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Fractional Brownian motion, volatility forecasting, option pricing, volatility surface, VIX, VVIX, variance swap curve, Flash Crash, Lehman Brothers collapse, Bergomi-Guyon expansion
Local volatility, Fokker-Planck equation, Levy processes
local stochastic volatility, implied volatility, implied skew, particle method
density expansions in small time, option pricing in small time, moderate deviations
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asymptotics, implied volatility, moderate deviations, option pricing
forests, trees, continuous martingales, diamond product, cumulants, mo- ments, Hermite polynomials, regular perturbation, KPZ type (Wild) expansion, trees, Le ́vy area, Wiener chaos, Heston and forward variance models;
