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What Type of Process Underlies Options? A Simple Robust Test


  • Peter Carr

    (New York University)

  • Liuren Wu

    (Fordham University)


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 at­the­money and out­of­the­money 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.

Suggested Citation

  • Peter Carr & Liuren Wu, 2002. "What Type of Process Underlies Options? A Simple Robust Test," Finance 0207019, EconWPA.
  • Handle: RePEc:wpa:wuwpfi:0207019
    Note: Type of Document - pdf; prepared on LaTex; to print on postscript; pages: 41 ; figures: included. prepared via dvipdfm

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    Jumps; continuous martingale; option pricing; Levy density; double tails; local time.;

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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