Магистратура
2024/2025
Количественные финансы 2
Статус:
Курс по выбору (Стохастическое моделирование в экономике и финансах)
Направление:
38.04.01. Экономика
Кто читает:
Школа финансов
Где читается:
Факультет экономических наук
Когда читается:
2-й курс, 1, 2 модуль
Формат изучения:
без онлайн-курса
Охват аудитории:
для своего кампуса
Прогр. обучения:
Стохастическое моделирование в экономике и финансах
Язык:
английский
Кредиты:
6
Course Syllabus
Abstract
The theoretical part of the course will refresh our knowledge of the basics of binomial model,stochastic calculus, various option pricing models as well as stochastic models of the short rate.In the practical (main) part of the course we will discuss basic numerical methods for the valuation of derivative securities, like Monte Carlo simulation, finite difference methods, and regression-based valuation of American options in detail. We will mostly focus on equity derivatives in the geometric Brownian motion framework, but we will also discuss alternative models like the Heston stochastic volatility model or Merton’s jump-diffusion model. The course is not meant to be a course in numerical mathematics with detailed and extensive theorems and proofs, its focus is rather on the basics of a set of very useful numerical techniques, which are widely applied in industry practice and in research. The implementation will be done in Python (also possible in Julia, Matlab, R).
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 the usage of exotic derivatives
- Understand calibration techniques of different stochastic models
Expected Learning Outcomes
- Implement basic Monte Carlo technique for different financial problems
- Implement variance reduction techniques
- Calculate sensitivities (delta, gamma, vega and others)
- 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
- Implement stochastic volatility models
- Calibrate term structure of interest rates
- Calculate Distance-to-Default
- Implement VaR and ES via Monte Carlo
- Implement calibration procedures for option pricing models
- Pricing American style options
Course Contents
- Tree-based pricing methods
- Review of derivative pricing methods
- Monte Carlo Simulations
- Estimating price sensitivities in MC
- Pricing of American Options
- Alternative option pricing models
- Interest rate modeling
- Credit risk modeling. Merton Distance-to-Default Model
- Monte Carlo Methods for VaR & ES
Assessment Elements
- Home Assignment 1Tree-base modeling
- Home Assignment 2Stochastic Calculus
- Home Assignment 3Review of Derivatives Pricing
- Home Assignment 4Monte Carlo methods
- Mid term test
- Home Assignment 5Pricing American Options
- Home Assignment 6Alternative option pricing models
- Home Assignment 7Stochastic short rate models
- Home Assignment 8Credit risk modeling. Merton Distance-to-Default Model
- Home Assignment 9Monte Carlo Methods for VaR
- Final testFinal test
Interim Assessment
- 2024/2025 2nd module0.3 * Final test + 0.05 * Home Assignment 1 + 0.05 * Home Assignment 2 + 0.05 * Home Assignment 3 + 0.05 * Home Assignment 4 + 0.05 * Home Assignment 5 + 0.05 * Home Assignment 6 + 0.05 * Home Assignment 7 + 0.05 * Home Assignment 8 + 0.05 * Home Assignment 9 + 0.25 * 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., 2018
Recommended Additional Bibliography
- Stochastic calculus for finance. Vol.2: Continuous-time models, Shreve, S. E., 2004