When it comes to the term “option valuation”, you can’t read anything on this topic without seeing the name “Black-Scholes” mentioned.

Fischer Black and Myron Scholes published an article in 1973 entitled “The Pricing of Options and Corporate Liabilities”, in which they laid out their formula for risk neutral portfolio management that effectively separated the option from the risk of the underlying security. This formula was then coined the “Black-Scholes options pricing model” by Robert Merton, and together Merton and Scholes received the 1998 Nobel Memorial Price in Economic Sciences for their work (Black unfortunately died in 1995).

While the use of the formula has been expanded on and adapted for many different applications such as used by investment banks and hedge funds, the formula itself is still very useful in determining a value for an option given a set of inputs.

The Black-Scholes formula relies on one risky asset – usually the share over which the option has been issued – and one riskless asset, which is usually a zero-coupon government bond yield rate.

The variables that are needed to input into the Black-Scholes model are:

- The share price on the grant date, or issue date
- The exercise price of the option
- The time to expiry (in years)
- The risk free rate
- The volatility of returns of the share price
- The dividend yield of the share

These variables are all quite easily determined for any exchange listed company, as they are publicly available, or can be quite easily calculated based on publicly available information.

One limitation of the formula is that it assumes the option to be a European option, or one that can only be excercised at the end of the option life. This contrasts to American options, which usually can be exercised at any time during their life.

While Black-Scholes is formulaic and relatively easy to calculate, when is it an appropriate valuation technique for AASB 2?

## AASB 2 and Black-Scholes

AASB 2 requires that for the valuation of share options, factors such as the typical long lives of options issued by companies, and the ability to exercise the options at any time during their life (American options), might preclude the use of the Black-Scholes formula which does not allow for the possible early exercise of options.

However, where the options have relatively short contractual lives, or they must be exercised within a short period of time after the vesting date, those factors may not apply and the Black-Scholes formula may produce a value that is substantially the same as a more flexible option pricing model.

We usually find that where the company does not pay dividends, then the value of the option will be very much the same regardless of which model is used. The reasoning behind this is that the option holder will want to hold their cash for longer and earn a rate of return on that cash, rather than invest it in the share and subject themselves to market risk.

Even where the option may be an American style option, in some instances a Monte Carlo simulation can be used to determine the expected exercise of the option, and this time period can then be used in a Black-Scholes formula to calculate the value of the option.

## How does Black-Scholes work for performance rights?

Performance rights usually do not require the employee or recipient to pay anything in return for the issue of a share. In this most basic form, the performance right can be considered to be a zero exercise price option, and the value can then be calculated using an option valuation methodology.

If there are no market conditions e.g. share price hurdles, or Total Shareholder Return (TSR) hurdles then the Black-Scholes model may be an appropriate way to value those performance rights issued by the company.

If there are market conditions such as share price hurdles or TSR hurdles, then another valuation methodology may be more appropriate. Even in these circumstances, the valuation technique will start with the basis of treating the performance right as a zero exercise price option, and then incorporate the specific terms and conditions to derive the value.

As the performance right is a zero exercise price option, then the value of the performance right for a non-dividend paying share will be the same as the share price on the date of issue. As a consequence, the time to expiry and volatility will have no influence on the valuation of the performance right.

## When is the best time to use Black-Scholes?

Black-Scholes is a good starting point for valuing options, as it is simple and doesn’t require too much complicated computing in order to get a result.

While this starting point can give you an indication of an option’s value, if there are any market conditions or any element of the conditions of the option that require more customisation of the valuation technique, then Black-Scholes can quickly become unsuitable as the primary valuation model.

## Unsure whether Black-Scholes is an appropriate valuation model?

Contact us at Value Logic to help you out with your valuation, and give yourself peace of mind that your valuation will be correct.