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