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Activity Number:
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174
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Type:
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Invited
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Date/Time:
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Monday, August 7, 2006 : 2:00 PM to 3:50 PM
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Sponsor:
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Business and Economics Statistics Section
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| Abstract - #305129 |
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Title:
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Optimal Filtering of Jump-Diffusions: Extracting Latent States from Asset Prices
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Author(s):
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Michael Johannes and Nicholas Polson*+ and Jonathan Stroud
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Companies:
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Columbia University and The University of Chicago and University of Pennsylvania
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Address:
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Graduate School of Business, Chicago, IL, 60637,
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Keywords:
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finance ; Bayes ; Monte Carlo
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Abstract:
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This paper provides a methodology for optimally filtering latent state variables in discretely observed jump-diffusion models. When prices are observed continuously, state variables such as volatility, jump times, and jump sizes also are observed. But with discrete observations, these variables are unobserved. We combine discretization schemes with Monte Carlo methods to compute the optimal filtering distribution: the distribution of the latent states conditional on the observed prices. Our approach is general, applying in models with nonlinear characteristics and even nonanalytic observation equations. We use simulations to investigate how sampling frequency affects jump and volatility estimates and then extract information about volatility jointly from equity index options and index returns.
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