Call & Put Payoffs

Call & Put Payoffs

Options are financial contracts that give the holder the right (but not obligation) to buy or sell an asset at a predetermined price called the strike price (K).

Call Option Payoff

A call option gives the right to buy the asset. At expiration, with the asset at price S:

• If S > K: exercise the option, profit = S - K
• If S ≤ K: let the option expire worthless, profit = 0

$\text{Call Payoff} = \max(S - K, 0)$

Put Option Payoff

A put option gives the right to sell the asset. At expiration:

• If S < K: exercise the option, profit = K - S
• If S ≥ K: let the option expire worthless, profit = 0

$\text{Put Payoff} = \max(K - S, 0)$

Example

If K = 100:

• Stock at 110 → call pays 10, put pays 0
• Stock at 90 → call pays 0, put pays 10

Implement both payoff functions below.