Бакалавриат
2024/2025
Количественные финансы
Статус:
Курс по выбору (Прикладной анализ данных)
Направление:
01.03.02. Прикладная математика и информатика
Где читается:
Факультет компьютерных наук
Когда читается:
4-й курс, 1, 2 модуль
Формат изучения:
без онлайн-курса
Охват аудитории:
для своего кампуса
Язык:
английский
Кредиты:
4
Контактные часы:
56
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.
Interim Assessment
- 2024/2025 2nd module0.05 * Class activity + 0.05 * Class activity + 0.35 * Final exam + 0.125 * Home assignments + 0.125 * Home assignments + 0.3 * Mid-term test
Bibliography
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