# Università degli Studi di Napoli "Parthenope"  ## Teaching schedule

2017/2018
Belonging course:
Disciplinary sector:
MATHEMATICAL METHODS OF ECONOMY, FINANCE AND ACTUARIAL SCIENCES (SECS-S/06)
Language:
Italian
Credits:
9
Year of study:
2
Teachers:
Cycle:
First Semester
Hours of front activity:
72

Italian

### Course description

The aim of the course is to provide students with a base of knowledge of the formalization and pricing of financial contracts and risk management; to introduce students to the valuation models of price and risk of contracts and portfolios; to provide criteria for choosing between different value-risk positions.
Knowledge and understanding: the student should know and understand the main issues related to the evaluation of financial contracts, in particular bonds and loans, the definition of contracts value in capital market, the construction of the term structure of interest rates, the measures of a bond's sensitivity to interest rate changes (duration, volatility,..).
Applying knowledge and understanding: the student should be able to apply the results of financial mathematics to the evaluation of contracts, to design the mathematical algorithms implementing financial models, to apply the acquired knowledge to the evaluation schemes of banks, insurances and industries.
Making judgments: the student should be able to use autonomously the acquired knowledge to solve economic and financial problems.
Communication: the student is expected to give clear and in-depth answers to the questions of the written exam and to the ones of the oral exam. The student should be able to communicate using financial and mathematical language and instruments.
Lifelong learning skills: the student should be able to show a good learning ability, by widening, for example, his/her knowledge with use of relevant bibliographic references. The student will have the opportunity to apply the knowledge gained in previous courses integrating them with the additional professional skills that characterize the course.

### Prerequisites

General knowledge of Calculus acquired in previous courses, in particular
functions, limits, continuity and differentiability of real-valued functions of
a single variable, derivatives, graphing, functions of several variables:
partial derivatives, linear algebra problems, solution of non-linear
equations, integrals: analytical and computational techniques.

### Syllabus

(The references in brackets concerning the book of G. Castellani, M. De Felice, F. Moriconi)
Part I Money, time and risk
- Temporal structure of money exchange, capital and interest (chap. 1)
- Contracts, prices, trading (chap. 2)
- Financial risks(chap. 3, except par. 3.3 and 3.5)
Part II Valuation under certainty
- Compound interest and its generalization to the exponential growth
model (chap. 4, par. 4.1-4.3)
- Loans amortization (chap. 5, par. 5.1, 5.2.1, 5.5.1, 5.5.2)
- Internal rate of return (chap. 6, except par. 6.3 and 6.4)
- Rules of financial equivalence (chap. 7, par. 7.1, 7.2, 7.4.1, 7.5, 7.6
except 7.61. and 7.6.2)
Part III Market evaluation of contracts
- Value function and market price (chap. 8)
- Term structure of interest rates (chap. 9, except par. 9.5)
- Measures of timing and sensitivity (chap. 10, except par. 10.1.8 and
10.2.6)
- Valuation methods of the term structure of interest rates (chap. 11, par.
11.2.1, 11.2.2, 11.4)
- No-arbitrage valuation of index contracts (chap. 12, except par. 12.5)

Part I Money, time and risk (16 hours)
- Temporal structure of money exchange, capital and interest
- Financial risks
Part II Valuation under certainty (16 hours)
- Compound interest and its generalization to the exponential growth
model
- Loans amortization
- Internal rate of return
- Rules of financial equivalence
Part III Market evaluation of contracts (40 hours)
- Value function and market price
- Term structure of interest rates
- Valuation models of the term structure of interest rates
- Bootstrap method and Zero Coupon Swap (ZCS) structure
- Svensson model
- Term structures of European Central Bank (ECB)
- Measures of timing and sensitivity
- No-arbitrage valuation of index contracts
- Case study: disputes over derivative contracts
Full program
(The references in brackets concerning the book of G. Castellani, M. De Felice, F. Moriconi)
Part I Money, time and risk
- Temporal structure of money exchange, capital and interest (chap. 1)
- Contracts, prices, trading (chap. 2)
- Financial risks(chap. 3, except par. 3.3 and 3.5)
Part II Valuation under certainty
- Compound interest and its generalization to the exponential growth
model (chap. 4, par. 4.1-4.3)
- Loans amortization (chap. 5, par. 5.1, 5.2.1, 5.5.1, 5.5.2)
- Internal rate of return (chap. 6, except par. 6.3 and 6.4)
- Rules of financial equivalence (chap. 7, par. 7.1, 7.2, 7.4.1, 7.5, 7.6
except 7.61. and 7.6.2)
Part III Market evaluation of contracts
- Value function and market price (chap. 8)
- Term structure of interest rates (chap. 9, except par. 9.5)
- Measures of timing and sensitivity (chap. 10, except par. 10.1.8 and
10.2.6)
- Valuation methods of the term structure of interest rates (chap. 11, par.
11.2.1, 11.2.2, 11.4)
- No-arbitrage valuation of index contracts (chap. 12, except par. 12.5)

### Teaching Methods

Frontal lections. Lab activities to develop Excel-based software
procedures to solve financial problems.

### Textbooks

G. Castellani, M. De Felice, F. Moriconi – Manuale di finanza I. Tassi
d’interesse. Mutui e obbligazioni – il Mulino editore.
J.C. Hull - Options, futures and other derivatives.

### Learning assessment

The achievement of the learning purposes will be evaluated by means of a written test aimed at verifying the operational abilities and an oral interview aimed at understanding the degree of theoretical knowledge and the communication skills of the student. In particular, students will have to take a 90-minute test, using Excel, consisting of three exercises related to the application of formulas and algorithms for: 1. calculation of premiums and technical reserves of traditional policies; 2. mark-to-market valuation of profit-sharing policies; 3. valuation of the SCR in the standard formula. The exercise 1 is worth 12 points, the exercises 2. and 3. are worth 9 points each. The admission to the oral interview requires at least a score of 8 for exercise 1., and at least 5 for each of the exercises 2. and 3.
The oral examination consists of two questions that focus on the theoretical issues related to the evaluation of the characteristic quantities of a life insurance policy: pricing, risk and reserve. For each question the maximum score is 15; the student must attain at least 9 points for each of the two questions.
The grade will be the average of the scores of the two tests.