by Jim Gatheral
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Suggested foundations for volatility models and surfaces and options and derivatives pricing. Specialist prerequisites vary by resource.
Follow diffusion-based models and their assumptions.
Separate conditional volatility from observed returns.
Build replication and risk-neutral probabilities in a tractable model.
Distinguish pricing probabilities from physical forecasts.
Study a correlated stochastic-variance model.
Interpret prices across strikes and expiries.
Connect the pricing equation, closed-form value and implied volatility.
Start in discrete time, move to Brownian motion, then read the original pricing argument and simulate it.