<![CDATA[This study explores the Employee Stock Option (ESO) model proposed by Liao and Lyuu, which provides a robust framework for addressing critical factors such as dilution, early exercise, and employee forfeiture rates. The model is solved using the trinomial tree method, allowing for the consideration of three possible stock price movements: increase, unchanged, or decrease. This approach combines forward and backward calculations to accurately evaluate ESO values by accounting for the complex interactions of these parameters. Dilution effects are modeled by adjusting stock prices based on outstanding shares and strike prices, while early exercise probabilities are addressed using a modified Chi-Square distribution to represent employee behavior. Additionally, the forfeiture rate is dynamically adjusted based on ESO returns and the ratio of stock-to-strike prices. The analysis reveals that ESO price negatively correlates with strike price and forfeiture rate, whereas parameters such as vesting time, maturity date, risk-free rate, volatility, and the number of ESOs granted exhibit positive correlations. This comprehensive methodology demonstrates the practical applicability of the Liao and Lyuu model for real-world ESO valuation. By integrating these critical factors into a unified framework, the study contributes significantly to the literature on financial modeling and provides actionable insights for companies seeking to optimize their ESO programs.]]>
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