2026/2027
Стохастический анализ в финансах
Статус:
Маго-лего
Кто читает:
Банковский институт
Где читается:
Банковский институт
Онлайн-часы:
20
Охват аудитории:
для своего кампуса
Язык:
русский
Кредиты:
3
Контактные часы:
8
Программа дисциплины
Аннотация
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.
Цель освоения дисциплины
- The goal of this course is the Black and Scholes model and option pricing using martingale approach
Планируемые результаты обучения
- 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
Содержание учебной дисциплины
- 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
Элементы контроля
- Graded tests averageThe graded tests will take place on the scheduled date at the specific time (the exact date will be announced by the instructor afterwards). Each student shall choose between two alternative timeframes of each test corresponding to two alternative time zones. Please note that the duration of the tests is limited to 2 academic hours.
- Project
- Attendance and participation in online quizzes
Промежуточная аттестация
- 2026/2027 4th module0.3 * Graded tests average + 0.1 * Attendance and participation in online quizzes + 0.6 * Project
Список литературы
Рекомендуемая основная литература
- 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.
Рекомендуемая дополнительная литература
- Damien Lamberton, & Bernard Lapeyre. (2011). Introduction to Stochastic Calculus Applied to Finance: Vol. 2nd ed. Chapman and Hall/CRC.