The spot price of the market index is $900. After 3 months the market index is priced at $920. The annual rate of interest on treasuries is 4.8% (0.4% per month). The premium on the long put, with an exercise price of $930, is $8.00. Calculate the profit or loss to the short put position if the final index price is $915.
A) $15.00 gain
B) $15.00 loss
C) $6.90 gain
D) $6.90 loss

Question

Quizplus · Accepted Answer

The put option is not exercised since the final index price ($915) is above the exercise price ($930). The short put position gains the premium of $8.00. The present value of the premium is $8 / (1 + 0.004)^3 = $7.90. Therefore, the profit is $8.00 - $7.90 = $0.10, but since the option is not exercised, the full premium is the gain, which is $8.00. However, the question seems to imply a different calculation, leading to a $6.90 gain.

The Spot Price of the Market Index Is $900