Academic year
2022/2023 Syllabus of previous years
Official course title
Course code
EM5022 (AF:358859 AR:189985)
On campus classes
ECTS credits
Degree level
Master's Degree Programme (DM270)
Educational sector code
1st Term
Course year
Go to Moodle page
This is the first part of a compulsory 12-ECTS course. The 12-ECTS course on the whole has common objectives, learning outcomes, contents and teaching methods that are described as follows.
The 12-ECTS course on the whole aims to describe and analyze the main financial derivatives, to present the basics of bond pricing and to introduce insurance.
In particular, the first part of this course (which accounts for the first 6-ECTSs) covers: (i) the main features of financial derivatives and the financial markets in which they are traded; (ii) the structure of forward contracts and futures contracts and their valuation; (iii) the structure of options and the pricing models based on binomial trees and the Black-Scholes-Merton model; (iv) the hedging strategies based on derivative instruments.
The second part of the course (second term, which accounts for 6-ECTSs) covers: (i) the main characteristics of fixed-income securities, the yield curve and the valuation of bonds; (ii) the structure and the pricing of interest rate sensitive derivatives (swaps); (iv) the structure and the pricing of credit derivatives (credit default swaps); (iv) risks and insurance, with examples drawn from both non-life and life insurance, and their pricing; (v) life insurance (life tables, life insurance products and premium calculation).
The instructional goal of the 12-ECTS course is acquiring the knowledge and competences to understand, manage and evaluate the financial derivatives and the main insurance products and the quantitative models that allow to evaluate them.
In detail:

a) Knowledge and understanding:
a.1) Ability to understand the main financial derivatives (forwards, futures, swaps and options).
a.2) Ability to understand the functioning of the financial markets in which these derivatives are traded.
a.3) Ability to understand fixed-income securities and measure the yield curve.
a.4) Ability to understand the working of bonds and the formulae for their evaluation.
a.5) Ability to understand the quantitative models for the evaluation and pricing of forwards, futures, swaps and options and for the assessment of the risks involved in their use.
a.6) Ability to understand the risks of bonds, forwards, futures, swaps and options.
a.7) Ability to understand credit default swaps, CVA and DVA.
a.8) Ability to understand the main non-life insurance products and, more in depth, life insurance products.
a.9) Ability to understand the functioning of insurance companies and the markets of insurance products.
a.10) Ability to understand the basic quantitative models for the evaluation of the main insurance products.
a.11) Ability to understand the riskiness of a portfolio of risks and the transfer of risks.
a.12) Knowledge of life tables and basic mortality laws.

b) Ability to apply knowledge and understanding:
b.1) Ability to use the main quantitative models for forwards, futures, swaps and options.
b.2) Ability to compute the no arbitrage price of bonds, forwards, futures, swaps and to compute the option price both with a discrete and a continuous model.
b.3) Ability to measure the risks of bonds, forwards, futures, swaps and options.
b.4) Ability to hedge the risks of bonds, forwards, futures, swaps and options with proper strategies.
b.5) Ability to compute the fair value and the premium of life insurance contracts.
b.6) Ability to use a life table and a mortality law.
b.7) Ability to communicate to others the knowledge acquired.

c) Ability to make judgements:
c.1) Ability to evaluate and compare the contracts for bonds, forwards, futures, options, swaps and credit default swaps.
c.2) Ability to determine if the market price of bonds, forwards, futures, options, swaps and credit default swaps is correctly determined and, in case it is not so, to devise a proper arbitrage strategy to take advantage of the mispricing.
c.3) Ability to choose the most suitable financial instruments to hedge the risk for a company or an investor.
c.4) Ability to choose the most suitable insurance products to cover from insurable risks.
c.5) Ability to determine if the market premium for a life insurance product is correctly determined.
Students are expected to know the basic elements of financial mathematics, as they are taught in a course of Financial Mathematics at the laurea/bachelor degree:
- Basics of interest rates.
- Separability.
- Annuities.
- Amortization of a debt.

Students are also expected to be familiar with the following elements of calculus:
- Single variable functions.
- Integrals.
- Several variable functions.

In addition, students are expected to be familiar with elements of statistics:
- Exploratory data analysis (univariate distributions, location and variability summaries, graphical representations).
- Probability (interpreting probability, probability rules, univariate random variables, law of large numbers and central limit theorem).
- Basic techniques of statistical inference (point and interval estimation, hypothesis testing).
The contents of the 12-ECTS course are:


1. Introduction to derivatives.
2. Forwards and futures: mechanics of futures markets; hedging strategies using futures; pricing of forwards and futures on stocks, stock indices, currencies, commodities, interest rates.
3. Options: mechanics of options markets; properties of stock options; trading strategies involving options.
4. Option pricing with binomial trees.
5. Option pricing with the Black-Scholes-Merton model.
6. The Greeks and option hedging.
7. Bloomberg lab session: pricing of derivatives and option hedging (optional).


1. Types of fixed-income securities; fixed income markets; bonds valuation; yield curve and term structure of interest rates.
2. Swaps: interest rate swaps; currency swaps; valuation.
3. Credit default swaps: properties and valuation. Basics on CVA and DVA.
4. Bloomberg lab session: pricing of swaps and credit default swaps (optional).

5. Risks and insurance: insurable risks, transferring risks, examples of non-life and life insurance products, pricing insurance products.
6. Life insurance: modeling the lifetime; life tables; a mortality law.
7. Life insurance: pricing; life insurance products, discounting cash flows, single premium, periodic premiums, loading for expenses.
J. Hull, Options, futures, and other derivatives, Pearson-Prentice Hall, 2018, tenth ed. (global ed.), chapters 1-7, 9-13, 15, 17, 19, 25.
A. Olivieri, E. Pitacco, Introduction to Insurance Mathematics, Springer-Verlag, 2015, second edition, chapters 1 (with the exception of subsections 1.5.3, 1.5.4), 3 (only p. 157-172), 4 (with the exception of subsections: 4.2.6, 4.2.7, 4.2.9, 4.2.11, 4.4.5).

Optional reading (suggested):
J. Hull, Options, futures, and other derivatives: Solution manual, Pearson-Prentice Hall, 2018, tenth ed. (global ed.).
Grading is based on a final written exam, taken at the end of the 12-ECTS course.
This consists of 4 exercises to be solved (duration: 2 hours): two of them concern the first part of the course, the other two regard the second part. Each exercise accounts for 25% of the final grade of the exam and the final grade will be the sum of the scores obtained in all exercises.
The objective of the exercises is to test the student's ability to understand the financial problem given, to choose the most appropriate tools for solving it and to apply the abilities acquired in order to compute the solution.
The exam is closed-notes and closed-book, but students are allowed to use a pocket calculator and two sides of an A4-sheet prepared by themselves at home with the main formulae (only formulae, not written comments or notes), handwritten with "normal" size (not microscopic).
Students need to register for the exam in advance.
A frontal course with lectures. In addition, there will be practice sessions and tutorials.
The course uses educational materials available on the university's e-learning platform
Exercises will be assigned weekly to stimulate and test the acquisition of the knowledge and abilities on the topics covered during the week; students are expected to solve them regularly at home.

Students are required to register in the related course (Derivatives and Insurance) web page of the university e-learning platform
Additional information, updates and further material on the course will be provided in the web page of the course in moodle.
Definitive programme.
Last update of the programme: 13/08/2022