Магистратура 2022/2023

Стохастический анализ в финансах

Лучший по критерию «Новизна полученных знаний»

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

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; price simple European options using martingale approach – price exotic European options using simulations in open sources like R or python

Course Contents

• Wiener process, conditional expected values, variance and covariance, definition of filtration and martingales
• Stochastic (Ito) integral and Ito process, Vasicek model
• Ito’s lemma, Black and Scholes model, Girsanov theorem
• Option pricing, Delta hedging, replicating portfolio
• Simulations of Wiener processes, stochastic integrals, pricing in python

Assessment Elements

• Tests
  Graded test : You have 1 attempt Time limit – 90 minutes
• Final Project
  The questions should be answered with text and plots and add the code in appendix. The report should not exceed 10 pages. The project may be done alone or in small groups of two or three students. The report should be upload as one pdf file. Deadline - 2022-04-28, 23:59.

Interim Assessment

• 2022/2023 4th module
  0.4 * Tests + 0.6 * Final Project

Bibliography

Recommended Core Bibliography

• Augustyński, I., & Laskoś-Grabowski, P. (2018). Clustering Macroeconomic Time Series. https://doi.org/10.15611/eada.2018.2.06
• Lütkepohl, H., & Krätzig, M. (2004). Applied Time Series Econometrics. Cambridge, UK: Cambridge University Press. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=164387

Recommended Additional Bibliography

• Steven Shreve. (2019). Stochastic Calculus for Finance I : The Binomial Asset Pricing Model (Vol. 2004). Springer.