by Valentin Tissot-Daguette
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Suggested foundations for options and derivatives pricing and monte carlo and numerical simulation. Specialist prerequisites vary by paper.
Build replication and risk-neutral probabilities in a tractable model.
Distinguish pricing probabilities from physical forecasts.
Understand convergence, sampling error and confidence intervals.
Generate reproducible samples and distinguish randomness from model assumptions.
Connect the pricing equation, closed-form value and implied volatility.
Turn a discounted payoff into an estimator.
Study dependence and alternatives to independent sampling.
Start in discrete time, move to Brownian motion, then read the original pricing argument and simulate it.