Comparative Valuation of Employee Stock Options Using CRR and Enhanced American Models with Vesting and Exit Effects
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Employee Stock Options, Enhanced American Model, Cox-Ross-Rubinstein Model, Vesting Period, Exit Risk, Fair Value Measurement
Abstract
Employee stock options (ESOs) are required to be measured at grant-date fair value under existing accounting standards, yet classical lattice models typically assume frictionless exercise behavior. In practice, ESO contracts incorporate vesting restrictions, employee exit risk, and behavioral exercise triggers that can materially affect valuation outcomes. This study provides a structural comparison between the Cox-Ross-Rubinstein (CRR) American model and the Enhanced American (EA) framework within a unified binomial setting in which the probabilistic return process constant to isolate employment-related frictions. An analytical dominance result is established, showing that EA valuations remain strictly below the CRR American benchmark under these frictions. Numerical experiments confirm the theoretical ordering and quantify its economic magnitude: under moderate frictions, valuation gaps remain limited to approximately 2-3%, whereas under high exit intensity and conservative trigger thresholds, the discount expands substantially to approximately 65-69%, particularly for long-dated and near-the-money contracts. Heatmap analysis across volatility and dividend regimes further demonstrates that this dominance ordering persists under economically relevant parameter variations. The findings indicate that employment-related frictions constitute a materially significant component of ESO valuation and that model choice within fair-value measurement frameworks can meaningfully influence reported compensation expenses.
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