2026/2027
Стохастический анализ в финансах
Статус:
Маго-лего
Кто читает:
Банковский институт
Где читается:
Банковский институт
Охват аудитории:
для своего кампуса
Язык:
русский
Кредиты:
3
Контактные часы:
32
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 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.
Содержание учебной дисциплины
- Sigma-algebras
- Conditional expectation
- Martingales
- Wiener process
- Ito’s integral
- Ito’s lemma and Girsanov theorem
- Black and Scholes model
Список литературы
Рекомендуемая основная литература
- Applied econometric time series, Enders, W., 2010
- Stochastic calculus for finance. Vol.2: Continuous-time models, Shreve, S. E., 2004
Рекомендуемая дополнительная литература
- Stochastic calculus for finance. Vol.1: The binomial asset pricing model, Shreve, S. E., 2004
- Stochastic calculus of variations in mathematical finance, Malliavin, P., 2006