Бакалавриат 2022/2023

Количественные финансы

Статус: Курс по выбору (Прикладной анализ данных)

Направление: 01.03.02. Прикладная математика и информатика

Кто читает: Департамент больших данных и информационного поиска

Где читается: Факультет компьютерных наук

Когда читается: 4-й курс, 2, 3 модуль

Формат изучения: без онлайн-курса

Охват аудитории: для своего кампуса

Преподаватели: Антипов Виктор Алексеевич, Житлухин Михаил Валентинович

Язык: английский

Кредиты: 5

Контактные часы: 72

Course Syllabus

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

• 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

• 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

• 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.
• Calibration of the Heston model.
• Efficient simulation of the Heston model.
• Overview of further directions.

Assessment Elements

• Homework
  Weakly or bi-weakly home assignments. Each home assignment may have one or two parts (theory and/or programming exercises), each part is graded on the scale 0-100.
• Project
  Individual practical project conducted after completion of the material on the Black-Scholes model and contains an assignment to implement a pricing algorithm for some financial security in Python.
• Class activity
  Explanation of solutions of home assignment and exercises during classes. Non-blocking.
• Exam
  Written examination conducted in the classroom. Duration 120 minutes. The examination paper contains 4 or 5 theoretical questions and problems. The use of printed materials is allowed. The use of electronic devices in not allowed.

Interim Assessment

• 2022/2023 3rd module
  Round(0.2 * HW + 0.1 * CA + 0.2* P + 0.5 * E), where HW— average grade for all homework assignments, CA — average grade for calss activity, P – grade for the project, E — exam grade.

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

• BESSMERTNYY ALEKSANDR IGOREVICH