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Monte Carlo vs. Black-Scholes

FAS Solutions stands ready to perform valuations of employee stock options for our clients that rigorously incorporate option holders’ exercise behavior, terminations, expected volatility, expected dividend yield, cost of equity and interest rates. The flexibility and rigor of our integrated valuation work is second to none.

Our valuation practice includes Black-Scholes, Monte Carlo simulation and Lattice modeling which we customize to each valuation client. In all cases we incorporate analyses of exercise behavior, termination modeling and volatility, dividend yield and cost of equity sensitivity for each client. Lattice stock option models have long been proved incapable of accurately capturing employee stock option value but what about Black Scholes and Monte Carlo values?

Intensity-based Monte Carlo simulation provides the “true” value of an employee stock option. However, most of our clients use Black-Scholes, which is the long established “best” practice. The following diagram shows the delta between Monte Carlo and a comparable Black Scholes valuation for a variety of assumption frameworks:


Notwithstanding the delta between true value and best practice, our clients employ intensity-based Monte Carlo expected term methodology to get a Black-Scholes valuation in very close proximity to the actual Monte Carlo stock option fair value. We are the pioneers in this methodology of Black-Scholes with Monte Carlo expected term and we believe that we have developed the world’s most extensive and broad-based dataset of cross-company stock option exercise.

Whether using own-company data exclusively or cross-company data exclusively (based on over a million exercises at hundreds of companies) or a blend of the two, FAS Solutions produces audit-tested expected term results for our many clients – small or large, new IPO, long established, even non-public. Our methodology, which has passed thousands of audits, applies to grant date valuations or for outstanding grants in mid-stream that are no longer “at the money”. The flexibility of Black-Scholes with Monte Carlo expected term allows our clients to rigorously value any time-based stock option with Black-Scholes. This is critical in handling changes to contractual policy (e.g., vesting or contract terms) as well as modification valuations. Our clients no longer feel constrained by SAB 107/110 or other simplified stock administration approaches that typically overstate expense. Of course, stock options with a market condition extend beyond the scope of Black-Scholes. However, the Monte Carlo fair value of such options must be consistent with Black-Scholes valuations for vanilla stock options. Again our intensity-based Monte Carlo technology allows for this consistency.