Question

Please show the work

The spot price of the market index is $900. The premium on a put, with an exercise price of $895 in three months, is $8.00. The annual rate of interest on treasuries is 2.4% (0.2% per month). After 3 months the market index is at $885. Calculate the profit or loss to a short position in the put option if the final index price is $885.

A. $6.9519 gain

B. $6.9519 loss

C. $1.9519 gain

D. $1.9519 loss

Answer 1

Short position in the put option means writing a put option

As the premium of put option is $8.00; therefore writer will get $8.00 as premium and can invest it for three months at the rate of 0.2% per month

Therefore future value of premium = $8.00 * (1+0.2%) ^3 = $8.0481

The exercise price of market index is $895

And after 3 months the market index is at $885

Therefore payoff from the put option to the writer of the option = Market Index price after 3 month - exercise price of market index

= $885 - $895 = -$10

Profit/loss from the put option = Future value of premium + payoff from the put option

= $8.0481 - $10 = - $1.9519 (negative sign indicates a loss)

Therefore correct answer is option D. $1.9519 loss