Question

Find the theoretical fair value of a put option written on a share of stock that is trading at $100 today. The exercise price of the put option is $112. A call option written on that same stock with the same exercise price sells for $3.19. The risk-free rate is 7.7% and both options expire in exactly 16 weeks.

Answer 1

Let the price of the put option be $ p. Current Price of Underlying Asset (Stock) = $ 100, Risk-Free Rate = 7.7% per annum

Call Option Price = c = $ 3.19

Both, the put and call options have the same expiry, same strike price, and same underlying asset

Common Option Strike Price = $ 112

Option Tenure = 16 weeks or (16/52) ~ 0.30769 years

Using, the put-call parity equation we have:

Call Price + Present Value of Option Strike Price = Current Stock Price + Put Price

3.19 + 112 / EXP [(16/52) x 0.077] = 100 + p

3.19 + 109.378 = 100 + p

p = $ 12.5676 ~ $ 12.57