In this paper, we work under GARCH models to value options on the maximum or the minimum of two prices. In addition, we consider not only two underlying asset prices but also geometric average ones. Further, default risk is also incorporated in a reduced-form model. In the proposed framework, closed-form pricing formulae of options on the maximum with or without default risk are derived and then used to perform numerical examples.

中文翻译：

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GARCH模型下最大两个具有违约风险的价格的期权估值


在本文中，我们使用 GARCH 模型来根据两个价格的最大值或最小值来评估期权。此外，我们不仅考虑两个标的资产价格，还考虑几何平均价格。此外，违约风险也被纳入简化模型中。在所提出的框架中，推导了带或不带违约风险的最大期权的封闭式定价公式，然后用于执行数值示例。