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Abstract
This paper examines the reliability of option fair value estimates in the presence of transaction costs. The Black Scholes Merton (BSM) framework assumes zero transaction costs and thus might not provide a reasonable approximation in this context. We investigate the model adjustments companies make to their BSM models to deal with these transaction costs. We specifically examine Employee Stock Option (ESO) plans listed on the French stock exchange, as detailed disclosure on modeling is available for these ESOs. Our analysis questions the reliability of these model adjustments, especially their bias and the extent to which they provide a faithful representation of option fair values. Holding parameter values constant, we find that the model adjustments lead to a median understatement of 52% compared to the BSM model price, higher than the discount we observe for the opportunistic determination of model parameters (below 20%). The paper contributes to the fair value literature by highlighting model risk in the fair valuation of options. This model risk stems from assumptions made about the size of transaction costs and complements the notion of parameter risk analyzed in previous literature. As a result, the model itself might be a possible channel for fair value management.
Acknowledgements
We thank John Donovan, Zhan Gao, Christian Hofmann, Géraldine Hottegindre, Volker Krug, François Le Grand, Marie-Claire Loison, Franz Lorenz, Becky Rawlings, Deborah Schanz, Thorsten Sellhorn, and seminar participants at EDHEC, EMLYON, HEC Paris, LMU Munich, at the Annual Congress of the American Accounting Association 2015, the Annual Congress of the European Accounting Association 2015, and the Annual Conference of the Multinational Finance Society 2013 for their helpful comments and suggestions. We benefited from the valuable research assistance of Lu Yu. We are grateful to the editor, Michel Magnan, and two anonymous referees, whose constructive comments added significant value to the content of the paper and enhanced the clarity of the exposition. Finally, we thank anonymous members of Deloitte and KPMG in France and Germany, who shared their expertise and insights with us in a series of interviews. François Larmande is a member of GREGHEC, CNRS Unit, UMR 2959.
Disclosure statement
No potential conflict of interest was reported by the authors.
Notes
1 The Black-Scholes and Merton model is set up in continuous time, while the Cox-Ross-Rubinstein binomial tree model is set up in discrete time. The Cox-Ross-Rubinstein model converges to the Black-Scholes and Merton model, providing the same prices for European call or put options. Note that the Black-Scholes framework is not restricted to the Black Scholes (BS) formula, which gives the price of a European option. Using trees or Monte-Carlo simulations, it is possible to price many other, more complicated options within this framework.
2 Information asymmetry – the cost of trading with investors that are potentially better informed – is often put forward to explain a large part of these costs.
3 Aboody et al. (Citation2006) define reliability as one of the primary factors that standard setters consider when assessing accounting amounts. The reliability of accounting amounts has several dimensions (FASB, Citation1980). One is verifiability, i.e. the extent to which different measures produce the same amount; another is neutrality, i.e. the amount should be an unbiased measure of the object of measurement. A third dimension of reliability is representational faithfulness, i.e. the extent to which the amount represents what it purports to represent.
4 Standard setters (IASB, Citation2011, BC150), use slightly different definitions. For them, model risk refers to using the wrong valuation technique, while parameter risk refers to using the wrong parameters. However, defining model risk as encompassing both ‘the wrong valuation technique’ and the wrong parameters seems to be the more widely used approach. See, for instance, the KPMG reports (KPMG, Citation2016b, Citation2016a), which state that ‘model risk can be understood as the risk of model failure due to incorrect inputs, flawed assumptions, and incorrect model design or model misuse’. According to one of the specialists we interviewed, Ms. C,
model risk is whenever an inadequate model, be it the wrong model for the exercise that needs to be performed, or a model that is incorrectly implemented, or a model that is run with inadequate data, leads to two types of problem […] a loss in the P&L calculation [… since] I performed pricing that was in favour of my trading counterparty but wasn’t in my favour [… or] inadequate financial figures or regulatory ratios being recognized, or something like that, which would then lead to reputational risk and maybe more effort dealing with requirements, and further audits with the regulator.
5 Hall and Murphy (Citation2002) state that ‘for financial accounting purposes, what should matter is the company’s cost of granting an option (which is reasonably approximated by Black-Scholes) not the value of the option to the executive recipient’. This point is supported by IFRS 2, which explains that ‘factors that affect the value of the option from the individual employee’s perspective only are not relevant to estimating the price that would be set by a knowledgeable, willing market participant’ (IASB, Citation2004, §B10).
10 We thank one of the specialists we interviewed, Ms. C for providing these examples.
11 We are aware of another setting where firms use discounts in a fair valuation process to account for transaction costs: employee-reserved capital with a resale restriction. ‘The cost of employee-reserved capital increases is immediately expensed. A discount reduces the expense in order to account for the non-transferability of the shares awarded to the employees over a period of five years.’ (Total 2013 Registration Document) It is a share and not an option, but the fundamental issue is similar: value for the employee versus cost for the company of this resale restriction.
12 Cox et al. (Citation1979) make the same assumption about transaction costs for their discrete time version of the Black-Scholes model, ‘We also ignore transaction costs, margin requirements and taxes.’ (p. 231, footnote 3)
13 As the quotation in the previous paragraph shows, the notion of ‘illiquidity’ or of lack of liquidity is often used instead of transaction costs. This notion of illiquidity relates to the fact that an asset cannot be easily sold without substantially affecting the price, which is closely related to the idea of transaction costs. To avoid any confusion, we will follow this example and use the term illiquidity until the end of this Section.
14 Note, however, that the BSM replication strategy is no longer optimal when transaction costs are factored in. Thus, how far above the model price the selling price should be set depends on the hedging strategy of the writer of the option, which in turn depends on his or her risk profile, and also on the amount and nature of transaction costs. Soner, Shreeve, and Cvitanic (Citation1995) point out that in a continuous-time Black-Scholes context, a dynamic hedging strategy has an infinite price. They therefore consider dominant strategies and show that a simple buy-and-hold strategy is the least expensive method of dominating a European call. Bensaid, Lesne, Pagès, and Scheinkman (Citation1992) also address the problem of finding the optimal portfolio among those that dominate a given derivative asset at maturity, and derive an interval for its price. They work with a discrete-time Cox, Ross, and Rubinstein (CRR) model, show that a replicating portfolio exists, and find that the replicating strategy can be more expensive than a dominating strategy.
15 The ESOs are referred to in French as Bons d’Acquisition d’Actions Remboursables (BAAR), Bons de Souscription d’Acquisition Remboursables (BSAR), and Bons de Souscription et/ou d’Acquisition d’Actions Remboursables (BSAAR). These terms basically refer to the fact that at the exercise date, the shares provided are treasury shares, shares to be issued, and treasury shares or shares to be issued, respectively.
16 There are only three cases in our sample of an exercisability window during which the ESO remains unlisted. We treat them in the same way as the other ESOs in our sample and assume that there is no possibility of early exercise in these three cases.
17 All prospectuses are available at: http://www.amf-france.org/en_US/Recherche-avancee.html
18 In 10% of cases there is no external expert. In these cases, a valuation report providing similar information is present. These reports come from the company’s investment bank or financial advisor, or are internally prepared by the company. We treat cases with no external expert in the same way as the others.
19 In order to check the robustness of our statistical tests, we also ran a sign test on medians in addition to the initial Wilcoxon signed ranks test. We obtain the same results for statistical significance with this second statistical test, proving the robustness of our initial results.
20 Or to see it in a more financial way, the company can use the proceeds from the sale at fair value to fund the ‘replicating portfolio’, which allows it to have the exact number of treasury shares required in case of exercise, alleviating the need to issue new shares.
21 Note that levers for ‘fair value management’ exist when modeling dilution for options not sold at their fair value. This relates to the extent to which one assumes the share price at the pre-grant announcement date already anticipates the effects of the grant. If the market is efficient and fully anticipates the grant and the dilutive effect of the option’s exercise, then Hull and White (Citation2004b) argue that the grant will not affect the share price, as the latter already reflects this information. This is the approach taken by US standard setters: SFAS 123R states, ‘For public entities, the [FAS] Board expects that situations in which such a separate adjustment [for the potential dilutive effect] is needed will be rare.’ However, this reasoning assumes that the market is efficient and that it has rational expectations. If this is not the case, then we need a warrant pricing model that takes dilution into account. Li and Wong (Citation2005) use this type of warrant pricing model and find an average price difference of 6% compared to an option pricing model that does not adjust for dilution.
22 Of course, there can be valid reasons for discounting a BSM price in a fair value context. Ikäheimo, Kuosa, and Puttonen (Citation2006) provide examples of listed ESOs in Finland. They find that, in addition to the suboptimal early exercise behavior of company employees due to vesting conditions, the expected life of the ESO could be shorter due to possible changes in corporate structure, such as mergers or demergers. Such behavior or changes would thus affect both counterparties of the ESO.
23 She states,
And if I have a trade that is very, very favorable for my regulatory capital ratios, I would negotiate differently, and that could, in many cases, also lead to mostly credit derivatives trades being done with a negative day 1 P&L, which is very, very helpful in terms of regulatory capital requirements, and that’s something we see quite often.
24 We found no mention in any expert report of an expected option life lower than the contractual one.
25 IFRS favors the use of implied or historical volatility as an unbiased estimate of volatility and requires any deviation from this approach to be clearly justified. Yet, since it is in fact the expected volatility over the option life that should be taken into account, standard setters leave room for possible distortion as a result of the influence of future events that are, by their nature, difficult to anticipate.
26 We note that the difference compared to the ex post realized volatility is statistically significant at the 5% level. This lower statistical significance can be explained by the barrier effect in the pricing model, which makes the option price less sensitive to the volatility estimate.
27 We have also tested for the impact of additional variables, specifically the valuation method, the model adjustment, or the arguments provided by the experts (results are untabulated). None of them is statistically significant. However, by including the three main expert firms as individual variables, we find that the coefficients of the second and third largest expert firms (in market share) are negative and significant at 10% (see next section on expert effect).
28 Francis et al. (Citation2013) find that the market share of the Big Four in France was 52% in 2007 for all listed companies. The study conducted by Ewert and London Economics (Citation2006) reveals that the market share for the Big Four in France was 73% in 2004 for the 40 largest listed companies (CAC40 index).
29 The difference between the two samples is not statistically significant (Median test sig = 0.159).