Valuation Models

As the options granted under share plans are not traded, determining fair values requires the use of an option pricing model that reflects the movement of the underlying share price.

The option pricing model requires assumptions regarding the future volatility of total shareholder return and the future dividend policy of the employer. The starting point for choosing these assumptions is an analysis of historic share price and dividend data.

A further key assumption concerns the point at which the option is exercised, which will largely depend on human behaviour.

The Black-Scholes Method

The most common form of option pricing model is the Black-Scholes formula. This is a relatively simple model that is quick and easy to apply. However, the model is unable to cope with many features applicable to executive share plans such as:

  • Long exercise windows
  • Performance conditions
  • Human behaviour in deciding when to exercise options

Indeed IFRS2 states the use of Black-Scholes is unlikely to be appropriate in many cases.

The Binomial Model

The binomial model uses the same methodology underlying the Black-Scholes method but allows for greater flexibility.

In the binomial model the duration of the option is broken up into small time periods. In any time period the price of a share is assumed to either move up or move down. The model can then represent possible future values of the underlying share.

The value of the option is then determined by working out the payoff at each of the possible vesting prices and then working backwards to allow for the probability of the share reaching each of these prices.

The binomial model can be further improved by creating an enhanced version that allows for human behaviour and early exercise of the award. It can also be modified to allow for some market-related performance conditions. However, many such conditions cannot be allowed for with sufficient accuracy.

The Monte Carlo Model

The Monte Carlo model is a sophisticated stochastic model. The projected path of the share price is simulated using a random variable to reflect its volatility. Any market-related performance conditions can be built into the model, as can any correlation effects between comparator groups. It is possible to build in even the most complex assumptions for human behaviour. Once the model is built it is run many thousands of times in order to develop an overall picture of all the possible paths of the share price and payoffs.