by Christopher D. Long
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Suggested foundations for optimisation and numerical methods and options and derivatives pricing. Specialist prerequisites vary by paper.
Read the linear algebra used to define a numerical problem.
Identify the objective, constraints and conditions for an optimum.
Build replication and risk-neutral probabilities in a tractable model.
Distinguish pricing probabilities from physical forecasts.
Understand identifiability and fitted model parameters.
Separate model error from unstable numerical computation.
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.