Inference for systems of stochastic differential equations from discretely sampled data: A numerical maximum likelihood approach

Thomas Lux

No 1781, Kiel Working Papers from Kiel Institute for the World Economy

Abstract: Maximum likelihood estimation of discretely observed diffusion processes is mostly hampered by the lack of a closed form solution of the transient density. It has recently been argued that a most generic remedy to this problem is the numerical solution of the pertinent Fokker-Planck (FP) or forward Kol- mogorov equation. Here we expand extant work on univariate diffusions to higher dimensions. We find that in the bivariate and trivariate cases, a numerical solution of the FP equation via alternating direction finite difference schemes yields results surprisingly close to exact maximum likelihood in a number of test cases. After providing evidence for the effciency of such a numerical approach, we illustrate its application for the estimation of a joint system of short-run and medium run investor sentiment and asset price dynamics using German stock market data.

Keywords: stochastic differential equations; numerical maximum likelihood; Fokker-Planck equation; finite difference schemes; asset pricing (search for similar items in EconPapers)
JEL-codes: C13 C58 G12 (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:zbw:ifwkwp:1781

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