Explanation

For a put option seller (writer), the profit calculation is:

Profit for put seller = Put premium received - Max(0, Exercise price - Spot price at expiration)

Given:

• Put price (premium received) = 50
• Exercise price = 1,640
• Spot price at expiration = 1,670

Step 1: Determine if the put option is exercised

• For a put option, the buyer exercises when the spot price is below the exercise price
• Spot price (1,670) > Exercise price (1,640)
• Since spot price is higher than exercise price, the put option is out-of-the-money and will NOT be exercised

Step 2: Calculate the seller's profit

• Since the option is not exercised, the seller keeps the entire premium
• Profit = Put premium received = 50

Step 3: Verify with the formula

• Max(0, Exercise price - Spot price) = Max(0, 1,640 - 1,670) = Max(0, -30) = 0
• Profit = 50 - 0 = 50

Key points:

• Put sellers profit when the underlying price stays above the exercise price
• The maximum profit for a put seller is limited to the premium received
• In this case, since the spot price (1,670) is higher than the exercise price (1,640), the option expires worthless and the seller keeps the full premium of 50