The Affine Nature of Aggregate Wealth Dynamics

Eckhard Platen () and Renata Rendek

No 322, Research Paper Series from Quantitative Finance Research Centre, University of Technology, Sydney

Abstract: The paper derives a parsimonious two-component affine diffusion model for a world stock index to capture the dynamics of aggregate wealth. The observable state variables of the model are the normalized index and the inverse of the stochastic market activity, both modeled as square root processes. The square root process in market activity time for the normalized aggregate wealth emerges from the affine nature of aggregate wealth dynamics, which will be derived under basic assumptions and does not contain any parameters that have to be estimated. The proposed model employs only three well interpretable structural parameters, which determine the market activity dynamics, and three initial parameters. It is driven by the continuous, nondiversifiable uncertainty of the market and no other source of uncertainty. The model, to be valid over long time periods, needs to be formulated in a general financial modeling framework beyond the classical no-arbitrage paradigm. It reproduces a list of major stylized empirical facts, including Student-t distributed log-returns and typical volatility properties. Robust methods for fitting and simulating this model are demonstrated.

Keywords: Aggregate wealth dynamics; nondiversifiable market risk; market activity; stochastic volatility; square root processes; benchmark approach (search for similar items in EconPapers)
JEL-codes: C10 C15 G10 (search for similar items in EconPapers)
Pages: 53 pages
Date: 2012-12-01
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (6)

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Persistent link: https://EconPapers.repec.org/RePEc:uts:rpaper:322

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