11-1 put and call options chapter 11. 11-2 a call option is the right to buy an underlying security...
TRANSCRIPT
11-1
Put and Call Options
Chapter 11
11-2
A call option is the right to buy an underlying security at an exercise (strike) price during a stated time interval.
C = Market value of the call option.
P = Market value of the underlying asset.
E = Exercise price (strike price).
Call Options
11-3
Expiration
Would like to find
value here
0
But first need to
determine value here
11-4
Value of call option at expiration, E = $100P < E P = E P > E
e.g., P = 90 P = 100 P = 110
C = 0 C = 0 C = P – Ee.g., C = 10
out-of-the-money at-the-money in-the-money
11-5
If C < P - E at expiration
Suppose P = 110, E = 100, C* = 6.
Arbitrage:
Buy Call -6
Exercise -100
Sell Underlying +110
Arbitrage Profit +4
Arbitrage Guarantees That C = P – E
11-6
Case of C > P – E:
Suppose P = 110, E = 100, C** = 17.
Arbitrage:
Write Call +17
Exercised +100
Buy Underlying -110
Arbitrage Profit +7
11-7
Value of call option before expiration, E = $100
P < E P = E P > Ee.g., P = 90 P = 100 P = 110
C > 0 C > 0 C > P – Ee.g., C > 10
11-8
Arbitrage
ArbitrageFeasible call prices
C
P – E
P
PE
Call Option Bounds
11-9
Time 0Write Call +CBuy Underlying -P
C – P > 0
ExpirationP < E P = E P > ESell Underlying +P +P = ECall Exercised +ENet +P +E +E
Arbitrage if C > P
11-10
Expiration
Determine Profit or Loss Overlooking Dividends and Interest
Take a position
0
Close entire
position
Profit Profiles
11-11
Expiration
Buy or Call-4
0
Close: Exercise if in-money. Let expire if out-of-money.
11-12
-4
- 4
Price of underlying at expiration
98 100 102104
Buy call -4
Exercise call at expiration
Sell underlying acquiredfrom exercise
Net profit = - C -4
Net profit = – C – E + P -2 0
-4
-100
+102
-4
-100
+104
Profits or Losses for Call Buyer
11-13
Pexp
E
Payoff Function: Buy Call
E + c
Breakeven
– c – c + [Pexp – E]
0
– c
+
–
11-14
$
P at Expiration
+Profit
Call in-money
0
-Loss -4
Call out-of-money
100E 104
Buy Call
Profit Profile for Buying a Call
-C -C+ [P–E]
11-15
Price of underlying at expiration
98 100 102104
Write call +4
Sell underlying
Buy underlying
Net profit = + C
Net profit = + C + E – P +2 0
+4
+100-102
+4
+100-104
+4 +4
Profits or Losses for Call Writer
11-16
$
P at Expiration
+Profit
0
-Loss
+4
104
Write Call
$
P at Expiration
+Profit
Call in-money
0
-Loss
Call out-of-money
100E 104
Profit Profile for Writing a Call
+C +C – [P-E]
11-17
Pexp
E
Payoff Function: Write Call
E + c
Breakeven
+ c + c – [Pexp – E]
0
+ c
+
–
11-18
Price of underlying at expiration
98 100 102104
Buy underlying -100Write call +4Sell underlying at exercise
price when call is exercisedSell underlying at market +100
priceNet profit +4
-100+4
+100
+4
-100+4
+100
+4
-100+4
+98
+2
Profits or Losses from Writing a Covered Call
11-19
$
+Profit
0
-Loss
C Write covered call
Buy underlying security
Call in-moneyCall out-of-money
100E
Underlying asset at expiration
Profit Profile for Writing a Covered Call Option
11-20
Profit
0
Loss
+4Write call
Buy underlying security
Call in-moneyCall out-of-money
100E
Underlying asset at expiration
104
-4
Buy call
Profit Profile for Call Option
11-21
Expiration
A put option is the right to sell the underlying security at an exercise price during a stated time interval.
0
First, find value at
expiration
Put Option
11-22
Value of put option at expiration, E = $100P < E P = E P > E
e.g., P = 90 P = 100 P = 110
Put = E – P Put = 0 Put = 0e.g., Put = 10in-the-money at-the-money out-of-money
Put Options
11-23
Case of Put < E – P:
Suppose P = 90, E = 100, Put* = 6.
Arbitrage:
Buy Put -6
Exercise +100
Buy Underlying -90
Arbitrage Profit +4
If P < E, There is Arbitrage unless Put = E – P
11-24
Case of Put > E – P:
Suppose P = 90, E = 100, Put** = 17.
Arbitrage:
Write Put +17
Exercised -100
Sell Underlying +90
Arbitrage Profit +7
11-25
Value of put option before expiration, E = $100
P < E P = E P > Ee.g., P = 90 P = 100 P = 110
Put > E – P Put > 0 Put > 0e.g., Put = 10in-the-money at-the-money out-of-money
11-26
Price of underlying at expiration
94 97 100104
Buy put -3
Buy underlying
Exercise put
Net profit = – Put -3 -3
Net profit = – Put + E – P +3 0
-3-3 -3
-94 -97
+100 +100
Profits or Losses for Buying a Put Option
11-27
Pexp
E
Payoff Function: Buy Put
E – Put
Breakeven
– put– put + [E – Pexp]
0
– put
+
–
11-28
Profit
0
Loss
Buy put
Put in-money Put out-of-money
100
E
Underlying asset at expiration
97
-3
Shortsell
Profit Profile for Put Option
-PUT-PUT + [E-P]
11-29
Writing a Put
Price of underlying at expiration
94 97 100104
Write put +3
Sell underlying
Put exercised
Net profit = + Put +3 +3
Net profit = + Put – E + P
+3
+97
-100
0
+3+3
+94
-100
-3
11-30
Pexp
E
Payoff Function: Write Put
E – put
Breakeven
+ put+ put – [E – Pexp]
0
+ put
+
–
11-31
Profit
0
Loss
Put in-money Put out-of-money
100
E
Underlying asset at expiration
97
Profit Profile for Writing a Put
+3
+PUT+PUT - [E-P]
11-32
Put-Call Parity
C = Put + P – E D
.price exercise the
of valuepresent the Borrowing
assetunderlying
of Price
puta of
Price
call a of
Price
0 Expiration
Presentvalue = .98 = D
= E D= 98
$1E
100
11-33
Profit of Put-Call Parity0 Expiration
Buy call
Cash flows from portfolio
Cash flows from call
Buy portfolio
If cash flows at Expiration are the same for call as for portfolio, then the Time 0 value must be the same.
11-34
P < E P = E P > ECash flows at expiration from buying callCall 0 0 P – E
Cash flows at expiration from buying put, buying underlying and borrowing present value of exercise pricePut E – P 0 0Underlying +P +P +PLoan –E –E –E
Put-Call Parity
11-35
Implications of Put-Call Parity
C = Put + [P – E D]
= Put + [Levered position in underlying]
5 = 3 + [100 – 98].
11-36
RORon levered
Leverage
iLower return from levered
Higher return from leveredUnlevered
Levered
ROR unleveredii = Interest rate
11-37
CP – E D
Call
PE
If C = Put + P – E D, then C P – E D
P – E
11-38
Arbitrage if C < P – ED
Suppose P = 110, E = 100, D = .98.
P – E = 10.
P – ED = 12.
11-39
Suppose C* = 11.
Arbitrage:
Time 0
Buy Call -11
Short Underlying +110
Lend ED -98
Arbitrage Profit +1
11-40
P < E P = E P > E
Call 0 0 P – E
Buy Underlying -P -P -P
Receive E +E +E +E
Net E – P > 0 E – P = 0 0
Expiration
11-41
Call--greater value of call
1. P--greater value of underlying
2. E--lower value of exercise price
3. Greater time to expiration
4. Higher volatility of underlying
Factors Affecting the Value of a Call Option
11-42
Impact of Longer Remaining Life on the Value of a Call Option
C
P
C2 has a longer life than C1
P ED is higher for C2
because D2 < D1
C 2
C 1
P EP ED 1
P ED 2
E
11-43
Call Option of Security 1Prices of underlying 90 100 110Value of call option 0 0 10Probability 1/3 1/3 1/3Mean value = (0)(1/3) + (0)(1/3) + (10)(1/3) = 3.33
Call Option of Security 2Prices of underlying 80 100 120Value of call option 0 0 20Probability 1/3 1/3 1/3Mean value = (0)(1/3) + (0)(1/3) + (20)(1/3) = 6.67
Value of a Call
11-44
Impact of the Volatility of the Underlying Asset on the Value of a Call Option
C
P
C2 has greater volatility of underlying asset
C 2
C 1
P EP E
D
E