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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

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

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

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

Assessment Elements

• home assignment
• final exam

Interim Assessment

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

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