We consider the hedging of European options when the price of the underlying asset follows a single-factor Markovian framework. By working in such a setting, Carr and Wu \cite{carr2014static} derived a spanning relation between a given option and a continuum of shorter-term options written on the same asset. In this paper, we have extended their approach to simultaneously include options over multiple short maturities. We then show a practical implementation of this with a finite set of shorter-term options to determine the hedging error using a Gaussian Quadrature method. We perform a wide range of experiments for both the \textit{Black-Scholes} and \textit{Merton Jump Diffusion} models, illustrating the comparative performance of the two methods.

翻译：考虑标的资产价格服从单因子马尔可夫框架下的欧式期权对冲问题。在此设定下，Carr与Wu \cite{carr2014static}推导出给定期权与一系列同一标的短期期权之间的跨越关系。本文将其方法扩展至同时包含多个短期期限的期权组合。随后，我们展示了基于有限短期期权集合的实际实现方案，通过高斯求积法确定对冲误差。针对\textit{Black-Scholes}模型与\textit{Merton跳扩散}模型开展广泛实验，阐明两种方法的相对性能表现。