by Mike Giles, Yuan Xia
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Suggested foundations for monte carlo and numerical simulation and options and derivatives pricing. Specialist prerequisites vary by paper.
Understand convergence, sampling error and confidence intervals.
Generate reproducible samples and distinguish randomness from model assumptions.
Build replication and risk-neutral probabilities in a tractable model.
Distinguish pricing probabilities from physical forecasts.
Turn a discounted payoff into an estimator.
Study dependence and alternatives to independent sampling.
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.