5
10
15
20
25
30
0 5 10 15 20 25 30 35 40
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Payoffs of a Put OptionLong Put at $20 Short Put at $20
-30
-25
-20
-15
-10
-5
0
5
10
15
20
25
30
0 5 10 15 20 25 30 35 40
-30
-25
-20
-15
-10
-5
0
5
10
15
20
25
30
0 5 10 15 20 25 30 35 40
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Profit/Loss of a Put OptionLong Put at $20 Short Put at $20
-30
-25
-20
-15
-10
-5
0
5
10
15
20
25
30
0 5 10 15 20 25 30 35 40
-30
-25
-20
-15
-10
-5
0
5
10
15
20
25
30
0 5 10 15 20 25 30 35 40
25
Profit/Loss of Long and Short on Put Option
-30
-25
-20
-15
-10
-5
0
5
10
15
20
25
30
0 5 10 15 20 25 30 35 40
-30
-25
-20
-15
-10
-5
0
5
10
15
20
25
30
0 5 10 15 20 25 30 35 40
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Call Option’s Payoff/Profit at Expiration Payoff for a Long Call:
Profit for a Long Call: payoff - option premium
Payoff for a Short Call:
Profit for a Short Call: option premium + payoff
XSif
XSifXS
T
TT
0
XSif
XSifXS
T
TT
0
)(
27
Put Option’s Payoff/Profit at Expiration Payoff for a Long Put:
Profit for a Long Put: payoff – option premium
Payoff for a Short Put:
Profit for a Short Put: option premium + payoff
XSif
XSifSX
T
TT
0
XSif
XSifSX
T
TT
0
)(
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Example A trader short a Call at X=20 with a premium of
$5. At maturity, the stock price is 30. What is the profit/loss to this trader?
Profit/Loss = 5 + [-(30-20)] = 5 -10 = -5
A trader long a Put at X=30 with a premium of $5. At maturity, the stock price is 15. What is the profit/loss to this trader?
Profit/Loss = (30-15) - 5 = 15 - 5 = 10
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Call option: Payoff & Profit at expiration (1)
Consider a call option on a share of IBM stock with an exercise price of $80 per share. Suppose this call option expires on July 16, 2004. Suppose today is the expiration date. The call option price (premium) was $5.
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Call option: Payoff & Profit at expiration (2)
1. Are you better off exercising the option?
2. What is the payoff from the option exercise?
3. What is the profit from the option exercise?
Answer these questions if IBM’s stock price is (a) 95, (b) 76 and (c) 81.
What is the breakeven point for this call option? Breakeven point is the stock price at which
profit is zero.
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Payoff & profit diagram of call option holder at expiration
-6
-4
-2
0
2
4
6
8
10
12
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Stock price at expiration
Pay
off/
prof
it
call payoff 0 0 0 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
call profit -5 -5 -5 -5 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95
cost of option
Payoff
Profit
Break even point
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Payoff and profit of call option writer
Compute payoff, profit and breakeven point, if the stock price at expiration is
(a) 95, (b) 76 and (c) 81.
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Payoff & profit diagram of call option writer at expiration
-20
-15
-10
-5
0
5
10
Stock price at expiration
Payo
ff/ p
rofit
call w riter payoff 0 0 0 0 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 -11 -12 -13 -14 -15
call w riter profit 5 5 5 5 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10
76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95
Break even point
option premium
Payoff
Profit
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Call Review Which of the following statements about the value (i.e.,
payoff) of a call option at expiration is false?
a. A short position in a call option will result in a loss if the stock price exceeds the exercise price.
b. The value of a long position equals zero or the stock price minus the exercise price, whichever is higher.
c. The value of a long position equals zero or the exercise price minus the stock price, whichever is higher.
d. A short position in a call option has a zero value for all stock prices equal to or less than the exercise price.
35
Put option: Payoff & Profit at expiration (1)
Consider a put option on a share of IBM stock with an exercise price of $80 per share. Suppose this put option expires on July 16, 2004. Suppose today is the expiration date. The put option price (premium) was $3.
36
Put option: Payoff & Profit at expiration (2)
1. Are you better off exercising the option?
2. What is the payoff from the option exercise?
3. What is the profit from the option exercise?
Answer these questions if IBM’s stock price is (a) 89, (b) 70 and (c) 79.
What is the breakeven point for this put option? Breakeven point is the stock price at which
profit is zero.
37
Payoff & profit diagram of put option holder at expiration
-4
-2
0
2
4
6
8
10
Stock price at expiration
Payo
ff/ p
rofit
put payoff 10 9 8 7 6 5 4 3 2 1 0 0 0 0 0 0 0 0 0 0
put profit 7 6 5 4 3 2 1 0 -1 -2 -3 -3 -3 -3 -3 -3 -3 -3 -3 -3
70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89
option premium
Break even point
Profit
Payoff
38
Payoff and profit of put option writer
Compute payoff, profit and breakeven point, if the stock price at expiration is
(a) 89, (b) 70 and (c) 79.
39
Payoff & profit diagram of put option writer at expiration
-10
-8
-6
-4
-2
0
2
4
Stock price at expiration
Payo
ff/ p
rofit
put w riter payoff -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 0 0 0 0 0 0 0 0 0
put w riter profit -7 -6 -5 -4 -3 -2 -1 0 1 2 3 3 3 3 3 3 3 3 3 3
70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89
option premium
Payoff
Profit
Break even point
40
Put Review Consider a put option written on ABC Inc.’s stock. The
put option’s exercise price is $80. Which of the following statements about the value (payoff) of the put option at expiration is true?
a. The value of the short position in the put is $4 if the stock price is $76.
b. The value of the long position in the put is -$4 if the stock price is $76.
c. The long put has value when the stock price is below the $80 exercise price.
d. The value of the short position in the put is zero for stock prices equaling or exceeding $76.
41
Practice 9 Chapter 15: 4, 5, 6.
42
Homework 8
You purchased one IBM July 100 call contract for a premium of $4.00. Assuming that the stock price on the expiration date is $105. What is the payoff and net profit/loss? What is the break even point? Draw the payoff and net profit/loss lines on the diagram.
43
Moneyness (1)—intrinsic value
An option (call or put) is:
1. In the money (ITM) if exercising it
produces a positive payoff to the holder
2. At the money (ATM) if the asset price and
exercise price are equal.
3. Out of the money (OTM) if exercising it
produces a negative payoff to the holder.
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Moneyness (2)
ST < X ST = X ST > X
Call option Out of the money
At the money In the money
Put option In the money
At the money Out of the money
45
Moneyness questions (1) Consider two call options written on ABC Inc.’s
stock. The first call, C1, has an exercise price of $50. The second call, C2, has an exercise price of $70. Both calls have the same expiration date. Today is the expiration date. C1 is in the money while C2 is out of the money. Which of the following is true about ST, the stock price on the expiration date?
a. ST > $50b. ST > $70c. $70 > ST > $50d. ST < $50
46
Moneyness questions (2) Consider two put options written on XYZ Inc.’s
stock. The first put, P1, has an exercise price of $20. The second put, P2, has an exercise price of $35. Both puts have the same expiration date. Today is the expiration date. P1 is out of the money while P2 is in the money. Which of the following is true about ST, the stock price on the expiration date?
a.ST < $20b.ST < $35c. $20 < ST < $35d.ST > $35
47
Option vs. Stock Investment (1) Compared to a stock investment, options offer
1) Leverage Pure option investment magnifies gains and losses
compared to pure stock investment.
2) Insurance Combining options with T-bills (money market fund)
limits losses compared to pure stock investment.
Consider the following…
48
Option vs. Stock Investment (2) Suppose you think Wal-Mart stock is going to appreciate
substantially in value in the next year. The stock’s current price, S0, is $100, and the call option expiring in one year has an exercise price, X, of $100 and is selling at a price, C, of $10. With $10,000 to invest, you are considering three alternatives:
a) Invest all $10,000 in the stock, buying 100 shares.b) Invest all $10,000 in 1,000 options (10 contracts)c) Buy 100 options (one contract) for $1,000 and invest the
remaining $9,000 in a money market fund paying 4% interest annually.
49
Option vs. Stock Investment (3) Compute the rate of return for each
alternative for four stock prices one year from now:
1. $80
2. $100
3. $110
4. $120
50
Option vs. Stock Investment (4)Price of stock 1 year from now
Stock price: $80 $100 $110 $120
a) All stocks (100 shares)
-20% 0% 10% 20%
b) All options (1,000 shares)
-100% -100% 0% 100%
c) Money market fund + 100 options
-6.4% -6.4% 3.6% 13.6%
51
Rate of return to strategies
All options
All stocks
Bills plus options
ST
100
–100
0
– 6.4
Rate of return (%)
100
110
52
Option strategies An option strategy is:
A portfolio of options (and possibly the underlying asset) designed to produce a particular payoff pattern.
We look at the following strategies:1. Protective put (Insurance on portfolio)2. Covered call3. Straddle
53
Protective put Portfolio consisting of a put option and the
underlying asset.
Guarantees that minimum portfolio value (payoff) is equal to the put’s exercise price.
54
Protective put: Payoff & profit at expiration
S0 = initial asset price, and P = put option premium.Cost of the position = asset price + put premium
= S0 + P
ST ≤ X ST > X
Payoff of stock ST ST
Payoff of put X – ST 0
Total payoff X ST
Profit X – (S0+P) ST – (S0 + P)
55
Payoff & profit of protective put position at expiration
56
Protective put problem You establish a protective put position on ABC
stock today by buying 100 shares of ABC stock at $40 per share and buying a 3-month put option contract on the same stock. Each put option has a strike price of $40 and a premium of $8.
1. At the end of 3 months, compute the profit from the position if ABC’s stock price is $30.
2. What is the breakeven stock price for this strategy?
57
Portfolio Insurance
Long 1 stock (portfolio) and Long a Put Option on the stock (portfolio), S=20, X=20, P=5.
-30
-25
-20
-15
-10
-5
0
5
10
15
20
25
30
0 5 10 15 20 25 30 35 40
58
Covered call Writing a call option on an asset together with
buying the asset.
Written option is “covered” because the potential obligation to deliver the stock is covered by the stock held.
Strategy produces immediate cash flows through the sale of the call options.
59
Covered call: Payoff & profit at expiration
S0 = initial asset price, and C = call option premium.Cost of the position = asset price - call premium
= S0 - C
ST ≤ X ST > X
Payoff of stock ST ST
- Payoff of call 0 – (ST – X)
Total payoff ST X
Profit ST – (S0 – C) X – (S0 – C)
60
Payoff & profit of covered call position at expiration
61
Covered call problem You establish a covered call position on XYZ
stock today by buying 100 shares of XYZ stock at $16 per share and writing a 3-month call option contract on the same stock. Each call option has a strike price of $17 and a premium of $0.25.
1. At the end of 3 months, compute the profit from the position if XYZ’s stock price is $14.
2. What is the breakeven stock price for this strategy?
62
Straddle A combination of a call and put, each with
the same exercise price (X) and expiration date (T).
Rationale You believe a stock will move a lot in price but
are uncertain about the direction of the move. Straddle allows you to benefit from a price
move in either direction.
63
Straddle: Payoff & profit at expiration
C = call option premium
P = put option premium
Cost of the position = call premium + put premium
= C + P
ST < X ST ≥ X
Payoff of call 0 ST – X
+ Payoff of put X – ST 0
Total payoff X – ST ST – X
Profit X – ST – (C + P) ST – X – (C + P)
64
Payoff & profit of straddle position at expiration
65
Straddle problems You establish a straddle position on ABC Inc.’s stock by
buying a three-month call option and a three-month put option. Both options have an exercise price of $50. ABC’s current stock price is $50 per share. The call option premium is $5 and the put option premium is $3.
1. Compute the straddle’s profit on the expiration date if ABC’s stock price on expiration date is $60.
2. How far would ABC’s stock price have to fall for you to make a profit on your initial investment?
66
Which strategy? (1) You are the portfolio manager of Nohope Equity Fund. One of your
stock holdings is Refin Corp. Your equity analyst tells you that Refin’s stock price is not expected to rise substantially within the foreseeable future. At the same time, you need to raise cash right now to meet fund redemptions. What would be a simple options strategy to exploit your conviction about the stock price’s future movements and allow you to earn immediate income?
a. Long call.
b. Long put.
c. Protective put.
d. Covered call.
e. Long straddle.
67
Which strategy? (2) PUTT Corporation’s common stock has been trading in
a narrow price range for the past month, and you are convinced it is going to break far out of that range in the next three months. You don’t know whether it will go up or down, however. What would be a simple options strategy to exploit your conviction about the stock price’s future movements?
a. Long call.b. Long put.c. Protective put.d. Covered call.e. Long straddle.
68
Practice 10 Chapter 15: 7,8,11,14 (b),15,20,21, 22, 25
Hints: to graph the payoff diagram of strategies, you need to firstly draw the payoff tables as demonstrated in slide 54, 59, 63. Based on the tables, you can draw the diagram. See the following example, which is the solution to 14 (a).
69
Position S < X1 X1 < S < X2 X2 < S < X3 X3 < S
Long call (X1) 0 S – X1 S – X1 S – X1
Short 2 calls (X2) 0 0 –2(S – X2) –2(S – X2)
Long call (X3) 0 0 0 S – X3
Total 0 S – X1 2X2 – X1 – S (X2–X1 ) – (X3–X2) = 0
X2 – X1
ST
X1 X2
Payoff
X3
70
Determinants of option value The values of call and put options are affected
by:
1. Underlying asset price
2. Exercise price
3. Volatility of the asset price
4. Option’s time to expiration
5. Riskfree interest rate
6. Cash payouts from underlying asset, e.g., dividend.
71
Determinants of call option valueIf this variable increases Value of call option
Asset price, S Increases
Exercise price, X Decreases
Volatility, Increases
Time to expiration, T Increases
Interest rate, rf Increases
Cash payouts e.g., dividend Decreases
72
Determinants of put option valueIf this variable increases Value of put option
Asset price, S Decreases
Exercise price, X Increases
Volatility, Increases
Time to expiration, T Increases/ Uncertain
Interest rate, rf Decreases
Cash payouts e.g., dividend Increases
73
Binomial option pricing model (16.2)
Proposed by Cox, Ross and Rubinstein “Option Pricing: A Simplified Approach”, Journal of
Financial Economics, 1979, 7, 229-263. Replication principle:
Two portfolios producing the exact same future payoffs must have the same value.
Otherwise, there will be opportunities for riskless arbitrage.
Use this model to price European call options.
74
Single-Period Binomial Model (1) S=100, it will move to either 110 or 90 in one year X=100 If the investors borrow money, the interest rate=6% for
one year. What is the price of the European call option?
75
Single-Period Binomial Model (2)
Try to find a synthetic portfolio including stocks and bonds, which will replicate the payoff of a Call option.
Solve:
4528.42
5.0
)06.01(900
)06.01(11010
B
N
BN
BN
76
Single-Period Binomial Model (3) S=100, it will move to either 110 or 90 in one year X=100, r=6% Form a synthetic portfolio: short position in a bond (sell a
bond to borrow money) at $42.4528 and long position in ½ share of stock
after 1 year ST=110 ST=90
Synthetic portfolio stock 55 45 bond -45 -45Net payoff 10 0
Call Call 10 0
77
Single-Period Binomial Model (4)
Since the payoff (value) for the synthetic portfolio is exactly the same as that for the Call option in all circumstances, the price (initial value) of the portfolio must be the same as that of the Call.
55.75472.74528.421005.000 BSNC
78
Another way to Price a call option (1)
Compute the price of a call option written on the stock of ABC Inc. The stock is currently selling for S0 = $100. The stock price will either increase by a factor of u = 2 to $200 or fall by a factor of d = 0.5 to $50 by year end. The call option has a strike price of $125 and a time to expiration of one year. The risk-free interest rate is 8% p.a.
79
Another way to Price a call option (2)
Terms:
Su = u x S0 = year end stock price if price rises to $200
Sd = d x S0 = year end stock price if price falls to $50
C0 = call option price
Cu = call option payoff if stock price is Su
Cd = call option payoff if stock price is Sd
1. Call option payoffs
Cu = 200 – 125 = 75
Cd = 0 (not optimal to exercise)
80
Another way to Price a call option (3)
2) Hedge ratio, H
H = (75 – 0)/(200 – 50) = 75 /150 = 0.5/1
3) Form a portfolio that is short 1 call and long 0.5 shares of ABC stock.
0 0
u dC CH
uS dS-
=-
81
Another way to Price a call option (4)
4) Compute the end-of-period payoff.
Payoff in 1 year for each possible stock price
Sd = $50 Su = $200
Write 1 call 0 -(200 – 125) = -75
Buy 0.5 shares 0.5 x 50 = 25 0.5 x 200 = 100
Total 25 25
Year end payoff is certain!
82
Another way to Price a call option (5)5) Compute present value of $25 with a one-year risk-free
interest rate of 8%.
PV = 25/1.08 = $23.1481
6) Set value of hedged position equal to present value of the certain payoff and solve for call option’s value.
0.5S0 – C0 = 23.1481
50 – C0 = 23.1481
C0 = 26.8519 = 26.85
83
Binomial option pricing model Basic idea:
You can form a portfolio consisting of stock and call options that produces a certain (no-risk) payoff in the future.
This is also called the hedged position. Discounting this payoff at the risk-free rate
gives the portfolio value today. Using this present value and the current stock
price, you solve for the call option price.
84
Another pricing problem You are attempting to value a call option with an
exercise price of $100 and one year to expiration. The underlying stock pays no dividends, its current price is $100, and you believe it has a 50% chance of increasing to $120 and a 50% chance of decreasing to $80. The riskfree interest rate is 10% p.a.
1. What is the hedge ratio?2. Calculate the call option’s value using the
Binomial pricing model. Verify that the call option price is $13.64.
85
Price a call option using hedge ratio
Implication: form a portfolio that is long A shares of stock and short B calls
B
A
dSuS
CCH du
00
86
Price a put option using hedge ratio
Implication: form a portfolio that is long A shares of stock and long B puts
Example: Chapter 16, 8
B
A
dSuS
PPH du
00
87
Multi-period Binomial Tree
88
Put-Call Parity Relationship (1) Links the prices of European call and put
options. Given:
European call option price underlying asset price Riskfree rate
The Put-Call Parity Relationship produces the put price.
89
Put-Call Parity Relationship (2)
Assumptions:
1. Options are European options.
2. Both call and put options are written on the same underlying asset.
3. Underlying asset does not pay any cash flow (e.g., dividends) before option expiration.
4. Continuous compounding.
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Put-Call Parity Relationship (3)
The relationship says that: A portfolio that is long 1 call and short 1 put
has the same payoffs at expiration as…
A portfolio made up of the underlying asset
plus a borrowing position. The riskfree interest
rate is r.
91
Put-Call Parity Relationship (4) Suppose you buy a call option and write a
put option, each with the same exercise price, X, and the same expiration date, T. At expiration, the portfolio payoff:
ST ≤ X ST > X
Long call 0 ST – X
Short put -( X – ST) 0
Total ST – X ST – X
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Put-Call Parity Relationship (5) Compare this payoff to that of a portfolio made
up of: 1 share of stock borrowing equal to the present value of the
exercise price, Xe-rT. At maturity, repay X. At expiration, the portfolio payoff:
ST ≤ X ST > X
Long stock ST ST
Loan repayment - X - X
Total ST – X ST – X
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Put-Call Parity Relationship (3)
0
0
( )rT
C P S PV X
C P S Xe-
- = -
- = -
Call option price
Put option price
Current stock price
r = Riskfree rate (per annum basis)
Time to expiration in years
Present value of exercise price
Using continuous compounding, we have
94
Pricing a put option (1) Put option price, P
0( )rTP C S Xe-= - -
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Practice 11Chapter 16: 5,8,9,29,30
