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Regular version of the site
2021/2022

Type: Optional course (faculty)
When: 1-3 module
Open to: students of one campus
Instructors: Yaroslav Lyulko, Anatoly Peresetsky, Dmitry Davidovich Pervouchine
Language: English
ECTS credits: 3

Course Syllabus

Abstract

Advanced statistics is a two-semester course and it is taught for the second year students in Autumn and Winter semesters. The course focuses on further in-depth look in probability theory and statistics, it naturally extends corresponding compulsory courses for first and second year students. The course is taught in English. The students are also studying for Russian degree in Economics, and knowing Russian terminology through reading in Russian is also required. Course prerequisites: Students are supposed to be familiar with basic probability theory and statistics at the level of Introduction to Probability Theory and Statistics as well as Calculus courses which are taught in the first year of studies. Ability to write basic programs in any programming language (C++, Python, R) is a plus but not strongly necessary. The course itself can be considered as complementary to Statistics course for second year students. Learning Objectives

• The purpose of the course is to increase knowledge in the area of probability theory and statistics, give examples of practical application of studied subjects and develop basis for independent studies, research and analysis. Specifically, the course aims at:
• comprehensive overview of the Introductory Statistics course;
• broadening the students’ knowledge in the fields of probability theory and statistics.
• familiarise students with advanced subjects such as financial mathematics, stochastic processes and stochastic calculus.
• give examples of statistics applications in real life problems which are facing researchers, financial engineers in banks and hedge funds.
• give enough knowledge and reading to allow students to further study selected topics. Expected Learning Outcomes

• use and apply statistical methods for data analysis, research and modelling. This includes ability to select appropriate method/model, check its correctness and applicability, back test methods on historical data and make conclusions.
• be prepared for further units which require a knowledge of statistics and basics of stochastic processes
• be capable to make independent research and analysis in broader topics of statistics Course Contents

• Comprehensive overview of the elementary statistics
Validation of the confidence level of confidence intervals by simulations; Exploratory data analysis using R-statistics and ggplot2
• Basics of financial mathematics in discrete setting.
Concept of random walk: distribution, basic properties, representation. Modelling of price evolution using random walk. Option pricing in discrete time, concept of hedging, Black-Scholes formula for random walk based model. Limiting process from discrete to continuous time.
• Basics of stochastic calculus.
Concept of stochastic process in continuous time. Examples. Brownian motion: definition, basic distribution properties. Connection with random walk using limiting process. Basics of Ito calculus. Concept of stochastic differential, Ito formula.
• Pricing of financial instruments in continuous time.
Overview of financial markets and investment banking. Banks vs Hedge funds, buy side and sell side. Financial instruments from various asset classes (with examples). Application of stochastic calculus to option pricing. Overview of Black-Scholes formula. Overview of three methods of financial derivatives valuation: analytic metods, partial differential methods and Monte Carlo simulation tequniques. Application to financial instruments.
• Probability and statistics methods in gambling
Economics of professional gambling: concepts of hourly rate, return on equity, in-the-money (ITM), capital, risk. Probabilities in poker-like games: outs, chances of the pot, uncertainty, expected cards to come, expected value (EV). Various statistics in poker-like games: analyzing opponents, constructing cards ranges, building counter-strategies for opponents, maximizing EV at the tables, explotative vs game-theory based approach.
• Linear algebra and Multivariate normal distribution
Linear algebra and Multivariate normal distribution Foudations of the theorems in applied mathematical statistics. Fisher Lemma, ANOVA, Multiple regression Assessment Elements

• exam
• home assignments part 1
• home assignments part 2
• home assignments part 3 Interim Assessment

• Interim assessment (3 module)
0.6 * exam + 0.14 * home assignments part 1 + 0.13 * home assignments part 2 + 0.13 * home assignments part 3 Recommended Core Bibliography

• Shir︠i︡aev, A. N. (1999). Essentials Of Stochastic Finance: Facts, Models, Theory. Singapore: World Scientific. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=91430