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 throughout the course.
The main goal of the course is to give to the student the comprehension of the way financial markets operate, giving also the capability of building models for pricing derivative instruments or for hedging positions. The course should also allow the student to become confident with excel implementation of the basic models studied during the course.
Another point is to give to the student the basic knowledge in order to be able to retrieve financial data from the markets.
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 throughout 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 assistance in his work visiting the office of the teacher during his consulting time.
Homework can be assigned from time to time that will be discussed in not compulsory extra lectures.
Type of Assessment
The exam is organized according three steps.
The first step is a written test: at this step the student faces a variable number of problems to be solved. For each correct solution the student receives specified a mark and the global grade is the sum of the obtained marks. In order to move to the second step the student must reach a minimum threshold.
The second step is an excel exercise to be carried out in the office of the teacher. The excel exercise is chosen in a list of the spreadsheets discussed during the course. The correct solution of the exercise is required to move to the third step.
The third step is an oral test where any argument presented in the classroom can be asked. This part of the exam requires good knowledge of the theoretical issues of the course, together with good knowledge of the practical aspects of the studied models.
The final mark of the exam is the arithmetic average of the written and oral tests.
-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.