In this paper, we develop the first formal nonparametric test for whether the observation errors in option panels display spatial dependence. The panel consists of options with different strikes and tenors written on a given underlying asset. The asymptotic design is of the infill type—the mesh of the strike grid for the observed options shrinks asymptotically to zero, while the set of observation times and tenors for the option panel remains fixed. We propose a Portmanteau test for the null hypothesis of no spatial autocorrelation in the observation error. The test makes use of the smoothness of the true (unobserved) option price as a function of its strike and is robust to the presence of heteroskedasticity of unknown form in the observation error. A Monte Carlo study shows good finite-sample properties of the developed testing procedure and an empirical application to S&P 500 index option data reveals mild spatial dependence in the observation error, which has been declining in recent years.

中文翻译：

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选项观察误差的空间相关性

在本文中，我们开发了第一个正式的非参数检验，用于检验选项面板中的观察误差是否显示空间依赖性。该面板由写在给定标的资产上的具有不同行使价和期限的期权组成。渐近设计属于填充类型——观察到的选项的罢工网格的网格渐近地缩小到零，而选项面板的观察时间和期限集保持固定。我们针对观察误差中没有空间自相关的原假设提出了 Portmanteau 检验。该检验利用真实（未观察到的）期权价格的平滑度作为其行使价的函数，并且对于观察误差中未知形式的异方差的存在是稳健的。