Derivatives Models on Models

Knock-out options are difficult to model, in practice stochastic volatility and jumps can be of great importance!

Pompeii (Oil painting on canvas)The city of Pompeii was lying in the tail of a sleeping volcano. The volcano suddenly woke up with a series of eruptions that destroyed the city completely. In the Gaussian hill we have the Sharpe ratio, basic Value at Risk and much of the modern Gaussian finance theory. In the fat-tail and the high peak volcano we have empirical financial discoveries going back to at least 1915, with Wesley Mitchell, and later Oliver (1926) and Mills (1927). ...