What Type of Process Underlies Options? A Simple Robust Test
AbstractWe 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.
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Bibliographic InfoPaper provided by EconWPA in its series Finance with number 0207019.
Length: 41 pages
Date of creation: 01 Sep 2002
Date of revision:
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.;
Other versions of this item:
- Peter Carr & Liuren Wu, 2003. "What Type of Process Underlies Options? A Simple Robust Test," Journal of Finance, American Finance Association, vol. 58(6), pages 2581-2610, December.
- 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
This paper has been announced in the following NEP Reports:
- NEP-ALL-2002-09-11 (All new papers)
- NEP-ETS-2002-09-11 (Econometric Time Series)
- NEP-FMK-2002-09-11 (Financial Markets)
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