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.