The course deals with quantitative models to be used in financial industry.
In this course, essentially self-contained, the student will learn how such models are built and used for strategic purposes.
The starting point of the course is a simple single period financial market model where the basic notions of equilibrium, arbitrage and pricing procedure are introduced.
Next, basic derivative instruments like forward contracts, futures and options are introduced focusing on pricing models.
All the learning material of the course, like classroom notes, articles, excel spreadsheets and other materials are directly sent to the students by the teacher through-out the course.
The main goal of the course is to give to the student the comprehension of the way financial markets operate, how to build mathematical models for pricing financial derivative instrument and how set up specific strategies using such inssrtuments.
The course has a strong quantitative content and consequently, math skills and knowledges are essential, also if rarely the level of mathematics used rises higher than the basic calculus. In detail, basic calculus notions are required together with basic linear algebra and matrix calculus, and basic statistics and probability.
On the financial-economic side here is assumed the knowledge of some jargon and little more.
Class lectures twice a week for twelve weeks. The students must attend at least 80% of the lectures in order to take the exam. In the classroom the teacher will develop the theoretical contents of the course and will present the basic applications of the studied arguments.
The computational part of the course is dedicated to the implementation in excel spreadsheet of the models analyzed throug-out the course. The teacher will give in the classroom the outlines of each spreadsheet letting the students to complete them as a homework. The student can receive any assistence in his work visiting the office of the teacher during his consulting time.
Homeworks can be assigned from time to time that will be discussed in not compulsory extra lectures.
Modalità di verifica apprendimento
A final exam is the way to verify the level of knowledge obtained by the student giving him a grade.
In order to be allowed to take the exam the student must have an attendance at the class lectures of at least 80%.
The exam is organized on three steps: a written test, an excel test and the oral final part.
The written test consists of a variable number of exercises to be solved by the student only using paper, pen and a small calculator.
Each exercise receives its mark only if the result is correct, otherwise no credit is accrued. This means that the student must pay attention in performing calculations remembering that in finance numbers are equivalent to money.
The admission to the second stage of the exam requires a minimum mark in the written test, this minimum can be variable from time to time.
The second step, the excel test, insists on an exercise that the student has to carry out in the office of the teacher respecting the specific time limit assigned. To succeed in this part the exercise must be concluded, working alone, arriving to the correct result. A failure in this stage implies the repetition also of the written test.
The oral part of the exam covers any argument presented in the course, that is any argument contained in the notes and in any other material sent by the teacher. In the oral test the student can be required to solve some problems and give the proof of all the propositions contained in the notes.
Programma del corso
-Single period financial market model.
Definition of a financial market: payoff matrix, price vector, portfolio vector, contingent claim.
Completeness of a market and replica of contingent claims.
Basic theorem of equilibrium. Pricing kernel.
Risk neutral probabilities and the pricing of contingent claims in complete markets in equilibrium.
Detecting equilibrium solving a constrained problem of minimum.
-Generalities of financial markets.
Modalities of trading. OTC markets and exchanges.
Typology of financial assets and derivative instrument.
Definition and functions of forward contracts. Underlyings of forward contracts. Typology of traders in futures markets.
Equilibrium conditions for forward prices.
Market value of forward contracts.
Generalities and features.
Futures exchanges and Clearing Houses.
The margin mechanism.
Forward prices and futures prices.
Hedging in futures markets and optimal hedging ratio.
Definition, typology of option contracts. Features.
Weak relationships involving prices of options, strikes and the price of the underlying.
Call-Put parity and related relationships.
Early exercise of American options.
Convexity properties of the prices of options.
Strategies involving options.
Binomial models for pricing options.
The Cox-Ross-Rubinstein model.
Pricing American options.
Pricing options on futures.
Implied volatility and volatility smile.
-An outline of simulation methods.
Simulation of Brownian motion.
Simulation of the evolution of the price of risky assets.
Mean reverting processes.
The Option Based Portfolio Insurance (OBPI)
The Constant Proportion Portfolio Insurance.