by A. Tourin, T. N. Li
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Suggested foundations for volatility models and surfaces and optimisation and numerical methods. Specialist prerequisites vary by paper.
Follow diffusion-based models and their assumptions.
Separate conditional volatility from observed returns.
Read the linear algebra used to define a numerical problem.
Identify the objective, constraints and conditions for an optimum.
Study a correlated stochastic-variance model.
Interpret prices across strikes and expiries.
Understand identifiability and fitted model parameters.
Start in discrete time, move to Brownian motion, then read the original pricing argument and simulate it.