Магистратура
2024/2025
Стохастический анализ в финансах
Статус:
Курс по выбору (Финансы)
Направление:
38.04.08. Финансы и кредит
Кто читает:
Банковский институт
Где читается:
Банковский институт
Когда читается:
1-й курс, 4 модуль
Формат изучения:
с онлайн-курсом
Онлайн-часы:
20
Охват аудитории:
для своего кампуса
Преподаватели:
Попова Светлана Валерьевна
Прогр. обучения:
Финансы
Язык:
английский
Кредиты:
3
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
Assessment Elements
- Graded tests average• 4 graded tests The 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.
- Attendance and participation in online quizzes• 3 quizzes at webinars
- Project• Project in small groups
Interim Assessment
- 2024/2025 4th module0.1 * Attendance and participation in online quizzes + 0.3 * Graded tests average + 0.6 * Project
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.