The practice of executives influencing their option compensation by setting a grant date retrospectively is known as backdating. Since executive stock options are usually granted at-the-money, selecting an advantageous grant date to coincide with a low stock price will be valuable to an executive. Empirical evidence shows that backdating of executive stock option grants was prevalent, particularly at firms with highly volatile stock prices. Executives who have the opportunity to backdate should take this into account in their valuation. We quantify the value to a risk averse executive of a lucky option grant with strike chosen to coincide with the lowest stock price of the month. We show the ex ante gain to risk averse executives from the ability to backdate increases with both risk aversion and with volatility, and is significant in magnitude. Our model involves valuing the embedded partial American lookback option in a utility indifference setting with key features of risk aversion, inability to diversify and early exercise.

中文翻译：

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幸运的价值：期权回溯和不可分散风险

高管通过追溯设置授予日期来影响其期权薪酬的做法被称为回溯。由于高管股票期权通常以平价方式授予，因此选择一个有利的授予日期以配合低股价对高管来说是有价值的。经验证据表明，执行股票期权授予的回溯很普遍，尤其是在股价高度波动的公司中。有机会回溯的高管在估值时应考虑到这一点。我们量化了一个幸运期权授予的风险规避执行官的价值，其中罢工选择与当月最低股价一致。我们展示了事前风险规避的高管从回溯能力中获得的收益随着风险规避和波动性的增加而增加，并且在幅度上是显着的。我们的模型涉及在效用无差异环境中评估嵌入的部分美式回溯期权，其关键特征是风险规避、无法多样化和早期行使。