Кто читает:: Банковский институт

Статус:: Курс по выбору

Когда читается:: 1-й курс, 4 модуль

Преподаватель

Попова Светлана Валерьевна

Full 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

Assessment Elements

Graded Test 1
Graded Test 2
Graded Test 3
Graded Test 4
Project

Interim Assessment

2023/2024 4th module
0.1 * Graded Test 1 + 0.1 * Graded Test 2 + 0.1 * Graded Test 3 + 0.1 * Graded Test 4 + 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.

Магистерская программа «Финансы»

Stochastic Analysis in Finance