Gary Joseph | August 2022

This article was originally published by The Lawyer’s Daily (www.thelawyersdaily.ca), part of LexisNexis Canada Inc.

As we discussed in the first of this two-part series, when employee stock options (ESOs) form part of the asset pool of a separated spouse, counsel must be familiar with the treatment of and valuation of this unique asset. In this article, we delve deeper into the two most commonly used option valuation models for ESOs: the "binomial model" and the "Black-Scholes-Merton (BSM) model." The latter model takes its name from the conomists who first published the model in 1973 - namely, Fischer Black, Myron Scholes and Robert Merton.

Beyond relying on the assumption of zero-arbitrage opportunity, the price of an option arrived at using the BSM model relies on several further assumptions. Amongst these are assumptions that there are no transaction costs or regulatory constraints; that traders can borrow and lend without any premium linked to risk; that early exercising is not allowed; and that both the return and volatility of the return on the underlying are constant.

The BSM model remains widely used despite its high level of abstraction and, at times, implausible and impractical assumptions. For example, constant hedging can be costly, and the volatility of movements in the prices of underlying assets are not generally constant over time. That said, in the years since the BSM model was first published, numerous variants have emerged that allow for a wider range of real-world applications. For the exact formula underlying the BSM model, see Note 1 below.

The valuation models discussed here recognize two sources of value within options: "intrinsic value" and "time value." The intrinsic value of an option or ESO amounts to the difference between the underlying stock price and
"strike price." Where the underlying stock price is equal to or below the strike price, the option's intrinsic value is nil, and the entire price of the option is linked to time value. An option's time value amounts to the premium for the possibility of generating higher returns in the future through the choice of exercising the ESO In-the-money (or above the Intrinsic value).

To illustrate, suppose that an employee Is granted ESOs as part of a compensation package on July 1, 2022, (grant date) with a strike price of $10. Further, suppose that, per the vesting requirements, these ESOs can be exercised only after a minimum of two years from the grant date (the vesting period), and must be exercised no later than five years from the grant date (expiry date). Finally, suppose that, on the same date that these ESOs are granted, the company stock Is trading at $15, and that a publicly traded call option Identical to the ESO in question is trading for $8. Based on the above, a valuator would determine the ESO's value as follows: the intrinsic value on July 1, 2022, is $5 - that is, the $15 stock price less the $10 strike price offered by the option. And the ESO's time
value on July 1, 2022, Is $3 - that is, the $8 price at which an identical call option Is trading on the open market less the $5 intrinsic value.

AI discussed, real-world applications of the BSM model often require modifications to the original framework. As relates to the valuation of ESOs, adjustments will generally be needed to factor in risks that would preclude future vesting (e.g., possible termination of employment, possible disability, possible death, or possible early exercise of the option rights). Other adjustments will generally be needed to factor in unique risks and contingencies associated with the ESOs relative to the more theoretical option entertained in the BSM model. Amongst these are a lack of marketability linked to restrictions on the selling or transferring ESOs, low trading volume where selling or transferring is permitted, restrictions on hedging imposed on holders of ESOs, and company-specific weakening and downturn into the future as assessed as of the separation date.

Lastly, the net fair market value of ESOs as of the separation date may require a downward adjustment to account for the present value of notional disposition costs likely to be incurred, including ESO acquisition costs and income taxes.

Note 1

The theoretical value of a call option for a dividend-paying stock under the BSM model is expressed as follows:

c = e-δTSN(d1) - e-rTXN(d2)

Where:

S = spot (or market) price of the underlying asset
X = strike price of the option
T = time to maturity (or expiration) on the option
σ = volatility during the term
δ = dividend yield during the term
r = risk-free interest rate during the term
d1 = ln(S/X) + (r +σ2/2)T
σ
d2 = d1 - σ
N(d) = cumulative standard normal density function (that is, the probability of obtaining a value less than d based on a random sample of observations taken from the normal distribution)

A Nobel Prize in economics in 1997 was awarded based in part on the work on the BSM model. Source: Chartered Financial Analyst {CFA): Fixed Income and Derivatives by CFA Institute.

This is the second of a two-part series. Read the first article: The valuation of employee stock options, part one.

Gary S. Joseph is the managing partner at MacDonald & Partners LLP. A certified specialist in family law, he has been reported in over 350 family law decisions at all court levels in Ontario and Alberta. He has also appeared as counsel in the Supreme Court of Canada. He is a past family law instructor of the Ontario Bar Admission course and the winner of the 2021 OBA Award for Excellence in Family Law. Jen Capuno specializes in asset and business valuations, litigation support and forensic accounting. She practises at VFDR Inc., focusing on matrimonial disputes and damage quantification. len is accredited as a chartered professional accountant, chartered financial analyst, chartered business valuator, chartered investment manager, certified fraud examiner and certified in financial forensics.

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