Spatial Dependence in Option Observation Errors

Abstract

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.

Estimating Option Pricing Models Using a Characteristic Function-Based Linear State Space Representation

“…This would, however, result in more complex expressions for the covariance terms in the measurement errors that we derive below. Furthermore, Andersen et al (2021) find evidence of limited dependence in the observation errors for S&P 500 index options. They also show that this dependence declined sharply for short-dated options in recent years, due to improved liquidity.…”

“…Assumption 2(i ) excludes in particular dependence of the observation errors across strikes and is also often imposed in the literature (see, for instance, Christoffersen, Jacobs, & Mimouni, 2010, Andersen et al, 2015a. This assumption can be relaxed by introducing a spatial dependence as in Andersen, Fusari, Todorov, and Varneskov (2021). This would, however, result in more complex expressions for the covariance terms in the measurement errors that we derive below.…”

Testing for Parameter Instability and Structural Change in Persistent Predictive Regressions

“…where E t captures a Jensen's inequality bias from the square-root transformation and measurement errors in VIX, generated by a (time-varying) truncation of the strike range in the construction of the and observation errors in the underlying options; see, e.g., Jiang & Tian (2005), Andersen & Bondarenko (2007), Andersen, Bondarenko & Gonzalez-Perez (2015) and Andersen, Fusari, Todorov & Varneskov (2020). 9 Hence, we have two sources of errors; one arising from standard measurement errors and another from the volatility risk premium.…”

Testing for Parameter Instability and Structural Change in Persistent Predictive Regressions

“…where E t captures a Jensen's inequality bias from the square-root transformation and measurement errors in VIX, generated by a (time-varying) truncation of the strike range in the construction of the index and observation errors in the underlying options; see, e.g., Jiang & Tian (2005), Andersen & Bondarenko (2007), Andersen, Bondarenko & Gonzalez-Perez (2015) and Andersen, Fusari, Todorov & Varneskov (2020). 9 Hence, we have two sources of errors; one arising from standard measurement errors and another from the volatility risk premium.…”