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Activity Number:
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462
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Type:
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Topic Contributed
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Date/Time:
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Wednesday, August 5, 2009 : 10:30 AM to 12:20 PM
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Sponsor:
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Business and Economic Statistics Section
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| Abstract - #303497 |
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Title:
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Particle Filter for Partially Observed Stochastic Partial Differential Equation with Fractional Levy Ornstein-Uhlenbeck Stochastic Volatility
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Author(s):
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Jaya Bishwal*+
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Companies:
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The University of North Carolina at Charlotte
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Address:
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Department of Mathematics and Statistics, Charlotte, NC, 28223,
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Keywords:
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Stochastic partial differential equation ; fractional Levy process ; Ornstein-Uhlenbeck process ; interest rate ; jumps and long memory ; particle filter and Bayes estimation
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Abstract:
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We study Bayesian estimation of parameters in an interest rate model in the Heath-Jarrow-Morton framework with stochastic volatility. The interest rate follows an infinite dimensional parabolic stochastic partial differential equation driven by a cylindrical Brownian motion with space being the time-to-maturity. We model the volatility by a fractional Levy Ornstein-Uhlenbeck (FLOU) process which is not observed. FLOU process is a generalization of the classical Ornstein-Uhlenbeck process with the Brownian motion being replaced by a fractional Levy process. A fractional Levy process is a generalization of fractional Brownian motion where in the Mandelbrot representation of fractional Brownian motion, one replaces the Brownian motion with a Levy process. Thus the stochastic volatility process here has both jumps and long memory. We use particle filter to estimate the parameters.
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