Option pricing, risk models and many simulators rest on one idea: a price is a sum of many tiny random steps. This skill explains that idea in plain steps, with short checks (numbers you compute, steps you order, concepts you match) and finance examples: why the squared changes of a random path add up to time, why a hedger's gain is an integral that looks only at the past, why the real expected return drops out of an option price, how a pricing PDE and an average over random paths give the same number, what mean reversion and jumps add, and how a simulation scheme trades speed against accuracy. The capstone is a code lab where you estimate a model from SPY returns, simulate it, price a call by formula and by Monte Carlo, and measure how much hedging error is left when you rebalance only every few days.
Calculus and probability are expected (derivatives, integrals, expectation, the normal distribution). No finance or stochastic background is needed.
