The Debate: Which share option model to choose?

# The Debate: Which share option model to choose?

What pricing formula is best for share option valuation? Peter Williams opts for the tried and tested Black-Scholes formula, but Alex Waite asks you to consider a more 'flexible approach'.

The share option supermodel

By Alex Waite, actuary and partner at Lane Clark & Peacock LLP

The tide towards fair value accounting is set to be endorsed by European harmonisation in 2005. With new rules expected later this year, the focus has now turned to Employee Share Option schemes (ESOs).

For those familiar with option valuation, there is a knee-jerk reaction to apply the ‘Black-Scholes’ option pricing formula.

This clever piece of mathematics was developed in the 1970s to value short-term option contracts.

However, in all but the simplest cases it is unlikely to provide an accurate fair value for employee options: it’s simply too inflexible for a typical ESO scheme. Whilst practitioners can amend the Black-Scholes parameters to approximate the correct result for an ESO scheme, much more reliable methods are now available.

One truly flexible solution is found in ‘Stochastic simulation’ methods, which directly model possible payments.

As a result, they can incorporate all of the key features of any ESO scheme.

Consider the following scheme: an option is granted today at 100p. The only day it can be exercised is three years away. This option can be accurately valued by Black-Scholes, at 14.6p, using a term of three years (and other assumptions).

However, as soon as we make it more realistic, say the option can be exercised at any time from three years to ten years, we have great difficulty in choosing a term for Black-Scholes. Should it be three years (but the option is more valuable) or should it be ten (but that is too long)?

Thankfully, this option can be modelled directly using the Stochastic approach, giving 21.6p. We can also adjust this model to allow for employees leaving employment: with a modest withdrawal allowance, the value decreases to 11.4p – 30% lower than the original figure.

New methods are important if we want true and fair accounts; but more importantly, accurate valuation methods may also be critical to employees.

To date the ESO liability has often been over stated; such a perception, irrespective of true cost, could see ESO schemes being scrapped as finance directors avoid further damage to their balance sheets – a realistic assessment of the true value will enable more informed HR decision making.

Although we can’t stop the tide of fair values, if we want to keep ESOs, we should at least make sure the cost we calculate is both true and fair. – Alex Waite is an actuary and partner at Lane Clark & Peacock LLP.

If it ain’t broke don’t fix it
By Peter Williams, freelance writer and chartered accountant

Black and Scholes are a couple of mathematicians who developed a model that determines the theoretical value of how much a call option is worth at any given time. The formula has been compared to the discovery of the structure of DNA. While the discovery of DNA gave rise to the science of genetic engineering, the Black-Scholes models has helped us with our knowledge of financial engineering.

The term ‘financial engineering’ sometimes gets a bad press as it is seen as a close ally of creative accounting. But in this case the financial engineering is an important tool in the risk management armour, designed to reduce vulnerability to financial insecurity arising from the fact that we live in a rapidly changing global economy. The Black-Scholes model is the precursor of modern option pricing models. The option-pricing formula is based on simple and reasonable assumptions in a continuous-time model.

The model was derived by observing that an investor can replicate the payoff to a call option by buying the underlying stock and financing part of the stock purchase by borrowing. It even works before the call option expires. You can still match its future payoff by recreating a replicating portfolio.

However, to do so you must buy a fraction of a share and the stock and borrow a fraction of the exercise price. The fraction depends on five factors, four are known. They are: the price of the stock; the exercise price of the option; the risk-free interest rate and; the time to maturity. The only bit you don’t know is the volatility of the underlying stock price.

In 1997 the Nobel Prize in Economics was awarded for the work that led to the Black-Scholes Options Pricing theory. The outstanding aspect of the theory is that is provides a sophisticated way of analysing and understanding the relationships among stock options, option prices and expected stock-market volatility.

The Black-Scholes model has obvious advantages: it is based on a model that has been around in some way or other for nearly three decades; it is widely used and most importantly, it appears to work. In essence, the Black-Scholes model has become the industry standard. Anything that hopes to dramatically improve on Black-Scholes, or even replace it, will have to be good. – Peter Williams is a freelance journalist and chartered accountant.

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