The aim of this course is to provide the general concepts about portfolio selection of bond and stock and an introduction of the pricing of derivatives.
Basic knowledge of mathematics and probabilities. Moreover a basic knowledge of portfolio theory and derivatives pricing theory is required.
The decision problem – sort operator and its properties – certainty equivalent – expected value operator and the Saint Petersburg paradox – the axiomatic framework of expected utility – representation theorem – measures of risk aversion – Jensen inequality – stochastic dominance.
Mean – variance approach with n securities: analytic resolution of the optimization problem – determination of Markowitz frontier – proof of the two funds theorem – the risk free bond and the capital market line – derivation of CAPM formula– market and equilibrium prices – CAPM e market prices – asset pricing theorem – risk neutral probability. (24 hours of lessons)
Part II: Derivatives contracts
Stochastic calculus: random variables, conditional probability, stochastic processes, martingales, Ito integral – derivation of Ito’s Lemma – european and american derivatives – Black & Scholes equation - Feynman-Kac representation. (24 hours of lessons).
The course includes lectures during which the themes of the program will be discussed together with applications and examples. The teaching material is also made available through the Moodle e-learning platform.
- Castellani, De Felice, Moriconi (2005), Manuale di Finanza vol.II – Teoria del portafoglio e mercato azionario, Il Mulino (selection of chapters)
- Castellani, De Felice, Moriconi (2005), Manuale di Finanza vol.III – Teoria del portafoglio e mercato azionario, Il Mulino (selection of chapters)
- Luenberger (2013), Investment Science. Oxford University Press Inc. (selection of chapters).
- Lecture notes by the teacher.
The test consists in the sustaining of an oral test made of three questions that are worth ten points each. One of the questions will consist in the resolution of a written exercise. The oral test aims to assess the depth of understanding of theoretical knowledge and students will also have to show that they are able to clearly explain the fundamental concepts learned during the course.
Knowledge and understanding: the student must show to comprehend the issues related to portfolio selection and derivatives pricing, especially looking to forwards, futures and options.
Ability to apply knowledge and understanding: the student must demonstrate the ability to apply the mathematical tools acquired for the selection of equity and bond portfolios and the pricing of derivative securities, both from a theoretical and applicative point of view.
Autonomy of judgment: the student must demonstrate the ability to deepen even independently the knowledge acquired by being able to apply more complex models.
Communication skills: the student must be able to respond in a clear, precise and exhaustive way both to the theoretical questions and to the resolution of the exercises.
Lifelong learning skills: the student must demonstrate a good learning ability by being able to deepen their knowledge on relevant bibliographic references relevant to the field under study.