A stylised model for extreme shocks: four moments of the apocalypse

Allan Brace, Mark Lauer and Milo Rado

MPRA Paper from University Library of Munich, Germany

Abstract: We present a method for calculating the extreme tail quantiles, over arbitrary holding periods, of a continuous-time stochastic volatility model of the form proposed by Scott (1987) with correlation between the processes for volatility and price. The fat tails of this model enable a consistent, tuneable, stylised representation of non-normality in extreme moves of prices across differing markets. Because the model is analytically intractable, four moments are derived by numeric integration and matched to a one-period version of the model, whose quantiles are then found by further numeric integration. We also present a novel Monte-Carlo simulation scheme, which we have used to confirm the accuracy of the moment-matching approximation for quantiles as extreme as one-millionth. Two methods for calibrating the model to market data are also proposed. The model is used in production stress testing at nabCapital to define consistent real-world probabilities for extreme shocks over heterogeneous holding periods.

Keywords: Stress testing; stochastic volatility (search for similar items in EconPapers)
JEL-codes: C60 (search for similar items in EconPapers)
Date: 2007-08-15
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Related works:
Working Paper: A Stylised Model for Extreme Shocks: Four Moments of the Apocalypse (2008)
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Persistent link: https://EconPapers.repec.org/RePEc:pra:mprapa:124773

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