by Andrew Papanicolaou
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Suggested foundations for options and derivatives pricing and stochastic processes and pricing. Specialist prerequisites vary by paper.
Build replication and risk-neutral probabilities in a tractable model.
Distinguish pricing probabilities from physical forecasts.
Understand what it means to condition on current information.
Follow Brownian dynamics and the second-order term in Itô calculus.
Connect the pricing equation, closed-form value and implied volatility.
Translate continuous dynamics into a numerical experiment.
Start in discrete time, move to Brownian motion, then read the original pricing argument and simulate it.