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The Affine Nature of Aggregate Wealth Dynamics

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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.

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File URL: http://www.qfrc.uts.edu.au/research/research_papers/rp322.pdf
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Bibliographic Info

Paper provided by Quantitative Finance Research Centre, University of Technology, Sydney in its series Research Paper Series with number 322.

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Length: 53
Date of creation: 01 Dec 2012
Date of revision:
Handle: RePEc:uts:rpaper:322

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Related research

Keywords: Aggregate wealth dynamics; nondiversifiable market risk; market activity; stochastic volatility; square root processes; benchmark approach;

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References

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  1. Madan, Dilip B & Seneta, Eugene, 1990. "The Variance Gamma (V.G.) Model for Share Market Returns," The Journal of Business, University of Chicago Press, vol. 63(4), pages 511-24, October.
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  3. Eckhard Platen, 2009. "A Benchmark Approach to Investing and Pricing," Research Paper Series 253, Quantitative Finance Research Centre, University of Technology, Sydney.
  4. Eckhard Platen & Renata Rendek, 2007. "Empirical Evidence on Student-t Log-Returns of Diversified World Stock Indices," Research Paper Series 194, Quantitative Finance Research Centre, University of Technology, Sydney.
  5. Truc Le & Eckhard Platen, 2006. "Approximating the growth optimal portfolio with a diversified world stock index," Journal of Risk Finance, Emerald Group Publishing, vol. 7(5), pages 559-574, November.
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Cited by:
  1. Ke Du & Eckhard Platen & Renata Rendek, 2012. "Modeling of Oil Prices," Research Paper Series 321, Quantitative Finance Research Centre, University of Technology, Sydney.

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