You are an executive at WX Resorts and you have executive stock options as part

Question

You are an executive at WX Resorts and you have executive stock options as part of your compensation. You hold 1,000 options that expire six months from today at a strike price of 50 but that can be exercised early. WX is trading at $55 and just announced a $1 dividend per share that will be paid four months from today to stockholders who own the stock three months from today.

(a) Using today's price of 50, what is the total value of your options using the Black-Scholes model if you hold European Options (assume ? = .30, r = .01)? (Hint: the stock price will fall by the discounted value of the dividend).

(a)If your options are American Options, what is the value today using Black's Approximation for dividend payments (assume ? = .30, r = .01)?

(c) Should you exercise early to receive the dividend? Explain.

Explanation / Answer

a) The stock price will fall by 55*1/1.1^(4/12) = $53.28

Now

Black scholes can now be applied to calculate the value of one call option

Since we own 1000 such options the total value of options = $7711.155

b) Using Blacks approximation

K*(1-exp^(-rf*t) = 50*(1-exp^(-0.1*3/12)) = $1.234

c) Since this value is greater than the dividend, the option should not be exercised before the ex-dividend date.

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