Too Much Is Not Enough: Incentives in Executive Compensation

By Robert W. Kolb | Go to book overview

Appendix

Binomial Valuation Method for Executive Stock Options

Variable definitions:

IOW= the initial outside wealth of the CEO
S= the stock price at the time the option is issued
X= the exercise price of the ESO
T= the time from the grant date of the option to its expiration
Rf= the continuous risk-free rate of interest
D= the continuous dividend rate on the stock
V= the vesting period
f= the continuous annualized departure rate of the CEO from the firm
ER= the CEO’s subjective expectation of the return on the stock
RA= the CEO’s level of risk aversion
σ= the standard deviation of the firm’s shares, which the CEO will choose
u= the up factor for the stock price movement in each period
d= the down factor for the stock price movement in each period
p= the risk-neutral probability of a stock price increase
Δt= the length of a single period, such that Δt = T/N
π= the CEO’s subjective probability assessment that the stock price will rise

Following the standard treatment for binomial models of Cox, Ross, and Rubinstein (1979), and drawing on the excellent discussion by Amman and Seiz (2004) we have:

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