When is a binomial/lattice model preferred over Black-Scholes for employee options?

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AcadiFi · Accepted Answer

Binomial (lattice) models discretize time into steps, building a tree of possible stock prices and calculating option value by rolling back from terminal payoffs. They're preferred for employee options when Black-Scholes assumptions break down.

Specific scenarios requiring lattice:

1. EARLY-EXERCISE BEHAVIOR: Black-Scholes assumes European exercise, but employees exercise when ITM by some multiple (e.g., 2×). A lattice can embed a rule: exercise node if S >= 2K AND vested.

2. PERFORMANCE CONDITIONS TIED TO PATH: If payoff depends on average price or hitting a barrier, Black-Scholes can't handle path dependence.

3. GRADED VESTING WITH DIFFERENT TERMS: Each tranche has a different expected term; a lattice handles this cleanly.

4. DYNAMIC VOLATILITY OR RATES: Term-structure adjustments are straightforward in a lattice.

5. BLACKOUT PERIODS: Restrictions on exercise during earnings windows.

Case: Olympia Data Corp grants a 10-year option with a rule that the median employee exercises when stock reaches 2.2× strike. Building a 100-step Cox-Ross-Rubinstein tree: u = e^(σ√Δt), d = 1/u, p = (e^(rΔt) − d)/(u − d). At each node from vesting forward, check if S >= 2.2K — if yes, treat as exercised (terminal payoff max(S−K, 0)); else continue. Discounting back yields a value often 15-25% below plain Black-Scholes.

SEC SAB 107 explicitly permits lattice models and notes they can better incorporate employee behavior. Companies using lattice typically report lower per-option fair values than pure Black-Scholes, reducing reported SBC expense.

When is a binomial/lattice model preferred over Black-Scholes for employee options?

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