Question

Consider the following data for a European option: Expiration = 6 months; Stock price = $80; Exercise price = $75; Call option price = $12; Risk-free rate = 5% per year. Using put-call parity, calculate the price of a put option having the same exercise price and expiration date.

Answer 1

To calculate the price of a put option using put-call parity, we can use the formula: Put Price = Call Price + Exercise Price - Stock Price - PV of Exercise Price. Using the given data, the price of a put option is approximately $33.11.

Step-by-step explanation:

To calculate the price of a put option using put-call parity, we can use the formula:

Put Price = Call Price + Exercise Price - Stock Price - PV of Exercise Price

Given the data provided, we have:

Call option price = $12

Exercise price = $75

Stock price = $80

Expiration = 6 months = 0.5 years

Risk-free rate = 5% per year

First, we need to calculate the present value (PV) of the exercise price:

PV of Exercise Price = Exercise Price * e^(-risk-free rate * expiration)

PV of Exercise Price = $75 * e^(-0.05 * 0.5) = $75 * e^(-0.025) ≈ $73.89

Now we can calculate the put option price:

Put Price = $12 + $75 - $80 - $73.89 ≈ $33.11

Therefore, the price of a put option with the same exercise price and expiration date is approximately $33.11.