Explanation

When an investor sells a put option, they receive the premium upfront. For a European put option, the seller's profit at expiration depends on whether the option is exercised.

Given:

• Put price (premium received) = 30
• Exercise price = 600
• Underlying price at expiration = 620

Analysis:

1. Put option payoff for the seller:

   • The buyer of the put option has the right to sell the underlying at the exercise price (600).
   • The buyer will exercise the option only if the market price is below the exercise price.
   • At expiration, market price (620) > exercise price (600), so the put option is out-of-the-money.
   • The buyer will not exercise the option.

2. Seller's profit calculation:

   • Seller received the premium of 30 upfront.
   • Since the option is not exercised, the seller has no obligation to buy the underlying.
   • Profit = Premium received = 30

Why other options are incorrect:

• Option A (10): This would be incorrect as it suggests some net payoff from exercise, but there is none.
• Option B (20): This would be incorrect as it suggests a partial premium or some other calculation error.

Key Concept: For a put option seller, maximum profit occurs when the option expires worthless (out-of-the-money), and the profit equals the premium received. The seller's profit is limited to the premium, while potential losses can be substantial if the underlying price falls significantly.