by Andrew W. Lo, Yacine Aït-Sahalia
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Suggested foundations for options and derivatives pricing and probability and statistical reasoning. Specialist prerequisites vary by paper.
Build replication and risk-neutral probabilities in a tractable model.
Distinguish pricing probabilities from physical forecasts.
Read the distributions and expectations used in probabilistic arguments.
Interpret expectations after information is observed.
Connect the pricing equation, closed-form value and implied volatility.
Assess uncertainty rather than treating an estimate as a fact.
Start in discrete time, move to Brownian motion, then read the original pricing argument and simulate it.
Move from conditioning and expected values to timed problems with a defensible solution.