ANALYTICAL METHODS IN FINANCE

Degree course: 
Corso di Second cycle degree in MATHEMATICS
Academyc year when starting the degree: 
2019/2020
Year: 
1
Academyc year when helding the course: 
2019/2020
Course type: 
Supplementary compulsory subjects
Credits: 
8
Period: 
First Semester
Standard lectures hours: 
64
Detail of lecture’s hours: 
Lesson (64 hours)
Requirements: 

Probability, Stochastic processes

Final Examination: 
Orale

Classroom lessons

Assessment: 
Voto Finale

At the end of the course the student must know the fundamentals of stochastic integration and their application to mathematical finance and the microstructure of financial markets

Models of Financial Markets on Finite Probability Spaces.
Models in Discrete and Continuous Time.
The Black and Scholes formula.
Stochastic Integration.
Financial Markets microstructure

Term Structure: Arbitrage theory, short-rate models, market models.
C) The Black and Scholes formula. Options and Arbitrage: Stock Options, Forward Contracts, Futures Contracts, Put-Call Option Parity Formula.
D) Stochastic Integration, Quadratic Variation and Covariation, Itô's Formula, Stochastic Differential Equations, Stochastic Exponential.

Part II: Financial Markets microstructure
A) The ecology of financial markets: the rules of trading , the risks of market-making, the liquidity game.

B) The statistics of price changes: the Random Walk model, jumps and Intermittency in financial markets, why do prices move? 

C) Limit Order Books: the mechanics of LOB trading. Order arrivals and cancellations, order size distributions, volume at the best quotes, volume profiles, tick-size effects.
D) Empirical properties of Limit Order Books, summary statistics, intra-day patterns, the spread distribution

Oral exam and homework

Classroom lessons

Students are received by previous telephone appointment..

Professors

Borrowers