到期后离散股息调整股票价格和执行价格
Discrete dividends after maturity adjust the stock and strike prices
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中文总结 AI 辅助
研究到期后离散股息对股票和执行价格的影响，提出扩展的布莱克-斯科尔斯公式，使期权定价模型一致，还针对美式看涨期权，建立提前行权最优情况并推导公式扩展，刻画最优行权策略。
中文摘要 AI 辅助
对支付离散股息的股票进行欧式看涨期权定价的标准方法是在布莱克-斯科尔斯公式中从初始股票价格中减去股息的现值。然而，当存在到期后股息时，这与模型不一致。在托管股息模型中，我们强调了布莱克-斯科尔斯公式的一种扩展，其中到期后股息会调整股票价格和执行价格，使得所有期限的看涨期权都能以模型一致的方式定价。作为对到期前有一次股息的美式看涨期权的相关应用，我们建立了一个总是提前行权最优的被忽视的情况，并推导出到期后有股息时Roll-Geske-Whaley公式的扩展，包括完全刻画最优行权策略。
英文摘要
The standard method to price European calls on a discrete dividend-paying stock is to subtract the present value of the dividends from the initial stock price in the Black-Scholes formula. However, when there are dividends after maturity, this is inconsistent with the model. Within the escrowed dividend model, we highlight an extension of the Black-Scholes formula in which those dividends after maturity adjust both the stock price and strike price, allowing for calls over all maturities to be priced in a model-consistent way. As a related application to American calls with a single dividend before maturity, we establish a neglected case where it is always optimal to early exercise and derive an extension of the Roll-Geske-Whaley formula when there are dividends after maturity, including fully characterising the optimal exercise policy.
