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Regular version of the site
Master 2020/2021

Stochastic Analysis in Finance

Type: Elective course (Financial Analyst)
Area of studies: Finance and Credit
Delivered by: HSE Banking Institute
When: 1 year, 4 module
Mode of studies: offline
Instructors: Boris Demeshev
Master’s programme: Financial Analyst
Language: English
ECTS credits: 3

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

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

  • 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

Course Contents

  • • Sigma-algebras
  • • Conditional expectation
  • • Martingales
  • • Wiener process
  • • Ito’s integral
  • • Ito’s lemma and Girsanov theorem
  • • Black and Scholes model
Assessment Elements

Assessment Elements

  • non-blocking home assignment
  • non-blocking final exam
Interim Assessment

Interim Assessment

  • Interim assessment (4 module)
    0.5 * final exam + 0.5 * home assignment
Bibliography

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