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# Modeling of Financial Operations

2019/2020
Учебный год
ENG
Обучение ведется на английском языке
3
Кредиты

### Course Syllabus

#### Abstract

As a result of the development of the discipline the student must: • Know the basic theoretical principles of the basic mathematical models of financial transactions; • Be able to use professional computer packages to analyze financial data, compare their capabilities, advantages and disadvantages; • Be able to use software products to solve problems; • Be able to find the necessary information in additional literature; • Be able to use this knowledge to describe and solve problems using the apparatus of mathematical and computer Sciences; • Have practical skills in analyzing real financial data; • To have skills in development and computer implementation of new methods of fi-nancial data analysis. This discipline belongs to the elective part of the professional block of disciplines for bachelor degree. The study of this discipline is based on the fundamental courses "Mathematical analysis", "Linear algebra", "Probability ", "Mathematical Statistics". The main provisions of this course are used in the study of disciplines of the block of decision-making.

#### Learning Objectives

• The objectives of the course is to get acquainted with the basic mathematical models of financial transactions, the development of skills in working with financial data, the main methods and algorithms of analysis of financial time series

#### Expected Learning Outcomes

• General concepts of stock market modeling
• Use Mean-variance approach
• Be able to construct Market portfolio and it’s interpretation
• Be able to calculate Index with PCA method, market portfolio in one index model
• Use Sharp theory, over evaluated and under evaluated portfolios
• Formulate and use Arbitrage conditions
• Be able to use Bi-nomial model for the stock price, formula for the option price

#### Course Contents

• Stock market modeling
Assets. Return on assets as a random variable. Distributions of returns. The relationship between the returns: correlation, linear regression, contingency table. Risk (standard deviation of return, Value at Risk)
• Markowitz Model
The return and risk of the portfolio. Mean-variance optimization. Efficient frontier. Theorem on two investments. Risk aversion. Selection of the optimal portfolio in relation to risk. Utility function. Selection of the optimal portfolio by utility function. Value at risk. Construction of the optimal portfolio by the criterion of minimizing the value at risk
• Markowitz-Tobin Model
Portfolios in the presence of a risk-free asset. Efficient frontier. Optimal portfolio. Calculation of the optimal portfolio
• Model with one index
Index definition. The coefficients alpha and beta of the asset. The coefficients alpha and beta of the portfolio. Determination of the optimal portfolio in the model with one index. Capital Asset Pricing Model (CAPM). Market portfolio. Capital line. The beta of asset. The beta of the portfolio. The ratio between the expected return and the beta ratio of the portfolio. Securities market line. Overvalued and undervalued portfolios. Aggressive and defensive portfolios
• Capital Asset Pricing Model (CAPM)
Market portfolio. Capital line. The beta of asset. The beta of the portfolio. The ratio between the expected return and the beta ratio of the portfolio. Securities market line. Overvalued and undervalued portfolios. Aggressive and defensive portfolios
• Factor model for the market
Arbitrage. The ratio between alpha and beta assets in the absence of arbitrage. Determination of arbitrage opportunities
• Options
Binomial model of prices. Black-Scholes Formula. Computational algorithms

• Home work 1
• Home work 2
• Exam

#### Interim Assessment

• Interim assessment (1 module)
0.6 * Exam + 0.2 * Home work 1 + 0.2 * Home work 2

#### Recommended Core Bibliography

• Методы и алгоритмы финансовой математики, [монография], пер. с англ. С. В. Жуленева под ред. Е. В. Чепурина, 751 с., Люу, Ю., 2007