THE STRESS-DEPENDENT RANDOM WALK

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

International Journal of Theoretical and Applied Finance (IJTAF), 2015, vol. 18, issue 08, 1-16

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.

Keywords: Market model; regime-switching; stochastic volatility; value at risk; market stress; lognormal random walk; volatility clustering; fat tails (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1142/S0219024915500545

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