Option Contracts

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 – K) Type of option –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 =30S T =40 Total payoff [profit/loss] Amy:0 [ 3]-5 [-2] Bob:0 [-3] 5 [ 2]

Option Values Prior to expiration: Call Put –In-the-moneyS t > X S t < X –At-the-moneyS t = X S t = X –Out-of-the-moneyS t 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 Payoff K STST K K K STST STST STST Put – short position: Call – long position: Call – short position: Put – long position:

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

Q: Option Contracts (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)