Question

A put option on a stock with a current price of $47 has an exercise price of $49. The price of the corresponding call option is $4.35. According to put-call parity, if the effective annual risk-free rate of interest is 5% 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 Put Value of the stock is 5.55

Step-by-step explanation:

To compute the Put Price;

Therefore,

Put price =
`(Exercise Price)/((1+ risk free interest)^(Maturity Time)) + Call Price - Current Price`

By substituting the value in the formula

Put Price =
`4.35 + [49 / (1 + 0.05)^(4/12)] - 47`

Put Price =
`4.35 + [49 / (1.05)^(4/12)] -47`

Put Price =
`4.35 + [49 / 1.02] -47`

Put Price = 4.35 + 48.21 – 47

Put Price = 5.55

Answer 2

The answer is 5.559539 or 5.56.

Step-by-step explanation:

From the given question let us recall the following statements

The current price of A put option on a stock = $47

With an exercise price of $49

Annual risk-free rate of annual interest is = 5%

The corresponding price call option is = $4.3

The next step is to find the put value

Now,

The Call price + Strike/(1+risk free interest) The Time to maturity =

Spot + Put price

Thus

The,Put price = Call price - Spot + Strike/(1+risk free interest)Time to maturity

When we Substitute the values, we get,

Put price = (4.35 - 47) + 49/1.05 4/12

Therefore, The Put Price = 5.559539 or 5.56