by Xin Tian
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Suggested foundations for monte carlo and numerical simulation and volatility models and surfaces. Specialist prerequisites vary by paper.
Understand convergence, sampling error and confidence intervals.
Generate reproducible samples and distinguish randomness from model assumptions.
Follow diffusion-based models and their assumptions.
Separate conditional volatility from observed returns.
Turn a discounted payoff into an estimator.
Study dependence and alternatives to independent sampling.
Study a correlated stochastic-variance model.
Start in discrete time, move to Brownian motion, then read the original pricing argument and simulate it.