What Type of Process Underlies Options? A Simple Robust Test

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Abstract
We develop a simple robust method to distinguish the presence of continuous and discontinuous components in the price of an asset underlying options. Our method examines the prices of at‐the‐money and out‐of‐the‐money options as the option's time‐to‐maturity approaches zero. We show that these prices converge to zero at speeds that depend upon whether the underlying asset price process is purely continuous, purely discontinuous, or a combination of both. We apply the method to S&P 500 index options and find the existence of both a continuous component and a jump component in the index.