## Introduction to Financial Mathematics

**Entry requirements:** Basics of mathematics, statistics, finance and programming skills

**Credits:** 3

**Course:** Elective

**Language of the course:** Russian

## Lecturer

## Objectives

In this course students will learn general principles of employing mathematical tools to solve financial tasks, methods of calculating typical processes, nomenclature of basic financial processes of various scale, analytical and numerical instrument of financial mathematics. An integral part of the course are the problems of classical financial mathematics (mathematics of credit) and the problems of stochastic financial mathematics. Students will also learn to set up routine problems of financial mathematics.

## Contents

- Problems of classical financial mathematics (mathematics of credit): Mathematical models of interest calculations. Problems connected to various debt instruments: bills, certificates of deposit, obligations. Analysis of payment flows used in banking, credits, investments.
- Problems of stochastic financial mathematics and actuarial computations: Stochastic models of money flows. Calculation of fair price of financial instruments. Insurance models: actuarial computations. Econometric models of financial markets.
- Interest calculations. Yield curve: Compounding and straight-rate discounting. Compound interest. Estimating loan term. Financial equality of liabilities. Payment conversion. Yield curve.
- Financial rents: Kinds of payment flows. Accreted rent value. Estimating parameters of fixed rents. Rents with payment growth. Continuous rents. Conversion of rents.
- Barrier values of financial factors: Barrier factors in financial analysis. Linear and non-linear models. Barrier points of issuance.
- Risks and diversification: Risk. Diversification of investments and revenue dispersion. Minimization of revenue dispersion.
- Investments and profitability: Total return. Equivalency equation, profitability of financial tools purchase. Calculation of bond yield. Efficiency of investments. Profitability index.
- Calculation of option: Essence of option. Option price. Black–Scholes Option Pricing Model.

## Format

Lectures and labs

## Assessment

Attendance is mandatory.