Question

What is the maximum loss for an option buyer?

Hint:

An option buyer has limited downside risk (capped at the premium paid) and theoretically unlimited upside potential.

Answer 1

Step 1: Analyzing Option Buyer Rights:
An option contract gives the buyer the right, but not the obligation, to buy (Call) or sell (Put) an underlying asset at a pre-specified strike price. To purchase this right, the buyer pays a non-refundable fee (premium) to the seller.

Step 2: Formulating the Downside Limit Mathematically:
Let $S_T$ be the spot price at expiration, $K$ be the strike price, and $P$ be the option premium paid.
• Call Option Buyer Payoff: $\max(0, S_T - K) - P$
• Put Option Buyer Payoff: $\max(0, K - S_T) - P$ If the price moves against the buyer's position, the buyer will simply let the option expire unexercised. The value of the option drops to zero, and the buyer's net profit is $-P$.

Step 3: Defining Maximum Loss:
Because option buyers can choose not to exercise their options, their maximum potential loss is strictly capped at the option premium paid upfront ($P$).