A method will be presented 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.

In direct form, the model is analytically intractable, so 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. 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, will also be presented.

Two methods for calibrating the model to market data will be explored. The model is used in production stress testing at nabCapital to define consistent real-world probabilities for extreme shocks over heterogeneous holding periods.

Mark Lauer is a risk consultant specialising in derivatives valuation and hedging. After completing a PhD in Computational Linguistics at Macquarie University, he joined Swiss Bank Corporation in 1996 on their trading floor in the CBOT. Since then he has held various quantitative finance roles in Chicago, New York, London, Melbourne and Sydney, including Global Head of Quantitative Research for FX Derivatives at UBS. He is also the stay-at-home father of twins, upon whom he has so far resisted conducting evil, yet fascinating, experiments

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