by Nizar Touzi, René Aïd, Stéphane Villeneuve
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Suggested foundations for options and derivatives pricing and risk measurement and stress. Specialist prerequisites vary by paper.
Build replication and risk-neutral probabilities in a tractable model.
Distinguish pricing probabilities from physical forecasts.
Represent losses as a distribution rather than one forecast.
Distinguish a loss quantile from the average loss in the tail.
Connect the pricing equation, closed-form value and implied volatility.
Compare risk estimators and their assumptions.
Check forecasts against realised losses.
Start in discrete time, move to Brownian motion, then read the original pricing argument and simulate it.
Connect diversification, common risk factors, investor views, and the properties of a risk measure.