by Alexander Lipton
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Suggested foundations for stochastic processes and pricing and options and derivatives pricing. Specialist prerequisites vary by resource.
Understand what it means to condition on current information.
Follow Brownian dynamics and the second-order term in Itô calculus.
Build replication and risk-neutral probabilities in a tractable model.
Distinguish pricing probabilities from physical forecasts.
Translate continuous dynamics into a numerical experiment.
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.