Магистратура
2025/2026
Стохастический анализ в финансах
Статус:
Курс по выбору (Финансы)
Кто читает:
Банковский институт
Где читается:
Банковский институт
Когда читается:
1-й курс, 4 модуль
Онлайн-часы:
20
Охват аудитории:
для своего кампуса
Язык:
английский
Кредиты:
3
Контактные часы:
8
Course Syllabus
Abstract
Stochastic calculus is used in financial engineering. The minimum of required math will be covered: sigma-algebras, conditional expectations, martingales, Wiener process, stochastic integration. The big problem is that stochastic calculus is very hard from a mathematical viewpoint. We will formulate all the required theorems mostly without proofs.
Learning Objectives
- The goal of this course is the Black and Scholes model and option pricing using martingale approach
Expected Learning Outcomes
- Understand the Wiener process, stochastic integrals and the Black and Scholes model
- Understand price simple European options using martingale approach – price exotic European options using simulations in open sources like R or python
Course Contents
- Week one. Wiener process, conditional moments and martingales
- Week two. Stochastic integral and Ito process
- Week three. Ito’s lemma, Black and Scholes model and Girsanov theorem
- Week four. Option pricing and Delta hedging
- Simulations of Wiener processes, stochastic integrals, pricing in python
Interim Assessment
- 2025/2026 4th module0.1 * 3 quizzes at webinars + 0.6 * Project in small groups + 0.3 * 4 graded tests
Bibliography
Recommended Core Bibliography
- Chandra, T. K., & Gangopadhyay, S. (2018). Introduction to Stochastic Processes. New Delhi: Narosa Publishing House Pvt. Ltd. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=2023979
- Steven Shreve. (2019). Stochastic Calculus for Finance I : The Binomial Asset Pricing Model (Vol. 2004). Springer.
Recommended Additional Bibliography
- Damien Lamberton, & Bernard Lapeyre. (2011). Introduction to Stochastic Calculus Applied to Finance: Vol. 2nd ed. Chapman and Hall/CRC.