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Course Syllabus

2023/2024

Stochastic Analysis in Finance

Category 'Best Course for Career Development'
Category 'Best Course for Broadening Horizons and Diversity of Knowledge and Skills'
Category 'Best Course for New Knowledge and Skills'
Type: Mago-Lego
Delivered by: HSE Banking Institute
When: 4 module
Online hours: 20
Open to: students of one campus
Instructors: Svetlana Popova
Language: English
ECTS credits: 3
Contact hours: 8

Course Syllabus

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

Learning Objectives

  • The goal of this course is the Black and Scholes model and option pricing using martingale approach
Expected Learning Outcomes

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

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

Assessment Elements

  • non-blocking Graded Test 1
  • non-blocking Graded Test 2
  • non-blocking Graded Test 3
  • non-blocking Graded Test 4
  • non-blocking Project
Interim Assessment

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

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.