1. Lec 9 Intro to Option contracts
Lec 1: Intro to Options Contracts (Hull Ch 9)
Call Options.
If you buy a CALL option on IBM,
1. You have the right, but not the obligation,
to buy 100 shares of IBM at a specified price (Exercise Price).
2. The price of the call is known as Call Premium.
3. Call will expire at a specified date (Expiration Date).
• American vs. European Options
Example: Buy a European December 70 call on IBM for $5.
• Expiration date = 3rd Friday of December
• Exercise price = K = $70
• Call premium (C0) = $5 ( x 100) = $500
Lec 9 Intro to Option contracts
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2. Lec 9 Intro to Option contracts
Cash Flow Analysis:
At t = 0 (now) you pay $500 to seller of call.
at t = Expiration, Possible scenarios:
Spot Price (ST )
Exercise?
Value of
{ +CT }
Gain or Loss
➀ $50 No
-$500
➁ 60
➂ 70
Yes/No
➃ 80
Yes
$1,000
+ 500
➄ 90
$2,000
+1,500
Lec 9 Intro to Option contracts
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3. Lec 9 Intro to Option contracts
Question: Why buy a call?, Why not buy the stock itself?
Assume S0 = $70. You expect stock price to ↑ to ST = $90 .
(N.B. This is the buyer's subjective expectation).
You have two choices:
Buy stock for $70, or buy a call for $5.
In December, the possible outcomes are: ST
Exercise?
Value of { CT }
ROR on {+C}
ROR on { +S}
➀ $50 NO
-100%
-28.6%
➁ 60
-100
-14%
➂ 70
No/Yes
➃ 80
Yes
$10
+100%
14%
➄ 90
$20
28.6%
Lec 9 Intro to Option contracts
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4. Lec 9 Intro to Option contracts
So, what do we learn from this exercise?
1. Long Call is appropriate for a VERY bullish investor
2. {+C} requires a (relatively) small investment
(equivalent to borrowing 93% of S0 = $70).
3. Max Loss = $500 (some degree of Downside Protection)
4. BUT {+C} is much more risky than {+S}
Q: buyer expects the price to go from $70 to $90.
Does the seller share this belief?
What about the market? Is the market Bullish or Bearish?
What do you think about the following ad?
... Another market that has our attention is for Heating Oil.
For the past 10 years, between the August low and the seasonal high, the price of heating oil increases by about 20¢ a gallon for potential profit of over $80,000 on just a $10,000 investment.
If you follow this ad, you will become rich!
Buy low (in summer) and Sell high (in winter).
Lec 9 Intro to Option contracts
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5. Lec 9 Intro to Option contracts
Sell a call (write a call, “naked” call writer, short call, -C)
If you sell a call,
you have the obligation (but not the right) to sell 100 shares
of IBM stock for $X,
if the "option holder" (the buyer) decides to exercise the call.
Example: Sell a December 70 call on IBM stock for $5.
• Expiration date = 3rd Friday of December
• Exercise price = $70
• Call premium (C0) = $5 ( x 100)
Cash Flow Analysis:
At t = 0 you (Short, call writer) receive $500 from call buyer
Lec 9 Intro to Option contracts
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6. Lec 9 Intro to Option contracts
At T = Expiration. Possible scenarios:
Question:
Suppose ST = $90 and the call writer already owned the stock, would the loss still be $20?
Spot Price (ST )
Exercise?
Value of { -CT}
Gain or Loss
➀ $50 No
+$500
➁ 60
➂ 70
Yes/No
➃ 80
Yes
- $1,000
- 500
➄ 90
- $2,000
- 1,500
Lec 9 Intro to Option contracts
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7. Lec 9 Intro to Option contracts
So, why would you sell a call?
1. Receive Cash immediately!
2. You are Bearish on the stock.
(a good “Conservative” Bearish strategy).
Notes:
• Excluding commissions, the options market is a zero-sum game.
Including transactions costs, it is a negative-sum game.
• The call premium reflects the "markets" expectation of the future
stock price.
Hence, to be successful at this game you must know
more than the market (or be lucky!).
Lec 9 Intro to Option contracts
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8. Lec 9 Intro to Option contracts
PUT Options.
Buy a Put (long a put, +P)
If you buy a PUT option on BAC,
1. You have the right, but not the obligation,
to sell 100 shares of BAC at a specified price (Exercise Price).
2. The put price is known as the Put Premium.
3. Put will expire at a specified date (Expiration Date).
Example: Buy a European December 70 Put on BAC for $3.
• Expiration date = 3rd Friday of December
• Exercise price = $70
• Put premium (P0) = $3 ( x 100) = $300
Lec 9 Intro to Option contracts
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9. Lec 9 Intro to Option contracts
Cash Flow Analysis:
At t = 0 (now) you pay $300 to seller of Put option.
at t = Expiration, Possible scenarios:
So, why Buy a put?
1. You are Very Bearish (“Aggressive Strategy”), and
2. Alternative to a short sale
Spot Price (ST )
Exercise?
Value of {+PT }
Gain or Loss
➀ $50
Yes
$20
$17
➁ 60
$10 $7
➂ 70
Yes/No
-$3
➃ 80 No
- 3
➄ 90
Lec 9 Intro to Option contracts
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10. Lec 9 Intro to Option contracts
Sell a Put (Write a Put, write a “naked” put, short put, -P)
If you Short a put (i.e. sell a put), you have the obligation,
but not the right, to buy 100 shares of XYZ stock
at a strike price of $X, for a specified period of time.
Example: Sell a December 70 PUT on BAC stock for $3.
• Expiration date = 3rd Friday of December
• Exercise price = $70
• Put premium (P0) = $3 ( x 100)
Cash Flow Analysis:
At t = 0 you (Writer) receive $300
Lec 9 Intro to Option contracts
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11. Lec 9 Intro to Option contracts
At Expiration time in December. Possible scenarios:
Why sell a put?
1. Receive cash now, and (if stock price ↑ ) there is no cost later.
2. It is a “Conservative Bullish” Strategy
3. You actually want to buy the stock. For example,
Let S0 = $70; if the stock price falls below $70 put is exercised,
you pay $70 and receive the stock.
Actual purchase price = = $67 (< S0).
Spot Price (ST )
Exercise?
Value of {+PT }
Gain or Loss
➀ $50
Yes
- $20
- $17
➁ 60
- $10
- $7
➂ 70
Yes/No
+ $3
➃ 80 No
+ 3
➄ 90
Lec 9 Intro to Option contracts
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12. Lec 9 Intro to Option contracts
In sum:
If you expect the stock price to go up:
Buy a call (Aggressive Bullish strategy)
Sell a put (less aggressive, a “Conservative Bullish” strategy).
If you expect price to go down:
Buy a put (Aggressive Bearish strategy)
Sell a call (less aggressive, “Conservative Bearish” bet).
Remember:
-C = obligation to sell +C = right to buy
-P = obligation to buy +P = right to sell
Alternatively:
LONG ( + ) SHORT ( - )
CALL right to BUY may have to SELL
PUT right to SELL may have to BUY
Lec 9 Intro to Option contracts
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13. EMBA Lec 5 Intro to Option contracts
Put-Call Parity (Law of One-Price) {+S, +P} = {+C, +B}
Example: {+Stock + Put(K=40)} vs. {+Call(K=40) +Bond(FV = $40)}
Intuition
If ST > $40, Stock + Put = Stock (because Put is worthless).
Call+Bond = Stock (Use Call plus proceeds from bond to buy the stock)
If ST < $40, Stock + Put = $40 (Sell stock thru the Put and receive $40)
Call +Bond = $40 (Call is worthless. But the bond matures for $40)
Spot Price (ST )
{+S+P}
{+C+B}
$30
30+10=40
0+40 = 40 35
35+5=40 40 45
5+40 = 45 50
10+40 = 50
EMBA Lec 5 Intro to Option contracts
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14. Lec 9 Intro to Option contracts
(How to Create Synthetic Securities )
Create a Synthetic Long-Stock position.
Example: Long Call(X=40), Short Put(X=40), Buy a bond(FV = $40)
If ST > $40,
Call is in the money. Use $40 from the bond to exercise call.
Put is worthless. You own stock, just like if you bought the stock itself.
If ST < $40,
Call is worthless. Put is in the money, You are obligated to buy the stock for $40. Again, you own stock.
Spot Price (ST )
{+C}
{-P}
{+B}
Total CF
$30
- $10
$40 35 -5 40 45 5 50 10
Lec 9 Intro to Option contracts
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15. Lec 9 Intro to Option contracts
Alternative intuition:
Call captures stock price increases.
Put captures stock price decreases.
Bond is needed to buy the stock at expiration.
{+S} = { +C(X), -P(X), +Bond(FV = $X) }
Lec 9 Intro to Option contracts
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16. Lec 9 Intro to Option contracts
Synthetic Long Call: {+S, +P, - Bond(FV=X=$40) }={+C}
Example:
If ST = $30,
Sell the stock thru the put, receive X=$40. Use it to payback $40 bond
CFT =0 (same as a call)
If ST = $50, Put is worthless.
Sell the stock in spot market. Use $40 to payback loan
CFT = +50 – 40 = $10 (same as the call)
Spot Price (ST )
{+S}
{+P}
{-B}
Total CF
$30
$10
-$40 $0 35 5
-40 40 45 50 10
Lec 9 Intro to Option contracts
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17. Lec 9 Intro to Option contracts
Synthetic T-Bill (i.e. bond) Long. (earn risk-free rate)
{+B} = { +S, -C, +P} X = $40 = face value of bond.
If ST ↑ >40, put is worthless.
Call is in the money ∴ exercised. Hand over stock, receive $40.
Is ST ↓ <40, call is worthless.
Put is in the money ∴ exercise it. Hand over stock to put holder and receive $40.
Thus, we end up with $40 just as if we had bought a bond.
Spot Price (ST )
{+S}
{-C}
{+P}
Total CF
$30
$10
$40 35 5 40 45 -5 50
-10
Lec 9 Intro to Option contracts
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18. Lec 9 Intro to Option contracts
Points to ponder:
1) The common foundation for these synthetic securities is the
Put-Call Parity Relationship: {+S, +P} = {+C, +B}
2. Hence, the following statements are equivalent:
+S = + C - P + B
+C = + S + P - B
+P = - S + C + B
+B = + S - C + P
2) By the law of one price the price today of each asset on left hand side must equal price of portfolio on right hand side.
3) To preclude arbitrage,
Price of {+B} must = Price of a T-Bill (maturity = life of option).
i.e., the ROR on {+B} = {+S, -C, +P} must be the risk-free rate!
Lec 9 Intro to Option contracts
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19. Lec 9 Intro to Option contracts
Thank You
(a Favara)