CRIF Working Paper No. 02009

What Type of Process Underlies Options? A Simple Robust Test

Title: What Type of Process Underlies Options? A Simple Robust Test

Authors: Peter Carr (New York University)

              Liuren Wu (Fordham University)

Contact: wu@fordham.edu

Keywords: Jumps, continuous martingale, option pricing, Levy density, double tails, local time.

JEL Classification: G12, G13, C52

Abstract: We develop a simple robust test for the presence of continuous and discontinuous (jump) components in the price of an asset underlying an option. Our test examines the prices of at-the-money and out-the-money options as the option maturity approaches zero. We show that these prices converge to zero at speeds which depend upon whether the sample path of the underlying asset price process is purely continuous, purely discontinuous, or a mixture of both. By applying the test to S&P 500 index options data, we conclude that the sample path behavior of this index contains both a continuous component and a jump component. In particular, we find that while the presence of the jump component varies strongly over time, the presence of the continuous component is constantly felt. We investigate the implications of the evidence for parametric model specifications. 

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Comments: The paper is forthcoming in Journal of Finance.