Call Option Contracts
•
Call option : right to buy an underlying asset at a pre-specified expiration time and exercise price
•
Position
– Long = purchased call option (right to buy asset)
• Payoff = max (0, S
T
– K)
– Short = sold or written call option
• Payoff = opposite of long position = - max (0, S
T
•
Type of option
– K)
– American: Can exercise anytime up to or on the expiration date
– European: Can exercise only on expiration date

Put Option Contracts
•
Put option : right to sell an underlying asset at a pre-specified expiration time and exercise price
•
Position
– Long = purchased put option (right to sell asset)
• Payoff = max (0, K – S
T
)
– Short = sold or written put option
• Payoff = - max (0, K – S
T
)
•
Type : American vs European
• Note:
– Long position in put is a short position in underlying asset, and vice versa

Option Premiums and Profits
•
Premium : up-front cost of purchasing a call or a put option
•
Payoff : option gain or loss upon exercise or expiration; ignores premium
•
Profit : net option gain or loss, including consideration of up-front premium
– Premium is brought forward to exercise / expiration date, for the time value of money, in the profit calculation. (Future value)

Example
• Amy sells Bob a 3-month European call option on one share of XYZ stock
• Suppose XYZ stock is trading at 32.5
• Exercise price = 35
• Premium = 3
• At expiration (time T), suppose:
S
T
=30 S
T
=40
Total payoff [profit/loss]
Amy:
Bob:
0 [ 3]
0 [-3]
-5 [-2]
5 [ 2]

Option Values
• Prior to expiration:
Call Put
–
–
–
In-the-money
At-the-money
Out-of-the-money
S t
S t
S t
> X
= X
< X
S
S
S t t t
< X
= X
> X
•
Intrinsic value : profit that could be made if the option was immediately exercised
– Call: stock price - exercise price
– Put: exercise price - stock price
•
Time value : the difference between the option price and the intrinsic value

Option Values: Payoff Charts
Call – long position:
Payoff
S
T
K
K
Call – short position: S
T
Put – long position:
S
T
S
T
Put – short position:
K
K

Call
Premium
Payoff vs. Profit/Loss:
Long Call Option
Payoff
Profit/Loss
S
T
K

Q: Option Contracts
(From Exam FM Fin Econ Sample Questions)

Q: Option Profit Calculation
(From Exam FM Fin Econ Sample Questions)

Q: Option Profit Calculation
(From Exam FM Fin Econ Sample Questions)

Q: Option Profit Calculation
(From Exam FM Fin Econ Sample Questions)

Q: Option Profit Calculation
(From Exam FM Fin Econ Sample Questions)

Q: Option Profit Calculation
(From Exam FM Fin Econ Sample Questions)

Q: Option Payoff Calculations
(From Exam FM Fin Econ Sample Questions)

Q: Forward and Option Payoffs
(From Exam FM Fin Econ Sample Questions)