Hexa Scholar
QuantFinancial mathematics

Stochastic calculus and SDEs

The Itô integral, Itô's lemma, local time and stochastic differential equations such as geometric Brownian motion.

1 lesson open · 5 planned

Steps 12, 13 and 14 are part of the option pricing path, a 22-step course from discounting to Black–Scholes.

Pages you can open

The Itô integral How do you integrate against a Brownian path, which has no slope? Option pricing path, step 12 · ~50 min

Planned

In learning order. These are not pages yet.

  1. Itô isometry: the variance of a stochastic integralGraduate
  2. Itô's lemmaAdvanced undergrad
  3. Simulating an SDE with the Euler-Maruyama methodAdvanced undergrad
  4. Geometric Brownian motionAdvanced undergrad
  5. Local time: how long Brownian motion lingers at a levelGraduate

How it connects

Builds on Stochastic processes Calculus Numerical methods Probability

Leads to PDE methods Monte Carlo and numerical pricing Volatility and jump models Derivatives Arbitrage and risk-neutral pricing Hedging and calibration Differential equations Optimization Stochastic processes Equities and portfolios Interest-rate models

Subjects marked “connection” are linked by a related idea, not by a prerequisite.

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