Teaching code

4S008402

Teacher

Alessandro Gnoatto

Coordinatore

Alessandro Gnoatto

Credits

9

Language

Italian

Scientific Disciplinary Sector (SSD)

SECS-S/06 - MATHEMATICAL METHODS OF ECONOMICS, FINANCE AND ACTUARIAL SCIENCES

Period

Primo semestre dal Oct 4, 2021 al Jan 28, 2022.

Lessons timetable Moodle Seminars

Learning outcomes

The course aims to introduce the main quantitative models for the analysis, evaluation and management of financial assets, and provides the fundamental elements for the quantitative study of the finance of bonds and stoke. The student will have the opportunity to learn the terminology and the appropriate concepts for understanding and using the tools of financial mathematics. The critical capacity of describing and developing the basic models of finance will be stimulated with particular attention to the management of the risk-return profile of a financial asset.At the same time the course develops the main quantitative methodologies useful as a basis to attend advanced finance courses.

Program

Part 1: classical financial mathematics - Main Reference: Scandolo

1) Basic financial operations, simple interest, interest in advance, compounding of interest, exponential regime.

2) Annuities and amortization: non-elementary investment and financing, annuities with constant rates, annuities with installments following a geometric progression, amortization, common amortization clauses, amortization with viariable interest rate.

3) Choice without uncertainty: return for elementary and generic investment, choice criteria for investment and financing operations.

4) Bonds: classification, zero coupon bonds, fixed coupon bonds. Term structure: yield curve, complete and incomplete markets.

5) Immunization: Maculay’s duration and convexity, immunized portfolios.

Part 2: mathematical finance in the presence of uncertainty - Main references: Föllmer Schied and Pascucci Runggaldier.

6) Probability theory refresher: probability spaces, independence, Radon-Nikodym theorem, expectation, conditional expectation, martingales, convergence of random variables.

7) Arbitrage theory in one period: foundations and fundamental theorem of asset pricing, contingnt claimds, market completeness.

8) Arbitrage theory in multiperiod models: fundamental on multiperiod models, absence of arbitrage, European contingent claims, binomial model (Cox-Ross Rubinstein).

9) American contingent claims: foundataions, valuation and hedging, arbitrage free prices and replicability in general markets.

Time permitting: Preferences and risk aversion: expected utility criterion (St. Petersburgh paradox), von Neumann Morgenstern axioms, stochastic dominance, mean variance criterion and static portfolio optimization, CAPM.

Bibliography

Examination Methods

2 Hour written exam: the exam will contain both exercises and theoretical questions (statements to be proved)

Course Objectives
- Knowing and understanding the fundamental concepts of basic financial mathematics in a deterministic setting
- Knowing and understanding the fundamental concepts of modern financial mathematics in a stochastic setting
- Obtaining adequate analytical and abstraction skills.
- Knowing how to apply the above knowledge to solve problems and exercise, demonstrating a good level of mathematical rigour.