## MATHEMATICAL FINANCE

## Syllabus

EN
IT

### Learning Objectives

The course provides the concepts necessary to the evaluation of financial assets. Upon completion of the course the students will be able to compute the present value of a cash

flow available in the future, to determine the yield of an investment, to use the theory of compound interest rates to construct and a evaluate a reimbursement scheme like a

mortgage or a sinking fund. Students will learn about the term structure of interest rates, how to use it and construct it (bootstrap). They will know the main features of the most

important fixed income instruments such as bonds, swaps, futures and forward. The course will end with a presentation of the portfolio theory in mean-variance setting.

Upon completion of the course a student is expected to solve problems taken from real life situations (often simplified), and to know the theory motivating the practical solutions.

flow available in the future, to determine the yield of an investment, to use the theory of compound interest rates to construct and a evaluate a reimbursement scheme like a

mortgage or a sinking fund. Students will learn about the term structure of interest rates, how to use it and construct it (bootstrap). They will know the main features of the most

important fixed income instruments such as bonds, swaps, futures and forward. The course will end with a presentation of the portfolio theory in mean-variance setting.

Upon completion of the course a student is expected to solve problems taken from real life situations (often simplified), and to know the theory motivating the practical solutions.

### Prerequisites

The course has no formal prerequisities, although a knowledge of basic concepts from mathematics is expected.

### Program

The course is an introduction to the theory of valuation of financial assets. It provides the basic tools for evaluating the risk of a portfolio whose value is affected by variation of interest rates. It also deals with random cash flows with a mean-variance approach. It covers the following topics:

Deterministic Cash Flow Streams

1. The Basic Theory of Interest

2. Fixed Income Securities

3. The term structure of interest rates

4. Forward and futures prices

4. Duration and Immunization

5. Mean-Variance Portfolio Theory

Deterministic Cash Flow Streams

1. The Basic Theory of Interest

2. Fixed Income Securities

3. The term structure of interest rates

4. Forward and futures prices

4. Duration and Immunization

5. Mean-Variance Portfolio Theory

### Books

David G. Luenberger, ” Investment Science” , Oxford University Press (2013)

### Teaching methods

Lectures consist in the explanation by the teacher of the main topics. After the Theory, part of the lecture is devoted to practical examples.

### Exam Rules

The students should be able to solve problems that show their understanding of the theory.

There will be weekly assignments during the course. At the end of the course there will be a final exam, which will be both written and oral.

There will be weekly assignments during the course. At the end of the course there will be a final exam, which will be both written and oral.