A Stylised Model for Extreme Shocks: Four Moments of the Apocalypse

Allan Brace, Mark Lauer () and Milo Rado
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Allan Brace: Group Market Risk, nabCapital, Australia
Milo Rado: Group Market Risk, nabCapital, Australia

No 224, Research Paper Series from Quantitative Finance Research Centre, University of Technology, Sydney

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 diering 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.

Date: 2008-06-01
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