Topic: Comparison of different employee stock option valuation techniques.
Summary: The purpose of this whitepaper is to set forth the fundamental concepts related to the Black-Scholes-Merton (“BSM”), Lattice and Monte Carlo Simulation (“MCS”) valuation models, how the techniques differ from each other and when certain valuation models are considered preferable for valuing employee stock options.
Discussion: The BSM, Lattice and MSC models are among the valuation models that meet the criteria required by ASC 718 Compensation-Stock Compensation (pre-Codification SFAS 123R Shared-Based Payments) for estimating the fair value of employee stock options. These valuation models are the most commonly applied techniques used to value stock options. ASC 718 does not explicitly recommend a particular option-pricing model for the valuation of employee stock options; however, the FASB suggests that in many circumstances a Lattice or MCS model will provide a better estimate of the fair value of certain employee stock options than a BSM model because of their flexibility which allows the inclusion of different assumptions.
I. EXPLANATION OF BLACK-SCHOLES-MERTON (“BSM”) MODEL
The BSM model is an example of a closed-form model which is described by the FASB as a “valuation model that uses an equation to produce an estimated fair value.” The BSM valuation model includes inputs for the trading stock price, the exercise price, the volatility of the stock and the risk-free interest rate. The model assumes that option exercises occur at the end of an option’s contractual term, and that expected volatility, expected dividends, and risk-free interest rates are constant over the option’s term. The traditional BSM model was created to value trading options in an active market; therefore, it may not include all the assumptions necessary to value non-trading instruments in an illiquid market.
II. EXPLANATION OF A LATTICE MODEL
ASC 718-10-20 defines a lattice model as “a model that produces an estimated fair value based on the assumed changes in prices of a financial instrument over successive periods of time”. This model is essentially a discounted cash-flow analysis which considers multiple possible outcomes. It considers the movement of the stock price at multiple periods of time and works somewhat like a tree whose branches (or nodes) represent different alternative future stock paths. Each node in the lattice model represents a possible price at a particular point in time and these nodes are then used to calculate the present value of the future values of the option using risk-free interest rates. A lattice model can take into account assumptions such as employee exercise patterns which vary based on changes in the company’s stock price and it allows for the use of other dynamic assumptions.
III. EXPLANATION OF MONTE CARLO SIMULATION MODEL
A MCS model uses a simulation technique to generate multiple random price paths for the stock price to simulate many possible future outcomes which are then discounted at the risk-free rate. These simulated paths are then averaged to determine the fair value of the option.
IV. COMPARISON OF MODELS
BSM model: This model is well known and relatively simplistic to use so it tends to be a low cost alternative for valuing employee stock options however, it is unable to support the valuation of options with market-related exercise conditions, or multiple assumptions related to volatility, term, early exercise, or risk free rate. The value obtained from a traditional BSM model is often higher than the fair values obtained by the use of alternative methods and in fact, the FASB has suggested that the use of the traditional BSM formula may not be the best approach to estimate the fair value of even a typical employee stock option.
Lattice model: This model is more complex than the BSM model and it is able to support the valuation of options with market-related exercise conditions and multiple assumptions related to volatility, term, early exercise and risk free rate.
MCS model: This model is the most complex and usually the most expensive valuation model. MCS can be adapted to include certain modeling techniques to determine the effect of changes in the stock price path and it can value options which include multiple vesting features which are tied to the company’s future stock price. A MCS model does not have any limitations on the number of assumptions which can be built into the model so it tends to be an appropriate model to use for options with multiple varying assumptions. The cost of valuing options using a MCS model varies depending on the number of assumptions which must be built into the model but it is often more expensive then the BSM and Lattice models due to the additional time it takes to build the model.
V. PREFERABILITY OF CERTAIN VALUATION MODELS
The initial exposure draft of SFAS123(R) established a lattice model as the preferable model rather than a closed-form model to value employee options because the FASB did not believe the closed-form model included enough inputs to properly reflect the value of all the substantive characteristics of certain stock options. Since certain adjusted BSM models produce accurate results, the FASB purposely removed the requirement to use a certain valuation model from SFAS 123(R), and in Appendix A15 stated that “both a lattice model and the Black-Scholes-Merton formula, as well as other valuation techniques that meet the requirements in paragraph A8, can provide a fair value estimate that is consistent with the measurement objective and fair-value-based method of this Statement”
Although the BSM method is an acceptable method to value stock options, ASC 718 provides that if BSM is used to estimate the fair value of stock options, the formula must be adjusted to take account of certain characteristics of employee share options and similar instruments that are not consistent with the model’s assumptions (for example, the ability to exercise before the end of the option’s contractual term). The BSM model may also be modified to include additional assumptions to incorporate the diluting effect of options, warrants and other equity-indexed financial instruments on the value of the stock if dilution is considered a substantive characteristic of the financial instrument.
Due to the limitations in the adjustments which can be made to the BSM model, this model is only considered appropriate for “plain-vanilla” options which do not contain any market conditions. ASC 718 indicates that using a more complex valuation model such as a Lattice or Monte Carlo model should be used to take into account variables such as employee exercise patterns based on changes in the company stock price or market conditions.
Since Lattice and Monte Carlo models embody flexible, iterative approaches to valuation they tend to capture the distinctive aspects of employee stock better than the BSM formula. These models can incorporate market conditions that may be part of the terms of an option, such as a provision that an option is only exercisable if the underlying stock price achieves a certain target price and other relevant variables such as employee exercise patterns.
Although Lattice models are often preferable to using a BSM model, if the stock options have complicated features or several different assumptions which need to be made, a MSC model may be required since a Lattice model may not be able to address all the necessary assumptions.
Conclusion: Although current accounting guidance does not specifically require a specific valuation technique for valuing employee stock options, there are certain techniques which are not considered adequate for valuing options with market conditions or other complicated features. Some of the less complex valuation methods such as BSM may be the least expensive approach; however, they often result in the highest option value which causes higher stock compensation expense. It is recommended that management talk to a valuation professional to determine the most appropriate and cost-effective approach to valuing their stock options. The LSC Group, LLC is pleased to discuss the different stock option valuation approaches with you and assist you in determining the most appropriate model to use in your specific circumstances.
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