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Payoff from Options

The payoff from an option at expiration depends on the relationship between the strike price and the underlying asset's price at that time.

Call Option Payoffs:

  • Buyer (Long Call):

    • Payoff: Max(0, Underlying Asset Price at Expiration - Strike Price)
    • Profit: Payoff - Premium Paid
    • Maximum Profit: Unlimited (as the underlying asset price can theoretically rise indefinitely)
    • Maximum Loss: Premium Paid

  • Seller (Short Call):

    • Payoff: -Max(0, Underlying Asset Price at Expiration - Strike Price)
    • Profit: Premium Received - Payoff
    • Maximum Profit: Premium Received
    • Maximum Loss: Unlimited (as they have to sell the asset at the strike price, no matter how high the market price goes)

Put Option Payoffs:

  • Buyer (Long Put):

    • Payoff: Max(0, Strike Price - Underlying Asset Price at Expiration)
    • Profit: Payoff - Premium Paid
    • Maximum Profit: Strike Price - Premium Paid (occurs if the underlying asset price goes to zero)
    • Maximum Loss: Premium Paid

  • Seller (Short Put):

    • Payoff: -Max(0, Strike Price - Underlying Asset Price at Expiration)
    • Profit: Premium Received - Payoff
    • Maximum Profit: Premium Received
    • Maximum Loss: Strike Price - Premium Received (occurs if they have to buy the asset at the strike price, and the market price drops to zero)

Example (Call Option):

  • Strike Price: $60
  • Premium: $4
  • Underlying Asset Price at Expiration: $70

Buyer (Long Call):

  • Payoff: Max(0, $70 - $60) = $10
  • Profit: $10 - $4 = $6

Seller (Short Call):

  • Payoff: -Max(0, $70 - $60) = -$10
  • Profit: $4 - $10 = -$6

Example (Put Option):

  • Strike Price: $40
  • Premium: $3
  • Underlying Asset Price at Expiration: $35

Buyer (Long Put):

  • Payoff: Max(0, $40 - $35) = $5
  • Profit: $5 - $3 = $2

Seller (Short Put):

  • Payoff: -Max(0, $40 - $35) = -$5
  • Profit: $3 - $5 = -$2

Payoff Diagrams:

Payoff diagrams are visual representations of the profit or loss from an option position at different underlying asset prices at expiration. They are helpful tools for understanding the risk and reward profiles of different option strategies.

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