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The Stress-Dependent Random Walk

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  • MARTIN GREMM

    (Pivot Point Advisors, LLC, 5959 West Loop South, Suite 333, Bellaire, TX 77401, USA)

Abstract

A log-normal random walk with parameters that are functions of market stress naturally accounts for volatility clustering and fat-tailed return distributions. Fitting this model to a stock and a bond index we find no evidence of significant misspecification despite the fact that the model has no adjustable parameters. This model can be interpreted as a stochastic volatility model without latent variables. We obtain a closed-form expression for the Value at Risk (VaR) that accommodates returns of any magnitude and discuss several other applications.

Suggested Citation

  • Martin Gremm, 2015. "The Stress-Dependent Random Walk," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(08), pages 1-16, December.
    • Handle: RePEc:wsi:ijtafx:v:18:y:2015:i:08:n:s0219024915500545
    DOI: 10.1142/S0219024915500545
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    Cited by:

    1. Martin Gremm, 2016. "Global Gauge Symmetries, Risk-Free Portfolios, and the Risk-Free Rate," Papers 1605.03551, arXiv.org.

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