Mathematical Finance
PROF. ALESSANDRA MAININI; PROF. PIERA MAZZOLENI
COURSE AIMS
The course is aimed at developing financial valuation over time and in conditions
of uncertainty.
The course presents, from a formal and operational perspective, the principles
which govern the financial markets and the most important financial instruments
for market intervention and control of risk.
At the end of the course, the student will have a grasp of the criteria used for
evaluation and decision of the most common financial problems.
COURSE CONTENT
MODULE I
Mathematics has come up with appropriate calculation methodologies, thus making
it possible to establish rules of equity for loans and capital accumulation plans, but
especially for pricing bonds. Such conditions of equity make it possible to analyse
the trend of interest rates, with the use of the non-arbitrage principle.
1. The time value of money: capital accumulation and loan amortisation.
The course presents the instruments for understanding the timing aspects of
financial transactions, showing how flexibility can make it possible to follow
the very volatile trend of the markets.
2. Method for valuing financial investment and financing projects: quantitative
theory for decisions; consistency of valuation criteria in conditions of certainty;
present value; implicit rate of return.
The course presents key instruments for the critical evaluation and selection of
business projects, respecting the characteristics of the projects.
3. Bonds: pure discount bonds and coupon bonds.
The student will learn to price bond securities, and to analyze their financial
characteristics, in particular with respect to interest rates.
4. The no-arbitrage principle
The relationships of equilibrium for financial products and the implications on
the structure of interest rates by maturity are described within the context of the
assumptions of a perfect market.
MODULE II
The module presents, from a formal and operational perspective, the principles
which govern the financial markets and the most important financial instruments
for market intervention and control of risk.
The role of time and the role of uncertainty are analysed, formalising tools for
deterministic control in the case of bond securities and mean-variance criterion for
the choice of equity securities.
Mathematical methods are developed that lead to a market model, with reference to
the application of statistical techniques for forecasting returns on equity
investments and for evaluating risk.
The no-arbitrage principle is outlined and applied for the construction of the
pricing of derivatives contracts.
At the end of the course, the student should have a command of the appropriate
valuation and decision criteria for the most widespread financial problems.
1. Financial immunisation:
Time is a clear source of uncertainty: a simplified approach leads to a
sensitivity analysis, to be considered as a first indicator of risk.
2. Optimal selection of investments: mean-variance analysis of equity portfolios
consisting of risky investments and those consisting of risk-free investments:
expected utility criterion.
The course examines the classical instruments for measuring risk and
evaluating equity investments.
3. The market model: distinction between systematic and non-systematic risk;
presentation of an index model; introduction to funds management, with key
performance indicators. Quantitative instruments are used for expressing the
conditions for the equilibrium of the markets themselves.
4. Introduction to modern financial instruments: derivatives and their valuation,
and hedging strategies: options and the binomial price model.
The course will analyse the main types of derivatives contracts with the
application of the no-arbitrage principle.
READING LIST
I Module
Text adopted
P. MAZZOLENI, Finanza matematica (First module), EDUCatt, 2013.
Recommended reading
F. CESARI, Introduzione alla Finanza Matematica: concetti di base, tassi e obbligazioni, McGraw –
Hill, 2012
II Module
Text adopted
P. MAZZOLENI, Finanza matematica (Module II), EDUCatt, 2007.
Recommended reading
F. CESARI, Introduzione alla Finanza Matematica: mercati azionari, rischi e portafogli, McGraw –
Hill, 2012
TEACHING METHOD
Lectures and practical assignments under the professor's guidance.
ASSESSMENT METHOD
Written examination for theory and applications.
NOTES
Further information can be found on the lecturer's webpage at
http://docenti.unicatt.it/web/searchByName.do?language=ENG or on the Faculty notice
board.