Question

The price of a European call option on a non-dividend-paying stock with a strike price of $50 is $6. The stock price is $51, the continuously compounded risk-free rate (all maturities) is 6% and the time to maturity is one year. Using the put-call parity, compute the price of a one-year European put option on the stock with a strike price of $50. Please show your work.

Answer 1

Answer: 2.09

Explanation:

Given the following ;

Strike price (K) = $50

Price (c) = $6

Rate (r) = 6% = 0.06

Stock price (So) = $51

Time (T) = 1

Recall, relation for a put-call parity(p) is given by:

p + So = c + Ke^-(rT)

p = c + [Ke^-(rT)] - So

p = 6 + [50e^-(0.06 × 1)] - 51

p = 6 + [50×e^-0.06] - 51

p = 6 + (50 × 0.9417645) - 51

p = 6 + 47.0882267 - 51

p = 53.0882267 - 51

p = 2.0882267

p = 2.09