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Title: Semiparametric estimation for a class of time-inhomogenous diffusion processes
Authors: Yu, Y
Yu, K
Wang, H
Li, M
Keywords: Bandwidth selection;Kernel smoothing;Local linear;Option pricing;Penalized likelihood;VaR;Variance estimation;Volatility
Issue Date: 2009
Publisher: Institute of Statistical Science, Academia Sinica & International Chinese Statistical Association
Citation: Statistica Sinica, 19(2), 843 - 867, 2009
Abstract: We develop two likelihood-based approaches to semiparametrically estimate a class of time-inhomogeneous diffusion processes: log penalized splines (P-splines) and the local log-linear method. Positive volatility is naturally embedded and this positivity is not guaranteed in most existing diffusion models. We investigate different smoothing parameter selections. Separate bandwidths are used for drift and volatility estimation. In the log P-splines approach, different smoothness for different time varying coefficients is feasible by assigning different penalty parameters. We also provide theorems for both approaches and report statistical inference results. Finally, we present a case study using the weekly three-month Treasury bill data from 1954 to 2004. We find that the log P-splines approach seems to capture the volatility dip in mid-1960s the best. We also present an application to calculate a financial market risk measure called Value at Risk (VaR) using statistical estimates from log P-splines.
Description: Copyright @ 2009 Institute of Statistical Science, Academia Sinica
ISSN: 1017-0405
Appears in Collections:Dept of Mathematics Research Papers
Mathematical Sciences

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