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Valuing Employee Stock Options: Does the Model Matter?

Manuel Ammann, Ralf Seiz

2004
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Financial analysts journal
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We present a numerical analysis of valuation models for employee stock options. In particular, we analyze the impact of the model on the resulting option prices and investigate the sensitivity of pricing differences between models with respect to changes in the parameters. We show that, for most models such as the FASB 123 model, the utilitymaximizing model by Rubinstein, the Hull-White model, and a simple reference model proposed in this paper, the price reduction relative to standard options
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... s uniquely determined by the expected life of the option. In fact, with the exception of the FASB 123 model, pricing differences are negligible if the models are calibrated to the same expected life of the option. Consequently, the application of models with several hard-to-estimate parameters such as the utility-maximizing model can be greatly simplified by this calibration approach because expected life is easier to estimate than utility parameters. Abstract We present a numerical analysis of valuation models for employee stock options. In particular, we analyze the impact of the model on the resulting option prices and investigate the sensitivity of pricing differences between models with respect to changes in the parameters. We show that, for most models such as the FASB 123 model, the utilitymaximizing model by Rubinstein, the Hull-White model, and a simple reference model proposed in this paper, the price reduction relative to standard options is uniquely determined by the expected life of the option. In fact, with the exception of the FASB 123 model, pricing differences are negligible if the models are calibrated to the same expected life of the option. Consequently, the application of models with several hard-to-estimate parameters such as the utility-maximizing model can be greatly simplified by this calibration approach because expected life is easier to estimate than utility parameters. Introduction Formelabschnitt 1 Employee stock options present a number of specific issues that prevent their valuation with standard option pricing models. Although several pricing models for employee stock options have been proposed, no standard model has been established to this date. As a contribution to the ongoing model discussion, we present a detailed side-by-side comparison of option prices obtained with several models. In particular, we investigate a utility-maximizing model as proposed by Kulatilaka and Marcus (1994), Huddart (1994) and Rubinstein (1995), a recent model by Hull and White (2002, 2004), and the model proposed by the Financial Accounting Standards Board (1995), referred to as FASB 123. Furthermore, we propose a new model that accounts for sub-optimal exercise because of non-tradability by a simple adjustment of the exercise price. This model is called Enhanced American because of its similarity with a standard American option. In addition, all these models are also compared to standard Black-Scholes and American-style options. Furthermore, for the utility-maximizing model, we found that arbitrarily chosen combinations of the utility-relevant parameters, such as risk aversion, expected return, and non-option wealth, produce identical option prices if they imply the same expected life of the option. Therefore, by using the expected life of the option as an implicit parameter, the utility-maximizing model, which relies on unobservable and hard to estimate parameters, can be simplified in its application because, instead of the original model parameters, only the expected life parameter needs to be estimated. As a further contribution, we show that modeling a time-varying employee exit rate can increase the value of the option if it is assumed that the exit rate decreases during the vesting period if the option is in-the-money. Hence, valuation models using constant exit rates tend to underestimate the value of employee options.

doi:10.2469/faj.v60.n5.2654
fatcat:eva6lxxzhfgnbcmdqoitr2gthi