DERIVATIVES AND INSURANCE - 1

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) describes the main features of financial derivatives (forwards, futures, options, swaps, credit default swaps, basics on CVA and DVA) and the financial markets in which they are traded; moreover, it presents the models used for their evaluation and pricing. In addition, the course briefly presents the main characteristics of fixed-income securities and markets, the valuation of bonds and the yield curve.
The second part of the course (second term, which accounts for 6-ECTSs) covers option pricing with the Black-Scholes-Merton model, option hedging and insurance. As to options, this completes the treatment of derivatives. With regard to insurance, it first discusses risks and insurance, with examples drawn from both non-life and life insurance, and their pricing; then portfolio riskiness and risk transfer are dealt with; finally, it presents life insurance (life tables, life insurance products and the 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 and financial laws.
- Separability.
- Annuities.
- Amortization of a debt.
- Discounted cash flows, internal rate of returns

Students are also expected to be familiar with the following elements of calculus:
- Real functions of one and several variables.
- Derivatives.
- Integrals.

In addition, students are expected to be familiar with the following elements of probability and 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).
- Stochastic calculus for finance.

The contents of the 12-ECTS course are:
PART 1: FIRST TERM

DERIVATIVES
1. Introduction to derivatives.
2. Forwards and futures: mechanics of futures markets; hedging strategies using futures.
3. Interest rates; types of fixed-income securities; fixed income markets; bonds valuation and return analysis; basics on yield curve, duration and convexity.
4. Forwards and futures: pricing of forwards and futures on stocks, stock indices, currencies, commodities.
5. Swaps: interest rate swaps and currency swaps; valuation of swaps; introduction to credit default swaps.
6. Options: mechanics of options markets; properties of stock options; trading strategies involving options.

PART 2: SECOND TERM

DERIVATIVES
1. Option pricing with binomial trees.
2. Option pricing with the Black-Scholes-Merton model.
3. Options on stock indices and currencies.
4. The Greeks and option hedging.
5. Credit issues in derivatives markets: basics on CVA and DVA.
6. Bloomberg lab session: option hedging (optional).

INSURANCE
1. Risks and insurance: insurable risks, transferring risks, examples of non-life and life insurance products, pricing insurance products.
2. Life insurance: modeling the lifetime; life tables; mortality laws.
3. 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, 2021, eleventh ed. (global ed.), chapters 1-7, 9-13, 15, 17, 19.
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 sections 3.1-3.5 and 3.9.5), 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, Student Solutions Manual for Options, Futures, and Other Derivatives, Global Edition, Pearson-Prentice Hall, 2018.
H.U. Gerber, Life Insurance Mathematics, Springer, 1997, third ed., Appendix C-D.

Grading is based on a final written exam, taken at the end of the 12-ECTS course.
This consists of 2 exercises to be solved and 2 open-ended questions (duration: 2 hours): two concern the first part of the course, the other two regard the second part. Each exercise and open-ended question 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 and questions. The exam will be passed with a grade not lower than 18.
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 objective of the open-ended questions is to test the acquisition of the knowledge acquired and the ability to understand the financial products studied.
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.

Especially for students attending classes, it is possible to pass the exam making:
1. An intermediate (mid-term) test on the first part of the course (duration: 1:30 hours), which accounts for 50% of the overall grade (the score obtained can range from 0 to 15). It is a written mid-term test taken at the end of the first trimester, with 2 exercises to be solved and an open-ended question, each of which gives a maximum score of 5.
2. A final test on the second part of the course (duration: 1:30 hours), which accounts for 50% of the overall grade (the score obtained can range from 0 to 15). It is a written test taken after the end of the second trimester, with 1 exercise to be solved and two open-ended questions, each of which gives a maximum score of 5.
3. An optional teamwork on a topic agreed upon with the teacher, which will result in a short paper (a few pages, say 5-10) and slides for a presentation that will be held at the end of the course; only for students who got a score of at least 7 in the mid-term test. The teamwork gives an additional score ranging from 0 to 3 and aims to stimulate the ability of the student to work in groups and to collaborate with colleagues.
The final grade of the examination is given by the sum of the scores obtained in the two written tests, plus the score obtained with the optional teamwork. For the successful completion of the exam, you must achieve an overall score not lower than 18, with at least 7 on each of the two written tests (mid-term and final tests).

A frontal course with lectures. In addition, there will also be practice sessions and tutorials.
The course also uses educational materials available on the university's e-learning platform moodle.unive.it.
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.

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Students are required to register in the related course (Derivatives and Insurance) web page of the university e-learning platform moodle.unive.it.
Additional information, updates and further material on the course will be provided in the web page of the course in moodle.

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