Question

A stock trades at 100 and offer a 5% annual dividend. Based on a risk free rate of 2% and a strike price of 90 , a 1 year fair valued put option trades at 4.3599 and 1 year fair value call option trades at 11.2649. Using continuous compounding at what strike rate would the fair value of the put and call price be equal?

Answer 1

The fair value of the put and call options would be equal at a strike price of approximately 95.099.

Step-by-step explanation:

To find the strike rate at which the fair value of the put and call options are equal, we can use the put-call parity formula.

The put-call parity relationship for European options is given by:

C−P=S−Xe^( −rt)

where:

C is the call option price,

P is the put option price,

S is the current stock price,

X is the strike price,

r is the risk-free rate, and

t is the time to expiration.
In this case, you have the following information:

C=11.2649, P=4.3599, S=100, X=? r=0.02, t=1.

Substituting these values into the put-call parity formula:

11.2649−4.3599=100−Xe^(−0.02×1) .

Now, solve for X:

6.905=100−Xe^(−0.02) .

Xe^−0.02=100−6.905.

Xe ^−0.02 =93.095.

X≈95.099.

Therefore, the fair value of the put and call options would be equal at a strike price of approximately 95.099.