What expected volatility should I use in the Black-Scholes model for IFRS 2 if the company has little trading history?

fe | | Expected dividend yield (q) | Estimate | Forecast annual dividend ÷ current share price; or continuous dividend yield | Formula (simplified): Fair value = S × e^(−qT) × N(d1) − K × e^(−rT) × N(d2) Where d1 and d2 incorporate all six inputs. Most preparers use a spreadsheet or specialist valuation tool — hand calculation is rarely required in practice. Black-Scholes limitations: - Assumes constant volatility and dividend yield over the option life. - Does not handle early exercise — important when employees typically exercise significantly before the contractual end date. - Cannot price market conditions directly (e.g., TSR hurdles) without modification. The Binomial (Lattice) Model The binomial model is preferred when: - Options can be exercised early (American-style features); - Vesting is gradual (graded vesting where each tranche has a different expected life); - Expected exercise behaviour varies across employee groups. The model builds a price tree at small time steps, calculates the option value at each node working backwards from expiry, and applies an early exercise rule at each node. Results converge to Black-Scholes as step size decreases for European options. The binomial model produces a lower fair value than Black-Scholes when early exercise is likely because it explicitly models the benefit foregone by exercising early. Monte Carlo Simulation — Market Conditions When the vesting condition is market-based — most commonly a total shareholder return (TSR) target relative to a peer index — neither Black-Scholes nor binomial models can price it directly. Monte Carlo simulation: 1. Simulates thousands of possible future share price paths for the entity and its comparator group. 2. Determines, in each simulation, whether the TSR condition i

Why does IFRS 2 require Monte Carlo simulation for TSR vesting conditions instead of Black-Scholes?

s met and what the payout would be. 3. Averages the present-value payouts across all simulations. Monte Carlo produces a grant-date fair value that already embeds the probability of meeting the TSR hurdle — which is why the IFRS 2 expense is not reduced if the TSR hurdle is subsequently missed. Key Inputs — Practical Guidance Expected Volatility This is the most judgmental and auditor-scrutinised input: - Historical approach: compute annualised standard deviation of daily log-returns over a look-back period equal to the expected option life. Most common approach. - Implied volatility: back out volatility from traded options on the entity's shares (if available). More forward-looking but less available for smaller entities. - Peer group: for newly listed entities without sufficient history, use volatility of comparable listed companies. - Blended approach: weight historical and implied, especially when the entity's risk profile has changed. Expected Option Life The contractual life is the maximum; actual expected life is shorter due to early exercise. Use: - Historical exercise patterns if data exist (weighted average of time to exercise or lapse for past grants). - Simplified approach (IFRS 2.B17): (vesting period + contractual life) ÷ 2. Dividend Yield Use the forecast annual dividend divided by the current share price. For entities with no dividend history, zero is appropriate, with sensitivity disclosure if the amount would be material. Worked Example — Black-Scholes Inputs: exercise price €25, share price on grant date €28, expected option life 4 years, expected volatility 35%, risk-free rate 3.5%, dividend yield 1.5%. Using standard Black-Scholes: - d1 = [ln(28/25) + (0.035 − 0.015 + 0.5 × 0.35²) × 4] / (0.35 × √4) ≈ 0.82 - d2 = d1 − 0.35 × √4 ≈ 0.1

What is the difference between expected option life and contractual life under IFRS 2?

2 - N(0.82) ≈ 0.7939, N(0.12) ≈ 0.5478 Fair value ≈ €8.30 per option Sensitivity: increasing volatility from 35% to 40% raises fair value to approximately €9.10 — a 10% increase. This illustrates why volatility assumptions are material and must be disclosed (IFRS 2.47). Disclosure Requirements (IFRS 2.47) Entities must disclose: - The option-pricing model used and why; - All key inputs: exercise price, share price at grant, expected life, volatility, dividend yield, risk-free rate; - The method used to determine expected volatility and whether it is based on historical or implied data; - Any other features incorporated into the measurement (e.g., market conditions). Common Pitfalls - Using contractual life instead of expected life: Black-Scholes with a 10-year contractual life significantly overestimates fair value. Expected life must reflect actual exercise patterns. - Ignoring dividends: omitting the dividend yield overstates fair value — the option holder misses dividends declared during the option life. - Applying Black-Scholes to market-condition awards without adjustment: standard Black-Scholes cannot price TSR conditions. Monte Carlo simulation or a barrier-option approach is required. - Not disclosing sensitivity to volatility: IFRS 2.47 requires disclosure of how fair value would change for reasonably possible changes in key inputs. Key Paragraphs - IFRS 2.16 — requirement to use an option-pricing model - IFRS 2.17 — inputs to the valuation: exercise price, life, share price, volatility, dividends, risk-free rate - IFRS 2.18 — additional factors (e.g., non-transferability, vesting conditions) included where market participants would price them - IFRS 2.24 — intrinsic value as narrow fallback - IFRS 2.47 — disclosure of measurement inputs and mod

IFRS 2 Fair Value Measurement of Share Options — Black-Scholes, Binomial, Monte Carlo

IFRS 2 Fair Value Measurement of Share Options — Core Rule

IFRS 2.16–18 requires that the fair value of options and other equity instruments granted to employees be estimated using an option-pricing model that accounts for: the exercise price, the option life, the current share price, the expected volatility of the share price, dividends expected on the shares, and the risk-free interest rate over the option term. Grant-date fair value is determined once and is never revised.

Why Option-Pricing Models Are Required

Employee share options cannot be valued using intrinsic value alone (share price minus exercise price) because intrinsic value ignores time value — the probability that the option will move deeper in-the-money before expiry. IFRS 2 requires fair value, which captures both intrinsic value and time value. Intrinsic value measurement is only a permitted fallback where fair value cannot be reliably estimated (IFRS 2.24), which in practice applies only to unlisted entities with complex equity structures.

The Black-Scholes Model

Black-Scholes is the default model for European-style options (exercisable only at expiry) and for options where early exercise behaviour is not material.