Options

Definitions

• Call Option : A right to buy the underlying
• Put Option : A right to sell the underlying
• European Option : Right only exercised at maturity
• American Option : Right can be exercised at anytime BEFORE maturity.
• Writing (an option) : Selling the option
• Premium : Price or value of an option
• (Option)
  • At the money : strike price == underlying price
  • In the money : immediate exercise is profitable
  • Out the money : immediate exercise is unprofitable

Long Call

• Payoff : max(S(T) - K, 0)
• Profit : max(S(T) - K, 0) - C(t, K, T), where K is the strike price, t is the call price
• Short call is just negative of long call

Long Put

• Payoff : max(K - S(T), 0)
• Profit : max(K - S(T), 0) - P(t, K, T)
• Short put is just negative of long put.