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Graduate-Level Modeling · Share-Based Payment Accounting & Valuation

Employee Stock Option Fair Value Model Under ASC 718 (Hull-White Enhanced Model)

An employee can't sell the option, only exercise it or lose it. That single fact means Black-Scholes was never built for this, and the real accounting number requires simulating how people actually behave.

How To Use This Model

Reading This Tool

Plain Black-Scholes assumes an option can be freely traded or held to the day it expires. An employee stock option can't be sold, vests over time, and gets forfeited or force-exercised the moment someone leaves the company, none of which Black-Scholes was built to handle.

This tool runs the Hull-White Enhanced model: a full Monte Carlo simulation where employees voluntarily exercise once the stock clears a multiple of the strike, or are forced to exercise-or-forfeit on departure, producing the grant-date fair value ASC 718 and IFRS 2 actually require, along with the expected term that number implies.

Option Grant Terms

Grant-Date Stock Price $50

Exercise (Strike) Price $50

Expected Volatility 30%

Risk-Free Rate 4.0%

Expected Dividend Yield 1.0%

Contractual Term (Years) 10

Vesting & Employee Behaviour

Cliff Vesting Period (Months) 48

Suboptimal Exercise Multiple (M × Strike) 2.0x

Annual Employee Turnover Rate 15%

Post-Termination Exercise Window (Months) 3

Monte Carlo Paths 15000

Number Of Options Granted 100,000

The post-termination exercise window here is simplified to an immediate exercise-or-forfeit decision at departure, rather than modeling a separate short window with its own stock price path.

Grant-Date Fair Value

ESO Fair Value Per Option (Hull-White)

Standard Black-Scholes (Contractual Term)

Implied Expected Term

Total Grant Fair Value (All Options)

Fair Value: Naive Black-Scholes vs. Hull-White Enhanced Model

Share-Based Payment Accounting & Valuation

The Core Simulation Logic

Each month, simulate S_t+1 = S_t·exp[(r−q−σ²/2)/12 + σ√(1/12)·Z]
If vested and S_t ≥ M·K: voluntary exercise, payoff = S_t−K
If a random departure draw fires: forfeit (if unvested) or exercise-if-ITM/forfeit-if-OTM (if vested)
If neither trigger fires by contractual maturity T: standard payoff max(S_T−K, 0)
Fair Value = mean of all simulated discounted payoffs

When To Actually Use This Model

Teaching share-based payment accounting and the mechanics behind the ASC 718 / IFRS 2 grant-date fair value requirement in a financial accounting or valuation course.
Estimating the stock compensation expense a company should expect to record for a new option grant, and how sensitive that expense is to turnover and vesting assumptions.
Cross-checking an auditor's or valuation specialist's ESO fair value against an independent model before relying on either.

Key Assumptions & Limitations

Uses a single cliff-vesting date, real grants often use graded vesting (e.g., 25% per year over four years), which this tool doesn't separately model.
Assumes a single, constant employee turnover hazard rate for the whole population, real companies segment this by seniority, tenure and role.
The suboptimal exercise multiple is treated as a single company-wide constant, real historical exercise behaviour, when available, is usually a better-fitting input than an assumed multiple.

Foundational Reference

Hull, J., & White, A. (2004). How to Value Employee Stock Options. Financial Analysts Journal, 60(1), 114-119.

Need the personal tax side of exercising these too?

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