英文标题：
《ESO Valuation with Job Termination Risk and Jumps in Stock Price》
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作者：
Tim Leung and Haohua Wan
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最新提交年份：
2015
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英文摘要：
Employee stock options (ESOs) are American-style call options that can be terminated early due to employment shock. This paper studies an ESO valuation framework that accounts for job termination risk and jumps in the company stock price. Under general L\\\'evy stock price dynamics, we show that a higher job termination risk induces the ESO holder to voluntarily accelerate exercise, which in turn reduces the cost to the company. The holder\'s optimal exercise boundary and ESO cost are determined by solving an inhomogeneous partial integro-differential variational inequality (PIDVI). We apply Fourier transform to simplify the variational inequality and develop accurate numerical methods. Furthermore, when the stock price follows a geometric Brownian motion, we provide closed-form formulas for both the vested and unvested perpetual ESOs. Our model is also applied to evaluate the probabilities of understating ESO expenses and contract termination.
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中文摘要：
员工股票期权（ESO）是美式看涨期权，可因就业冲击而提前终止。本文研究了一个考虑离职风险和公司股价波动的ESO估值框架。在一般的列维股价动态下，我们发现较高的离职风险会促使ESO持有人自愿加速行使，从而降低公司的成本。通过求解非齐次偏积分微分变分不等式（PIDVI），确定持有者的最优执行边界和ESO成本。我们应用傅里叶变换来简化变分不等式并发展精确的数值方法。此外，当股票价格服从几何布朗运动时，我们给出了既得利益和未既得利益的永久性股票期权的闭式公式。我们的模型也被用于评估低估ESO费用和合同终止的概率。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Pricing of Securities 证券定价
分类描述：Valuation and hedging of financial securities, their derivatives, and structured products
金融证券及其衍生产品和结构化产品的估值和套期保值
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