The FE-610 review consolidates the first half of the course: probability spaces and filtrations, martingales, Brownian motion, quadratic variation, the Itô integral, Itô's formula, and the Black–Scholes hedge.
\nThe compact rules worth carrying forward are
\n$$dW_t\\,dt=0,\\qquad (dW_t)^2=dt,\\qquad (dt)^2=0.$$
\nThey are a mnemonic for the limiting variation calculation, not ordinary algebra. The review also separates three questions that are easy to conflate: what is measurable now, which process is a martingale under the current measure, and which payoff is being priced.
","contentMarkdown":"The FE-610 review consolidates the first half of the course: probability spaces and filtrations, martingales, Brownian motion, quadratic variation, the Itô integral, Itô's formula, and the Black–Scholes hedge.\n\nThe compact rules worth carrying forward are\n\n$$dW_t\\,dt=0,\\qquad (dW_t)^2=dt,\\qquad (dt)^2=0.$$\n\nThey are a mnemonic for the limiting variation calculation, not ordinary algebra. The review also separates three questions that are easy to conflate: what is measurable now, which process is a martingale under the current measure, and which payoff is being priced.","dataUrl":"https://sharifhsn.dev/api/posts/stochastic-calculus-review.json","date":"2024-10-31","datePublished":"2024-10-31","description":"The FE-610 review consolidates the first half of the course: probability spaces and filtrations, martingales, Brownian motion, quadratic variation, the Itô integral, Itô's formula,…","site":"https://sharifhsn.dev","slug":"stochastic-calculus-review","source":"FE-610 | Stochastic Calculus","sourceUrl":null,"tags":["Stochastic Calculus","Review","Pricing"],"title":"Stochastic Calculus Review","url":"https://sharifhsn.dev/blog/stochastic-calculus-review/","version":"1","wordCount":80}