Question

A put option on a stock with a current price of $45 has an exercise price of $47. The price of the corresponding call option is $4.05. According to put-call parity, if the effective annual risk-free rate of interest is 6% and there are four months until expiration, what should be the value of the put? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Answer 1

The value of the put option, using put-call parity and the provided information, is approximately $5.13.

Step-by-step explanation:

You've asked how to calculate the value of a put option using the put-call parity relationship. In financial markets, put-call parity is a concept that defines a specific relationship between the price of European put and call options with the same strike price and expiration date. To calculate the value of the put option, you need to use the following version of the put-call parity formula:

Put price = Call price - (Stock price - Exercise price / (1 + Risk-free rate)^(Time to expiration in years))

Given:
- Call price = $4.05
- Stock price = $45
- Exercise price = $47
- Effective annual risk-free rate = 6%
- Time to expiration = 4 months or 1/3 year

First, calculate the present value (PV) of the exercise price

PV of exercise price = $47 / (1 + 0.06)^(1/3) = $47 / 1.02 ≈ $46.08
Next, use the put-call parity formula to find the put price:
Put price = $4.05 - ($45 - $46.08) = $4.05 - (-1.08) = $4.05 + $1.08 = $5.13
The value of the put option, according to put-call parity, should be approximately $5.13 when rounded to two decimal places.