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Course Syllabus

Bachelor 2024/2025

Quantitative Finance

Type: Elective course (Data Science and Business Analytics)
Area of studies: Applied Mathematics and Information Science
Delivered by: Big Data and Information Retrieval School
Where: Faculty of Computer Science
When: 4 year, 1, 2 module
Mode of studies: offline
Open to: students of one campus
Instructors: Токаева Александра Александровна, Mikhail Zhitlukhin
Language: English
ECTS credits: 4

Course Syllabus

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Abstract

This course gives an introduction to quantitative finance – the mathematical theory of pricing of financial securities like futures, options, swaps, etc. This is a deep and interesting subject and the corresponding theory is actively used in modern financial markets.
Learning Objectives

Learning Objectives

  • The purpose of the course is to explain the theory behind securities pricing based on the probability theory and random processes, and to discuss practical implementations of pricing algorithms and models.
Expected Learning Outcomes

Expected Learning Outcomes

  • Know the basic discrete-time models of stock markets, e.g., the binomial model and its derivatives.
  • Know the foundations of stochastic calculus, including the concept of Brownian motion and Ito’s integral.
  • Know how to derive the Black-Scholes formula for option pricing
  • Understand the limitations of the Black-Scholes formula and how it should (and should not) be used in practice.
  • Understand the concept of implied volatility and how it is used in derivatives trading
  • Know how to price the exotic securities using the Monte-Carlo method
Course Contents

Course Contents

  • Basic concepts of financial markets.
  • The one-period binomial model.
  • The Cox-Ross-Rubinstein model.
  • Auxiliary results from the theory of random processes in discrete time.
  • Martingale methods for discrete time markets.
  • The fundamental theorem of asset pricing.
  • The limit of the binomial model.
  • Ito’s integral and Ito’s processes.
  • The Black-Scholes model.
  • Implied volatility, Greeks.
  • The Black model.
  • The Heston model.
Assessment Elements

Assessment Elements

  • non-blocking Mid-term test
  • non-blocking Final exam
  • non-blocking Home assignments
  • non-blocking Class activity
Interim Assessment

Interim Assessment

  • 2024/2025 2nd module
    0.05 * Class activity + 0.05 * Class activity + 0.35 * Final exam + 0.125 * Home assignments + 0.125 * Home assignments + 0.3 * Mid-term test
Bibliography

Bibliography

Recommended Core Bibliography

  • Introduction to mathematical finance : discrete time models, Pliska, S.R., 2005
  • Options, futures, and other derivatives, Hull, J. C., 2018
  • Paul Wilmott introduces quantitative finance, Wilmott, P., 2009
  • The volatility surface : a practitioner's guide, Gatheral, J., 2006

Recommended Additional Bibliography

  • Föllmer, H., & Schied, A. (2011). Stochastic Finance : An Introduction in Discrete Time (Vol. 3rd, and extended ed). Berlin: De Gruyter. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=388088
  • Martingale methods in financial modelling, Musiela, M., 2005

Authors

  • ZHITLUKHIN MIKHAIL VALENTINOVICH