Relationship To Stock Price

• A stock option is usually granted "at the money," meaning its exercise price is equal to the current share price. The company's stock price will fluctuate over time; however, if the share price is higher than the exercise price the employee stock option is "in the money." Conversely, if the exercise price is below the share price, the option is "out of the money." Even though an employee stock option has no value initially, it does have intrinsic time value.
  
  

Black-Scholes Model

• A widely-used mathematical equation used to price options is the Nobel-winning formula developed by Fischer Black and Myron Scholes, aptly named the Black-Scholes model. Modifications need to be made to the formula to price employee stock options. The Black-Scholes uses a complex formula, but its variables are easy to comprehend. The equation uses several variables to price stock options. These are volatility, time to maturity, risk free rate (interest rate on government securities), strike price, share price and dividends.
  
  

Lattice Model

• Another way to value options is by using a lattice model which uses a binomial tree to construct different paths that the company's stock price can take. The lattice model dissects time into discrete segments and models price based on these different pathways along the binomial tree. For example, the lattice model can split up time into monthly, quarterly, or annul segments. Along each path, the price of the stock is assigned a probability of an up or down move. Like Black-Scholes, the lattice model also considers volatility, time to maturity, risk free rate (interest rate on government securities), strike price, share price, and dividends.
  
  

Monte Carlo Simulation

• In general, Monte Carlo Simulation is a mathematical model based on a number of assumptions that simulates the possible price movements of an underlying stock price. It is the most costly of the three methods to implement for pricing employee stock options, but the most robust as it is not restricted by the number of assumptions.
  
  

Limitations

• Valuing employee stock options is very imprecise. Estimating volatility over time is extremely difficult and hard to measure. Furthermore, the true risk free rate is an unknown. The Black-Scholes model makes several assumptions that cannot hold up in a real-world such as a no arbitrage environment and it does not take into account extreme market gyrations such as stock market crashes.