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Telling from Discrete Data Whether the Underlying Continuous-Time Model Is a Diffusion

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Yacine Aït-Sahalia (Princeton University and NBER)

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Abstract

Can discretely sampled financial data help us decide which continuous-time models are sensible? Diffusion processes are characterized by the continuity of their sample paths. This cannot be verified from the discrete sample path: Even if the underlying path were continuous, data sampled at discrete times will always appear as a succession of jumps. Instead, I rely on the transition density to determine whether the discontinuities observed are the result of the discreteness of sampling, or rather evidence of genuine jump dynamics for the underlying continuous-time process. I then focus on the implications of this approach for option pricing models. Copyright The American Finance Association 2002.

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Article provided by American Finance Association in its journal The Journal of Finance.

Volume (Year): 57 (2002)
Issue (Month): 5 (October)
Pages: 2075-2112
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Handle: RePEc:bla:jfinan:v:57:y:2002:i:5:p:2075-2112

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  1. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold, 2005. "Roughing it Up: Including Jump Components in the Measurement, Modeling and Forecasting of Return Volatility," NBER Working Papers 11775, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
    Other versions:
  2. Sergei Levendorskii, 2004. "The American put and European options near expiry, under Levy processes," Quantitative Finance Papers cond-mat/0404103, arXiv.org. [Downloadable!]
  3. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold, 2003. "Some Like it Smooth, and Some Like it Rough: Untangling Continuous and Jump Components in Measuring, Modeling, and Forecasting Asset Return Volatility," PIER Working Paper Archive 03-025, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 01 Sep 2003. [Downloadable!]
    Other versions:
  4. Antonio Di Cesare, 2004. "Estimating expectations of shocks using option prices," Temi di discussione (Economic working papers) 506, Bank of Italy, Economic Research Department. [Downloadable!]
  5. René Garcia & Eric Ghysels & Éric Renault, 2004. "The Econometrics of Option Pricing," CIRANO Working Papers 2004s-04, CIRANO. [Downloadable!]
  6. George J. Jiang & Ingrid Lo & Adrien Verdelhan, 2008. "Information Shocks, Jumps, and Price Discovery -- Evidence from the U.S. Treasury Market," Working Papers 08-22, Bank of Canada. [Downloadable!]
  7. Jeannette H.C. Woerner, 2002. "Variational Sums and Power Variation: a unifying approach to model selection and estimation in semimartingale models," OFRC Working Papers Series 2002mf05, Oxford Financial Research Centre. [Downloadable!]
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