Executive Stock Options (Spreadsheet Programming)

Part of the controversial issues around expensing the employee compensation stock options is the valuation. Neither the accounting approach, such as minimum value (see the definition below), or the complex Black-Scholes option model gives satisfactory results.

Because of the feature of the freeze-out period, (also known as vesting) period, employee options are often modeled as forward starting options. A forward start option with time to maturity T starts at-the-money or proportionally in or out-of-the-money after a known elapsed time t in the future. The strike price is set equal to a positive constant a times the asset price S after the known time t. Rubinstein (1990) uses the following formula for the call option:[1] Consider an employee who receives a call option with forward start three months from today. The options start 10% out-of-the-money, time to maturity is one year from today, the stock price is 60, the risk-free interest rate is 8%, the continuous dividend yield is 4%, and the expected volatility of the stock is 30%. In other words,

S = 60, a = 1.1, t = 0.25, T = 1, r = 0.08, b = 0.08-0.04 = 0.04, and =0.30

Build a spreadsheet model to calculate the call price. Submit the printout with the formula.

[1] Rubinsteins model is based upon the Black-Scholes option pricing model. Notice, the input an actually is X/S, b is the carrying cost, which is equal to r d, where r is the riskfree rate and d is the dividend yield, assuming the company pays dividends. Beware that t stands for the vesting period, T is the maturity. Make sure that your model copies the formula exactly as it shows here.