Question

Exam prep question I am struggling with. Could anyone give me a solution with steps? Thank you!

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 a strike price of $50 and today's stock price of $55, what is the total value of your options using the Black-Scholes model if you hold European Options (assume σ = .30, r = .01)? (Hint: the stock price will fall by the discounted value of the dividend).

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

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

Answer 1

PV of the dividend today = D x e-rt = 1 x e-0.01 x 4/12 = 0.9967

Hence, the effective current stock proice = Current price - PV of future dividend = 55 - 0.9967 = 54.0033

Part (a)

Please see the snapshot of my Black Scholes Model in the table below. The last row highlighted in yellow is your answer. Figures in parenthesis, if any, mean negative values. All financials are in $. Adjacent cells in blue contain the formula in excel I have used to get the final output.

Hence, the total value of your options using the Black-Scholes model if you hold European Options = $ 6,830.49

Part (b)

Using Blacks approximation:

Price of one option = K x (1 - e-r x t) = 50 x (1 - e-0.01 x 4/12) = 0.2494

Value of the American optons = Higher of the two values x number of the options = max (6.8305, 0.2494) x 1,000 = 6,830.49

Part (c)

No, the early exercise doesn't make sense, here.