Icef-scalc-2024-fall

Course notes courtesy of Sofia Sobina

Lecturer: Boris Demeshev

Assistant: Ivan Gordeev

Grading:

Final grade = Stochastic calculus home assignment * 0.05 + December Exam * 0.35 + First module grade * 0.6

Schedule: Thursday from 2024-11-07, 13:00 Moscow time

Week 1. Sigma algebras, conditional expected value.

Week 2. Conditional variance, martingales, stopping times.

Week 3. Doob's theorem, ABRACADABRA, Wiener process.

Week 4. Stochastic integral: intuition.

Week 5. Stochastic integral: properties, Ito's lemma.

Week 6. Option pricing: binomial, Black and Scholes model.

Week 7. QA.

Sources of wisdom:

Brzezniak, Zastawniak, Basic Stochastic Processes

Steven Shreve, Stochastic Calculus for Finance: volume II and volume I

Michael Steele, Stochastic Calculus with Financial Applications

Past courses: