Master
2020/2021

## Financial Economics

Type:
Compulsory course (Financial Economics)

Area of studies:
Economics

Delivered by:
International College of Economics and Finance

When:
1 year, 3, 4 module

Mode of studies:
offline

Open to:
students of one campus

Master’s programme:
Financial Economics

Language:
English

ECTS credits:
6

### Course Syllabus

#### Abstract

Prerequisites: microeconomics (concepts of utility functions, constraint utility maximization, market clearing), a good understanding of calculus, algebra, and basic probability theory. This course gives an introduction to the economics and mathematics of financial markets. Being the first course in finance within the ICEF Master Programme in Financial Economics, it introduces the students to the relevant modeling techniques for asset pricing. This will be useful for later courses in Corporate Finance, Fixed Income, Derivatives and Risk Management. The course introduces to the two pricing principles: absence of arbitrage and equilibrium based on individual optimality. The first principle is especially useful for pricing derivative instruments (e.g. an option contract) whenever we know (or assume to know) the dynamics of the price of the underlying asset (e.g. a stock). In order to price the whole universe of financial assets, however, we need to investigate how investors choose their consumption and the composition of their investment portfolios (individual optimality) and how the coordination of these investors on the financial markets leads to the formation of prices (equilibrium analysis). Most of the course covers one-period models and dynamic models in discrete time. However, some equilibrium models are presented in continuous time since this makes them more tractable and they have more elegant solutions. Option pricing in continuous time is left for the 2nd year course in Derivatives. Although the focus of the course is on theory, we shall comment on some empirical evidence and on how these theories are used in financial practice.

#### Learning Objectives

- The goal of the course is to introduce the students to the relevant modeling techniques for asset pricing.

#### Expected Learning Outcomes

- - use basic concepts and terminology met in books and articles on finance
- be able to price vanilla bond instruments
- explain the application o findividual preferences theory in the financial models
- explain and apply the No-Arbitrage Principle for pricing contingent claims
- differentiate between two types of arbitrage strategies
- explain The Fundamental Theorem of finance and market completeness concept
- construct replication portfolio and Binomial trees for option pricing
- construct efficient frontiers and find the optimal portfolio by applying mean-variance analysis
- use mean-variance analysis in the environment with and without risk-free rate
- outline principles of dynamic programming in financial models
- Explain the basic Arrow-Debreu framework and how it relates to the financial market framework
- Outline the notions of Pareto and constrained Pareto optimality
- Be able to build a social welfare function
- List the particular properties of economies where agents have linear risk tolerance
- Apply representative agent analysis to solve a simple portfolio choice problem and determine equilibrium expected returns
- Explain the intuition behind the two-fund separation theorem and the CAPM formula
- List the properties of mean-variance economies and be able to compare them to economies with linear risk tolerance
- Explain the application of probability theory to the modeling of the flow of information in dynamic economies
- Apply no-arbitrage pricing in the dynamic context
- Be able to express equilibrium prices under the physical and the risk-neutral measures
- Explain the connection with informational efficiency

#### Course Contents

- Basic Concepts in Financial Markets:The terminology of financial markets; Bond prices and interest rates under certainty. Individual preferences, utility theory, and risk-aversion.
- Contingent Claims, No-Arbitrage Principle and Derivative PricingUncertainty, replicating portfolios, Arrow-Debreu securities, absence of arbitrage, market completeness. The Fundamental Theorem of finance. Pricing forwards and futures. Bounds on option prices following from the absence of arbitrage. Binomial model of Option pricing.
- Optimal Consumption and Portfolio ChoiceOne-period model. Mean-variance analysis. Dynamic models. Introduction to dynamic programming.
- Equilibrium Models: Static Economies1.1. Set up 1.2. Contingent Claim Equilibrium: Definition, Existence, Pareto Optimality 1.3. Financial Market Equilibrium 1.4. Constrained Pareto optimality: Definition and Hart (1975) example 1.5. Representative Agent Analysis 1.5.1. In Complete Markets 1.5.2. With Linear Risk Tolerance 1.6. Bond-equity economy: Two-Fund Separation Theorem and CAPM 1.6.1. using Representative Agent Analysis 1.6.2. using Mean-Variance Analysis
- Equilibrium Models: Dynamic Economies2.1. Set up and reminder probability theory 2.2. The Fundamental Theorem of Asset Pricing 2.3. State Price Density and Equivalent Martingale Measure 2.4. Dynamic Portfolio Choice (time allowing) 2.4.1. Martingale Approach 2.4.2. Dynamic Programming Approach 2.5. Equilibrium (time allowing)