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

Answer:

The answer is 5.559539 or 5.56.

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

Answer 2

Answer:

The Put Value of the stock is 5.55

Explanation:

To compute the Put Price;

Therefore,

Put price = $\frac{Exercise Price}{(1+ risk free interest)^{Maturity Time}} + Call Price - Current Price$

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