Employee stock options (ESOs) are an integral component of compensation in the US. In fact, almost all S&P 500 companies grant options to their top executives, and the total value accounts for almost half of the total pay for their CEOs. In view of the extensive use and significant cost of ESOs to firms, the Financial Accounting Standards Board (FASB) has mandated expensing ESOs since 2004. This gives rise to the need to create a reasonable valuation method for these options for most firms that grant ESOs to their employees. The valuation of ESOs involves a number of challenging issues, and is thus an important active research area in Accounting, Corporate Finance, and Financial Mathematics.In this exciting book, the author discusses the practical and challenging problems surrounding ESOs from a financial mathematician's perspective. This book provides a systematic overview of the contractual features of ESOs and thoughtful discussions of different valuation approaches, with emphasis on three major aspects: (i) hedging strategies; (ii) exercise timing; and (iii) valuation methodologies. In addition to addressing each of these categories, this book also highlights their connections and combined effects of the cost of ESOs to firms, as well as examines the implications to modeling and valuation approaches. The book features a unique approach that combines stochastic modeling and control techniques with option pricing theory, and provides formulas and numerical schemes for fast implementation and clear illustration.