Магистратура
2020/2021
Стохастический анализ в финансах
Статус:
Курс по выбору (Финансовый аналитик)
Направление:
38.04.08. Финансы и кредит
Кто читает:
Банковский институт
Где читается:
Банковский институт
Когда читается:
1-й курс, 4 модуль
Формат изучения:
без онлайн-курса
Преподаватели:
Демешев Борис Борисович
Прогр. обучения:
Финансовый аналитик
Язык:
английский
Кредиты:
3
Контактные часы:
32
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
- Successful student will: • understand the following mathematical concepts with their properties: – sigma-algebra – expectation with respect to sigma algebra – martingale – Wiener process – Ito’s stochastic integral; • be able to formulate and apply in simple context the following theorems: – Ito’s lemma – Girsanov’s theorem;
- • understand the Black and Scholes model: – price simple European options using martingale approach – price exotic European options using simulations in open sources like R, python or juli.
Course Contents
- • Sigma-algebras
- • Conditional expectation
- • Martingales
- • Wiener process
- • Ito’s integral
- • Ito’s lemma and Girsanov theorem
- • Black and Scholes model
Bibliography
Recommended Core Bibliography
- Enders, W. (2015). Applied Econometric Time Series (Vol. Fourth edition). Hoboken, NJ: Wiley. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=1639192
Recommended Additional Bibliography
- Augustyński, I., & Laskoś-Grabowski, P. (2018). Clustering Macroeconomic Time Series / Grupowanie makroekonomicznych szeregów czasowych. Econometrics. Advances in Applied Data Analysis / Ekonometria, (2), 74. https://doi.org/10.15611/eada.2018.2.06
- Stochastic calculus for finance. Vol.1: The binomial asset pricing model, Shreve, S. E., 2004