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

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Yacine Ait-Sahalia

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Abstract

Asset returns have traditionally been modeled in the literature as following continuous-time Markov processes, and in many cases diffusions. Can discretely sampled financial rate 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: by nature, even if the underlying sample path were continuous, the discretely sampled data will always appear as a sequence of discrete jumps. Instead, this paper relies on a characterization of the transition density of the discrete data to determine whether the discontinuities observed in the discrete data 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.

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Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 8504.

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Date of creation: Oct 2001
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Handle: RePEc:nbr:nberwo:8504

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Find related papers by JEL classification:
G12 - Financial Economics - - General Financial Markets - - - Asset Pricing
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions

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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)
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  2. 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!]
  3. René Garcia & Eric Ghysels & Éric Renault, 2004. "The Econometrics of Option Pricing," CIRANO Working Papers 2004s-04, CIRANO. [Downloadable!]
  4. Sergei Levendorskii, 2004. "The American put and European options near expiry, under Levy processes," Quantitative Finance Papers cond-mat/0404103, arXiv.org. [Downloadable!]
  5. 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!]
  6. 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:
  7. 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!]
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