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Calibrated rank volatility stabilized models for large equity markets

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  • David Itkin
  • Martin Larsson

Abstract

In the framework of stochastic portfolio theory we introduce rank volatility stabilized models for large equity markets over long time horizons. These models are rank-based extensions of the volatility stabilized models introduced by Fernholz & Karatzas in 2005. On the theoretical side we establish global existence of the model and ergodicity of the induced ranked market weights. We also derive explicit expressions for growth-optimal portfolios and show the existence of relative arbitrage with respect to the market portfolio. On the empirical side we calibrate the model to sixteen years of CRSP US equity data matching (i) rank-based volatilities, (ii) stock turnover as measured by market weight collisions, (iii) the average market rate of return and (iv) the capital distribution curve. Assessment of model fit and error analysis is conducted both in and out of sample. To the best of our knowledge this is the first model exhibiting relative arbitrage that has statistically been shown to have a good quantitative fit with the empirical features (i)-(iv). We additionally simulate trajectories of the calibrated model and compare them to historical trajectories, both in and out of sample.

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  • David Itkin & Martin Larsson, 2024. "Calibrated rank volatility stabilized models for large equity markets," Papers 2403.04674, arXiv.org.
    • Handle: RePEc:arx:papers:2403.04674
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    References listed on IDEAS

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    1. Christa Cuchiero & Janka Moller, 2023. "Signature Methods in Stochastic Portfolio Theory," Papers 2310.02322, arXiv.org, revised Oct 2024.
    2. David Itkin & Benedikt Koch & Martin Larsson & Josef Teichmann, 2022. "Ergodic robust maximization of asymptotic growth under stochastic volatility," Papers 2211.15628, arXiv.org.
    3. Banner, Adrian D. & Ghomrasni, Raouf, 2008. "Local times of ranked continuous semimartingales," Stochastic Processes and their Applications, Elsevier, vol. 118(7), pages 1244-1253, July.
    4. David Itkin & Martin Larsson, 2020. "Robust Asymptotic Growth in Stochastic Portfolio Theory under Long-Only Constraints," Papers 2009.08533, arXiv.org, revised Aug 2021.
    5. Constantinos Kardaras & Jan Obłój & Eckhard Platen, 2017. "The Numéraire Property And Long-Term Growth Optimality For Drawdown-Constrained Investments," Mathematical Finance, Wiley Blackwell, vol. 27(1), pages 68-95, January.
    6. Ioannis Karatzas & Johannes Ruf, 2017. "Trading strategies generated by Lyapunov functions," Finance and Stochastics, Springer, vol. 21(3), pages 753-787, July.
    7. Robert Fernholz & Tomoyuki Ichiba & Ioannis Karatzas, 2013. "A second-order stock market model," Annals of Finance, Springer, vol. 9(3), pages 439-454, August.
    8. David Itkin & Martin Larsson, 2021. "Open Markets and Hybrid Jacobi Processes," Papers 2110.14046, arXiv.org, revised Mar 2024.
    9. Martin Larsson & Johannes Ruf, 2020. "Relative Arbitrage: Sharp Time Horizons and Motion by Curvature," Papers 2003.13601, arXiv.org, revised Feb 2021.
    10. Martin Larsson & Johannes Ruf, 2021. "Relative arbitrage: Sharp time horizons and motion by curvature," Mathematical Finance, Wiley Blackwell, vol. 31(3), pages 885-906, July.
    11. Kardaras, Constantinos & Robertson, Scott, 2021. "Ergodic robust maximization of asymptotic growth," LSE Research Online Documents on Economics 121039, London School of Economics and Political Science, LSE Library.
    12. Robert Fernholz & Tomoyuki Ichiba & Ioannis Karatzas, 2013. "A second-order stock market model," Papers 1302.3870, arXiv.org.
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