# Bloomberg

Connecting decision makers to a dynamic network of information, people and ideas, Bloomberg quickly and accurately delivers business and financial information, news and insight around the world.

# Customer Support

• Americas

+1 212 318 2000

• Europe, Middle East, & Africa

+44 20 7330 7500

• Asia Pacific

+65 6212 1000

# Options: Old Question, New Answer

By Timothy Luehrman After lengthy deliberation, the Financial Accounting Standards Board (FASB), the industry's standard-setting group, is expected to issue an exposure draft by the end of March for a proposed new standard governing the treatment of stock options issued to employees as compensation. We at Standard & Poor's Corporate Value Consulting expect that this will require companies to record an expense reflecting the fair value of such options at the time they're granted. The draft solicits public comment on FASB's recommendations before the new standards are finally issued.

While the expensing aspect of the board's pending decision has been discussed at length, less attention has been paid to an equally noteworthy potential outcome: FASB will recommend that companies jettison the venerable Black-Scholes model for determining the fair value of employee options. And the new method the FASB may recommend could have a profound impact on the valuations themselves.

RISK AND REWARD. What would FASB put in the current model's place? Preliminary indications are that the board will recommend the use of so-called lattice models (while their use will technically not be required, most companies are expected to comply with the board's recommendation). A lattice is a way to organize and summarize the possible future paths for a share's price. It looks a bit like a decision tree in which each separate calculation, or node, corresponds to a particular price at a particular time.

The most common sort of lattice model is called the binomial model. A basic version for valuing options uses two such lattices: One to keep track of the stock price and another to calculate corresponding option values, node by node.

From an economic perspective, the binomial model is essentially identical to the Black-Scholes model for simple options. Both are based on the equilibrium concept of "no arbitrage" -- that is, at all times, stock and option prices must be such that no instantaneous and riskless profit is available to traders. Both models also make equivalent assumptions about possible future movements in stock prices. However, Black-Scholes incorporates these assumptions into elegant mathematical expressions, which in turn imply the now-standard formula that gives an option's value.

REALISTIC FEATURES. In contrast, the binomial model divides the future into a large number of tiny periods, each one of which is very simple -- but collectively may be as complex as necessary. Brute computing power is then applied to make millions of simple arithmetic calculations that together imply the option value. In short, the two models use the same underlying economic assumptions -- but employ different mathematical means to arrive at the same answer.

If both models give the same answer, why should it matter which one is used to value employee options? Well, options aren't simple. The advantage of a lattice model lies precisely in the millions of separate, simple calculations into which the problem is broken down. With so many nodes to represent the future, it's possible to add features (or even to add whole separate, intermediate lattices) to represent realistic probabilities of death, disability, termination, premature exercise, and other factors.

These features do affect option values but are mostly impossible to reflect in the compact Black-Scholes formula. Prior accounting standards either ignored this problem or made sweeping, simplifying assumptions in order to apply a simple model (e.g., intrinsic value or Black-Scholes).

REAL-WORLD EFFECTS. The new standard pushes for a model that accommodates the complexities of real employee stock-option contracts and the real world. Practically speaking, that means a binomial lattice. We at S&P CVC have developed basic lattices for handling many features that are difficult or impossible to accommodate in Black-Scholes, including, for example:

The lengthy contractual life of the option

Vesting schedules, including the accelerated vesting upon death or disability that's common in many grants

Probabilities of termination or voluntary separation and forfeiture

Blackout periods

Early exercise by employees, both as a random event and as a function of time, stock price, voluntary separation, etc.

Possible term structures for interest rates and volatility

While detailing the new model's methodology is important, most investors will be concerned with its real-world effects. Below, we have tried to answer some of the key questions surrounding the potential implementation of the new options-valuation model:

How different are the fair-value estimates for Black-Scholes with expected option life vs. a full binomial lattice?

A lattice-based model with realistic inputs regarding employee characteristics and capital-market data will generate fair-value estimates that differ significantly from Black-Scholes with expected option life. Just how great the difference depends on many factors, such as the demographics and exercise behavior of the employee population.

For many companies the difference in estimated fair value will be significant. Its magnitude also depends greatly on what a given business has been using as its estimate within Black-Scholes for expected life and volatility.

We at S&P CVC have seen instances where companies obtain binomial values fully 50% lower than what had been previously estimated using Black-Scholes with expected option life -- a big difference. But the disparity would be less (or more) dramatic if the company had been using a longer (or shorter) expected life in its original calculations.

How difficult and expensive will it be for companies to use the binomial model?

Learning the basics of binomial option pricing is not difficult -- they're presented in many finance texts and similar inexpensive resources. However, customizing a basic binomial model to handle the demographic and behavioral assumptions requires more training and some special care. Some businesses will do this in-house, while others will choose to outsource it.

How accurate will the valuations assigned under this new model be?

The underlying principle that allows the model to be solved is one of the most powerful and reliable ideas in financial economics: No arbitrage. Some of the inputs, such as actuarial data, will be estimated with error, but this is already true for many accounting exercises.

Ultimately, a diligent effort by well-trained professionals to implement the lattice models should significantly improve the information in company income statements about option grants. And that should be a real positive for Corporate America -- and investors. Boston-based Luehrman is managing director for Standard & Poor's Corporate Value Consulting

LIMITED-TIME OFFER SUBSCRIBE NOW