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Why Distinguishing Jumps from Volatility is Difficult (But Not Impossible)

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  • Yacine Ait-Sahalia

Abstract

This paper examines the estimation of parameters of a discretely sampled Markov process whose continuous-time sample paths are generated by a continuous Brownian term and a stochastic jump term, a realistic setting for many financial asset prices. In discretely sampled data, every change in the value of the variable is by nature a discrete jump, yet we wish to estimate jointly from these data the underlying continuous-time parameters driving the Brownian and jump terms. The paper focuses on the effect of the presence of jumps on the estimation of the volatility parameters, and the effect of the presence of the continuous Brownian part on the estimation of the jumps parameters, in the context of maximum-likelihood and method of moments estimators. These effects are studied as a function of the frequency at which the continuous-time process is sampled

Suggested Citation

  • Yacine Ait-Sahalia, 2004. "Why Distinguishing Jumps from Volatility is Difficult (But Not Impossible)," Econometric Society 2004 North American Winter Meetings 575, Econometric Society.
  • Handle: RePEc:ecm:nawm04:575
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    File URL: http://www.princeton.edu/~yacine/jumps.pdf
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    More about this item

    Keywords

    Jumps; Diffusion; Fisher's Information; Poisson Process; Cauchy Process;

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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