ESOP valuation model
Background
A crucial point in ESOP valuation in accordance with IFRS 2 and ASC 718 is the selection of a valuation model. The standard explicitly mentions the BlackScholesMerton formula (BSM formula) and the binomial model. However, the IASB does not commit itself to one of the two methods. It rather points out that factors “that knowledgeable, willing market participants would consider when selecting the option pricing model to be used” must be taken into account when selecting the model. Conversely, this means that other recognized financial mathematical models, such as the Monte Carlo method, should be considered.
Black Scholes Model
When deciding for or against a particular model, it is therefore crucial that all details of the plan can be mapped. A fundamental rejection of the BSM formula is not justifiable from both a financial theory and practical perspective. Nor is it possible to make a blanket statement that the binomial model is the superior model to the BSM formula in all cases. However, the standard points out that the BSM formula can only be used to correctly model very simple programs. This refers to the structure of the formula meaning that early exercise, for example, cannot be taken into account. Due to the trend towards increasingly complex ESOPs, the rejection of the BSM formula in accounting practice is therefore understandable.
ESOP valuation based on Monte Carlo Model and Binomial Model
The Monte Carlo model and various tree models, offer far more flexible approaches to the valuation of share options. The flexible structure of both methods allows complex contract details to be mapped. One example of this is share price or indexrelated performance targets. These features can be modeled using both the Monte Carlo simulation and the binomial model. The possibility of exercising an option early can also be integrated into both models.
Summary
It is not possible to make a general statement regarding a flexibility advantage of the Monte Carlo compared to tree models. Valuation practice shows that in cases of doubt, the model that is best able to depict the situation at hand is preferred. If several models come into consderation, the calculation time as well as the comprehensibility can be used as decision criteria. The effort required to develop a suitable model depends largely on the scope and complexity of the respective program. Last but not least, implementation requires an indepth understanding of financial mathematics and programming skills. In practice, this represents a major challenge for many companies. It is therefore often necessary to call on experienced valuation specialists or tools.
Background
In many cases, share options are exercised before the end of the contractual term if the contractual provisions permit this. From a purely financial mathematical point of view, an early exercise of nondividend shares cannot generally be justified. This is because the employee forgoes the fair value of the option, whereas he could realize both the intrinsic and the fair value of the option by selling it. However, this is not the case for employee stock options. In most cases stock options cannot be sold or transferred during their term. Therefore the holder only has the opportunity to generate cash flow before maturity by exercising the option.
Factors determination early exercise in ESOP valuation
The possibility of early exercise has to be reflected in the valuation model on the basis of individual factors. In addition to the question about factors determining exercise behavior, it is also crucial how these factors can be taken into account in the model. Although early exercise can have a significant effect on the value of the option, only a few studies have dealt with this topic to date. There is little consensus on the factors that determine exercise behavior. While factors such as leaving the company before the end of the term and the lack of tradability have an obvious influence on exercise behavior, the effect of other variables require closer analysis. These factors include expected dividend payments, expected future volatility and past share price movements. Individual factors such as financial situation, lack of diversification or risk behavior also play a decisive role.
Model incorporation
Once the factors have been identified, the next step is to integrate them into the valuation model. The model is regularly not based on the actual term of the option but on the expected term. This means that an estimate is made of the probable exercise date (“expected life” method). As this method is based solely on management estimates, the applicability of the method is questionable.
Hull and White consider the possibility of early exercise by taking into account a ratio covering the share price and the exercise price of the option in an adjusted binomial model. Early exercise occurs if the share price at a certain point in time is higher than the target price which is determined by the ratio. Brisley and Anderson compare the cash flow on exercise with the BSM value at each possible exercise date in the binomial model.
Summary
To date, no standard approach has been established for mapping early exercise in the context of share option valuation. As the models developed to date are based on different variables for modeling early exercise. In practice the approach should be selected for which reliable and plausible estimates of the underlying variables can be made.
Early exercise
Expected volatility
Background
The expected volatility represents the degree of fluctuation of the share price during a period. Formally, this risk parameter can be defined as the annualized standard deviation of the steady returns of the share. Volatility represents one of the strongest parameters influencing the level of the option price.
The particular significance of volatility for the measurement of stock option programs is underlined by the FREP’s reference to the problems involved in determining volatility in practice in its 2006 examination report. In practice, volatility tends to be set too low. Given the demonstrably high influence of volatility on the option price, this is not surprising. Nevertheless, a careful estimate of this factor is essential in the valuation of share options in the context of accounting in accordance with the standard.
Concepts of volatility measurment within ESOP valuation
IFRS 2 deals in detail with various factors that must be taken into account:
 implied volatility,
 the historical volatility and
 the tendency of volatility to return to its longterm average.
In principle, the use of implied volatility is to be preferred, as it is based purely on market data and leaves hardly any scope for valuation. However, in the case of companies for which no options are traded on the market, implied volatility cannot be used. In this case, the historical volatility must be taken into account. In many cases, this means that the average historical volatility of the share price over a period that generally corresponds to the remaining term of the option is used for the expected volatility. A problem that frequently arises is the calculation of historical volatility for newly listed companies. In this case, the standard recommends “longest period for which trading data is available”.
Challenges with historical volatility
For unlisted companies, on the other hand, historical volatility cannot be used for estimation purposes. In both cases, the standard stipulates that the volatility of comparable companies (a socalled peer group) should be taken into account when estimating the expected volatility. However, a comparison of the volatilities of listed companies shows that historical volatility does not necessarily correspond to the volatility actually occurred. It can be seen that over a period of 8 years, the volatility estimated using historical volatility deviates from the volatility that actually occurred by an average of 9.8%. It is worth noting that the mean value of the maximum deviations of the 30 companies is 54.7%.
Alternatives
In recent years, other models have become established in the financial world, including the EWMA model (exponentially weighted moving average) and the GARCH model (generalized autoregressive conditional heteroscedasticity). The advantage of these models is that they take into account the fact that volatility is not constant but fluctuates over time. These models have the basic characteristics that, among other things, they calculate the expected volatility from the current value of volatility and the estimator of the previous period(s), i.e. the GARCH or EWMA equation of the previous period. The GARCH model also takes into account the tendency of volatility to return to its longterm average. It is questionable whether these models will also prevail in the estimation of volatility in the course of the valuation of stock options. Last but not least, it must be investigated whether these methods have a better predictive ability compared to the other models.
Background
The ESOP valuation of the equity instruments granted should be performed on the basis of market prices, if such prices are available [IFRS 2.16]. If market prices are not available, a valuation technique should be used to estimate “the price that would have been received for the equity instruments at the measurement date in a transaction between knowledgeable, willing parties […]. The valuation technique must be consistent with generally accepted valuation techniques. It also must take into account all factors and assumptions that knowledgeable, willing market participants would consider. [IFRS 2.17]
Challenges within ESOP valuation
When applying the standard in the context of unlisted companies, market prices are naturally not available; accordingly, suitable valuation methods must be used for estimation. In principle, a variety of valuation methods can be used. In practice, discounted cash flow methods (DCF) and multiple methods (multiples) are frequently used. DCF methods are based on the payment surpluses of integrated corporate planning. These are discounted to the valuation date using a discount rate appropriate to the risk and term. In the multiple method, the value is determined on the basis of financial parameters of comparable listed companies. Both methods have advantages and disadvantages, which should be taken into account in the decisionmaking process. The following table outlines the main advantages and disadvantages of both methods.
Pros  Cons  

Multiple 


Discounted Cashflow 


Considerations and critics within ESOP valuation
The appropriate method must always be selected after weighing up requirements and consideration of consistent parameter derivation. In the literature, the socalled multiple method is one of the applicationrelated valuation approaches, as the value of a company is derived using the market prices or stock market prices of comparable listed companies or the actually realized market prices of analogous transactions in order to reflect the view of the capital market, which is intended to replace the subjective view of a valuer with the objectivity of the capital market.
Summary
The frequent use of the ESOP valuation method is regularly justified by easytounderstand implementation and comprehensible results. As a result, this method is intended to provide a value range which, in combination with its correct interpretation, provides the user with a basis for a possible price determination. The multiple method for determining the share price proves to be advantageous in practice, particularly with regard to the interactions of the practical problems described in determining volatility and the consistency in determining the individual valuation parameters. In analogy to the determination of volatility in approach two, comparably listed companies form the starting point. On the one hand, this makes it possible to ensure sufficient data availability and, on the other, to derive the share price on the basis of listed share prices of comparable companies within a comprehensible value range.