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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.

Suggested Citation

  • Eckhard Platen & Renata Rendek, 2012. "The Affine Nature of Aggregate Wealth Dynamics," Research Paper Series 322, Quantitative Finance Research Centre, University of Technology, Sydney.
    • Handle: RePEc:uts:rpaper:322
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    Cited by:

    1. David Heath & Eckhard Platen, 2014. "A Monte Carlo Method using PDE Expansions for a Diversifed Equity Index Model," Research Paper Series 350, Quantitative Finance Research Centre, University of Technology, Sydney.
    2. Ke Du & Eckhard Platen & Renata Rendek, 2012. "Modeling of Oil Prices," Research Paper Series 321, Quantitative Finance Research Centre, University of Technology, Sydney.
    3. Mathias Barkhagen & Jörgen Blomvall & Eckhard Platen, 2016. "Recovering the real-world density and liquidity premia from option data," Quantitative Finance, Taylor & Francis Journals, vol. 16(7), pages 1147-1164, July.
    4. Renata Rendek, 2013. "Modeling Diversified Equity Indices," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 23, July-Dece.
    5. Baldeaux, Jan & Grasselli, Martino & Platen, Eckhard, 2015. "Pricing currency derivatives under the benchmark approach," Journal of Banking & Finance, Elsevier, vol. 53(C), pages 34-48.
    6. Renata Rendek, 2013. "Modeling Diversified Equity Indices," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 4-2013.

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    More about this item

    Keywords

    Aggregate wealth dynamics; nondiversifiable market risk; market activity; stochastic volatility; square root processes; benchmark approach;
    All these keywords.

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

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