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Selecting the right model – Black-Scholes, binomial lattice or Monte Carlo Simulation
The Choices
FASB standards require that companies expense options at fair value as computed with an option valuation model. The most widely accepted models are:
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The Black-Scholes model with the traditional Black-Scholes closed-form, but modified for employee stock options by inputting an expected term in place of the contractual option term — say ten years.
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Lattice models consisting of a discrete binomial or trinomial tree of stock prices in which options can be valued inductively by stepping back through the tree from the contractual expiration date to the grant date.
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Monte Carlo simulation models that use computer generated pseudo- random numbers to iteratively generate many possible future stock price paths. Options are valued one path at a time with the ultimate fair value computed as the average over the many path-specific values.
Should your company use Black Scholes?
Whether your company has decided to use Black Scholes or to consider lattice or simulation models, FAS 123 Solutions can help with expert guidance. If your company has already made the critical decision, we stand ready with extensive modeling capability and experience to help make the most of the path you've chosen. If not, then we can help your company in the decision-making process taking into consideration historical data, as well as short and long-term strategy. We assess the costs and benefits of the various methods as they apply to your company. We can make the decision easier by clearly demonstrating the valuation differences using Black-Scholes, binomial lattices with a suboptimal exercise factor, and more sophisticated lattice models and Monte Carlo simulation models that incorporate an exercise policy and departure rate at each stock price and point in time.
Let's briefly consider the choices. From the pure perspective of financial modeling, the numerical models in categories (ii) and (iii) have the potential to be better than Black-Scholes. Here, "better" means more accurate, whether it be a matter of averting overstatement, or averting valuation error, generally. The advantage of lattice models and simulation models lies in their flexibility to incorporate richer market-based information, such as the term structure of volatility or interest rates, and richer employee behavioral information as it relates to voluntary suboptimal exercise as well as post-vesting departure rates of optionees. In contrast, Black-Scholes, when modified for employee stock options, summarizes all behavioral information with a single number — the expected term. All options are treated as if they disappear at the same time independent of how the stock price evolves over the option term. Think of a mortgage prepayment model where all mortgages are treated as if they prepay at the same time independent of interest rate movements.
Notwithstanding the theoretical limitations, Black-Scholes might be the right choice for your company, at least from a practical perspective over the short-term. First, in order to realize the potential of lattices and simulation to be "better" than Black-Scholes, voluntary suboptimal exercise, in particular, must be incorporated in a sensible way. This can be a challenging task. The method as illustrated in FAS 123(R) of using a "barrier option" binomial lattice with a suboptimal exercise factor is parsimonious, but it is not generally "better" than Black-Scholes; in fact, it is often worse. The specified suboptimal exercise factor — the barrier — is an average computed from exercises distributed across a range of stock price levels. And the barrier takes effect from one day after vesting through contract term. For simplicity, FAS 123(R) uses this model in its illustrations, but FASB is not advocating its use over better numerical methods.
Second, Black-Scholes is easy to implement once we estimate the expected term. What might be less obvious to preparers of financial statements is the fact that producing a really supportable estimate of expected term is no less challenging than estimating voluntary suboptimal exercise.
More discussion on estimating expected term
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