Stochastic Calculus

Feynman-Kac for Dummies

Why an equation with nothing random in it computes an expected payoff: a fair game can’t drift.

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What to remember

  • An expected payoff, followed along the path, is a martingale.
  • A martingale can’t drift, so the dt term of Itô’s formula must vanish: that is the PDE.
  • Discounting adds exactly one term, r f; the risk-neutral stock turns it into Black-Scholes.
Read the lessonFeynman-Kac, with a checkpoint at the end.