Stochastic Volatility Model with Time-dependent Skew

Vladimir Piterbarg

Applied Mathematical Finance, 2005, vol. 12, issue 2, 147-185

Abstract: A formula is derived for the 'effective' skew in a stochastic volatility model with a time-dependent local volatility function. The formula relates the total amount of skew generated by the model over a given time period to the time-dependent slope of the instantaneous local volatility function. A new 'effective' volatility approximation is also derived. The utility of the formulas is demonstrated by building a forward Libor model that can be calibrated to swaption smiles that vary across the swaption grid.

Keywords: Stochastic volatility; volatility smile; time-dependent local volatility; effective volatility; effective skew; average skew; homogenization; averaging principle; effective media; forward Libor model; Libor market model; LMM; BGM; volatility calibration; skew calibration (search for similar items in EconPapers)
Date: 2005
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Citations: View citations in EconPapers (11)

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DOI: 10.1080/1350486042000297225

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