The Black-Scholes, Monte Carlo simulation and lattice models all stem from the same financial concepts: (a) that a portfolio can be built that exactly replicates the payoff on an option or equity instrument at each point along the time spectrum that extends from the award's grant date through its expected term and (b) that the fair value of risky financial instruments can be modeled in a risk-neutral framework. Each of these valuation techniques uses many of the same variables (assumptions) to estimate an award's fair value. These include the exercise price (if applicable), an expected term, the price of the underlying stock, the stock's expected volatility, the risk-free interest rate, and the dividend yield over the award's expected term.
The Black-Scholes model reduces all expected employee exercise behavior and post-vesting cancellation activity to a single average expected term assumption. Lattice models replace this single assumption with a more complex set of assumptions. Thus, lattice models can accommodate a wider range of assumptions about employees' future exercise patterns than the Black-Scholes model, as well as assumptions that may change over time. These additional assumptions should yield a more refined estimate of fair value.
Lattice and Monte Carlo simulation models can accommodate a wide range of employee exercise behavior as well. In addition, when valuing equity awards other than options, the primary advantage of Monte Carlo simulation or lattice models is that they can accommodate a much wider variety of award terms and provisions than the Black-Scholes model.
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