by Fernholz, E. Robert, Karatzas, Ioannis, Ruf, Johannes
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Suggested foundations for volatility models and surfaces and stochastic processes and pricing. Specialist prerequisites vary by paper.
Follow Brownian dynamics and the second-order term in Itô calculus.
Separate conditional volatility from observed returns.
Understand what it means to condition on current information.
Study a correlated stochastic-variance model.
Interpret prices across strikes and expiries.
Connect stochastic dynamics to no-arbitrage prices.
Start in discrete time, move to Brownian motion, then read the original pricing argument and simulate it.