by Stanford University Mathematics Department
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Suggested foundations for options and derivatives pricing and optimisation and numerical methods. Specialist prerequisites vary by resource.
Build replication and risk-neutral probabilities in a tractable model.
Distinguish pricing probabilities from physical forecasts.
Read the linear algebra used to define a numerical problem.
Identify the objective, constraints and conditions for an optimum.
Connect the pricing equation, closed-form value and implied volatility.
Understand identifiability and fitted model parameters.
Separate model error from unstable numerical computation.
Start in discrete time, move to Brownian motion, then read the original pricing argument and simulate it.