Master
2022/2023
Stochastic Analysis in Finance
Category 'Best Course for New Knowledge and Skills'
Type:
Elective course (Master of Finance)
Area of studies:
Finance and Credit
Delivered by:
HSE Banking Institute
Where:
HSE Banking Institute
When:
1 year, 4 module
Mode of studies:
distance learning
Online hours:
20
Open to:
students of one campus
Instructors:
Svetlana Popova
Master’s programme:
Finance
Language:
English
ECTS credits:
3
Contact hours:
8
Course Syllabus
Abstract
Stochastic calculus is used in financial engineering. The minimum of required math will be covered: sigma-algebras, conditional expectations, martingales, Wiener process, stochastic integration. The big problem is that stochastic calculus is very hard from a mathematical viewpoint. We will formulate all the required theorems mostly without proofs.
Learning Objectives
- The goal of this course is the Black and Scholes model and option pricing using martingale approach
Expected Learning Outcomes
- Understand the Wiener process, stochastic integrals and the Black and Scholes model; price simple European options using martingale approach – price exotic European options using simulations in open sources like R or python
Course Contents
- Wiener process, conditional expected values, variance and covariance, definition of filtration and martingales
- Stochastic (Ito) integral and Ito process, Vasicek model
- Ito’s lemma, Black and Scholes model, Girsanov theorem
- Option pricing, Delta hedging, replicating portfolio
- Simulations of Wiener processes, stochastic integrals, pricing in python
Assessment Elements
- TestsGraded test : You have 1 attempt Time limit – 90 minutes
- Final ProjectThe questions should be answered with text and plots and add the code in appendix. The report should not exceed 10 pages. The project may be done alone or in small groups of two or three students. The report should be upload as one pdf file. Deadline - 2022-04-28, 23:59.
Bibliography
Recommended Core Bibliography
- Augustyński, I., & Laskoś-Grabowski, P. (2018). Clustering Macroeconomic Time Series. https://doi.org/10.15611/eada.2018.2.06
- Lütkepohl, H., & Krätzig, M. (2004). Applied Time Series Econometrics. Cambridge, UK: Cambridge University Press. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=164387
Recommended Additional Bibliography
- Steven Shreve. (2019). Stochastic Calculus for Finance I : The Binomial Asset Pricing Model (Vol. 2004). Springer.