Assume a stock has a value of $100. The stock is expected to pay a dividend of $

Question

Assume a stock has a value of $100. The stock is expected to pay a dividend of $2 per share at year-end. An at-the-money European-style put option with one-year maturity sells for $7. If the annual interest rate is 5%, what must be the price of a 1-year at-the-money European call option on the stock?

Assume a stock has a value of $100. The stock is expected to pay a dividend of $2 per share at year-end. An at-the-money European-style put option with one-year maturity sells for $7. If the annual interest rate is 5%, what must be the price of a 1-year at-the-money European call option on the stock?

Explanation / Answer

To calculate the European call option price on the stock we can use put-call parity equation

P= C - S0 + PV(X) + PV (D)

Where,

Price of put option P =$7

Price of call option C =?

PV(X) is present value of strike price, as the stock is at the money so strike price X = $100

Discount rate is Annual interest rate = 5%,

Initial stock price S0 = $100

PV (D) is the present value of dividend where Dividend D = $2

Now putting the values in above equation

$7 = C - $100 + $100/ (1+5%) + $ 2/ (1+5%)

$7 = C - $100 + $95.24 + $ 1.91

Or C = $7+ $100 - $95.24 - $ 1.91

Or C = $9.86

Therefore the price of a 1-year at-the-money European call option of the stock is $9.86

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