Магистратура
2023/2024
Количественные финансы
Лучший по критерию «Полезность курса для Вашей будущей карьеры»
Лучший по критерию «Полезность курса для расширения кругозора и разностороннего развития»
Лучший по критерию «Новизна полученных знаний»
Статус:
Курс по выбору (Финансовые рынки и финансовые институты)
Направление:
38.04.08. Финансы и кредит
Кто читает:
Школа финансов
Где читается:
Факультет экономических наук
Когда читается:
2-й курс, 2 модуль
Формат изучения:
без онлайн-курса
Охват аудитории:
для своего кампуса
Преподаватели:
Дергунов Илья Евгеньевич
Прогр. обучения:
Финансовые рынки и финансовые институты
Язык:
английский
Кредиты:
3
Контактные часы:
28
Course Syllabus
Abstract
The theoretical part of the course will refresh our knowledge of the basics of binomial model, stochastic
calculus, Black-Scholes model and Heston stochastic volatility model. Then course will proceed
to introduce the basics of the Monte Carlo simulation technique as well as main methods for efficient
numerical valuation of derivative contracts in a Black-Scholes world and implementation of
various pricing methods, for instance, in Julia or Python programming languages (e.g simulation of
the stochastic differential equations; finite-difference-based methods for the solution of the partial
differential equations; calculation of greeks, implied volatility and etc.).
Learning Objectives
- Understand tree-based approach to pricing derivatives
- Understand PDE-based approaches to pricing financial products
- Understand Monte Carlo approach
- Coding appropriate algorithms for pricing derivatives
- Understand basics of Stochastic Calculus and Black-Scholes Model
Expected Learning Outcomes
- Implement basic Monte Carlo technique for different financial problems
- Implement variance reduction techniques
- Calculate sensitivities (delta, gamma, vega and others)
- Price American Options via Monte Carlo using Longstaff-Schwartz algorithm
- Implement numerical schemes to solve Black-Scholes-Merton PDE
- Price derivatives via solving Black-Scholes-Merton PDE
- Price derivatives via Binomial tree approach
- Apply Ito formula. Solve basic stochastic calculus problems. Simulate Brownian motion paths
Course Contents
- Binomial Model
- Stochastic Calculus
- Monte Carlo Simulations
- Black-Scholes model
- Black-Scholes specific properties of Plain Vanilla Options and Implied Volatility
- Solving the Black-Scholes PDE numerically with finite differences
- Pricing American Options
- Heston stochastic volatility model
Assessment Elements
- Home Assignment 1Binomial model.
- Home Assignment 2Stochastic Calculus
- Home Assignment 3Black-Scholes, Greeks, Implied Vola
- Home Assignment 4Monte Carlo methods
- Mid term testMid-term test
- Final testFinal test
- Home assignment 5Volutarily home assignment. Longstaff-Schwartz algorithm.
Interim Assessment
- 2023/2024 2nd module0.2 * Final test + 0.15 * Home Assignment 1 + 0.15 * Home Assignment 2 + 0.15 * Home Assignment 3 + 0.15 * Home Assignment 4 + 0 * Home assignment 5 + 0.2 * Mid term test
Bibliography
Recommended Core Bibliography
- Arbitrage theory in continuous time, Bjork, T., 2004
- Bjork, T. (2009). Arbitrage Theory in Continuous Time. Oxford University Press. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsrep&AN=edsrep.b.oxp.obooks.9780199574742
- Hull, J. C. (2017). Options, Futures, and Other Derivatives, Global Edition. [Place of publication not identified]: Pearson. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=1538007
- Monte Carlo methods in financial engineering, Glasserman, P., 2004
- Options, futures, and other derivatives, Hull, J. C., 2009
Recommended Additional Bibliography
- Stochastic calculus for finance. Vol.2: Continuous-time models, Shreve, S. E., 2004