Rational shapes of local volatility

Rational shapes of local volatility

Robust implementation of a Dupire-type local volatility model (Dupire, 1994) is important for every equity option trading floor. Typically, this problem is solved in a two-step procedure: a smooth parameterisation of the implied volatility surface; and computation of the local volatility based on the resulting call prices. The first of these, and in particular how to extrapolate the implied volatility in extreme strike regimes, is widely recognised as an important risk management issue, first discussed in the Quant Congress 2000 presentation Rational shapes of the [implied] volatility surface by Jim Gatheral. In the Heston stochastic volatility model, implied variance grows asymptotically linearly in log-strike. This and related matters were then studied by numerous authors, starting with Lee (2004). Subsequently, this has inspired parameterisations of the implied volatility surface, notably stochastic-volatility inspired (SVI) parameterisation (see Gatheral, 2006, and Gatheral & Jacquier, 2012).

Rational shapes of local volatility

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• Topics
• Bruno Dupire
• Derivatives
• Implied volatility
• Local volatility models
• Monte Carlo simulation
• Option pricing
• Saddle-point method
• Stochastic volatility
• Volatility smile
• Derivatives
• Banking