Mathematical finance (2013/2014)

Course code
Luca Di Persio
Academic sector
Language of instruction
Teaching is organised as follows:
Activity Credits Period Academic staff Timetable
Teoria 1 1 I semestre Luca Di Persio
Teoria 2 4 I semestre Leonard Peter Bos
Esercitazioni 1 I semestre Luca Di Persio

Lesson timetable

I semestre
Activity Day Time Type Place Note
Teoria 1 Monday 1:30 PM - 3:30 PM lesson Lecture Hall M from Oct 1, 2013  to Oct 20, 2013
Teoria 1 Thursday 1:30 PM - 3:30 PM lesson Lecture Hall M from Oct 1, 2013  to Oct 20, 2013
Teoria 2 Monday 1:30 PM - 3:30 PM lesson Lecture Hall M from Oct 21, 2013  to Jan 31, 2014
Teoria 2 Thursday 1:30 PM - 3:30 PM lesson Lecture Hall M from Oct 21, 2013  to Jan 31, 2014
Esercitazioni Wednesday 3:30 PM - 5:30 PM practice session Lecture Hall M from Oct 21, 2013  to Jan 31, 2014

Learning outcomes

The Mathematical Finance course for the internationallized Master's Degree (delivered completely in English) aims to introduce the main concepts of stochastic discrete and continuous time part of the modern theory of financial markets. In particular, the fundamental purpose of the course is to provide the mathematical tools characterizing the setting of Itȏ stochastic calculus for the determination, the study and the analysis of models for options and / or interest rates determined by stochastic differential equations driven by Brownian motion. Basic ingredients are the foundation of the theory of continuous-time martingale, Girsanov theorems and Faynman-Kac theorem and their applications to the theory of option pricing with specific examples in equities, also considering path-dependent options, and within the framework of interest rates models.

Please refer to: for details about the course: course material, seminars, special events, etc. [ in particular take a look to the Teaching area and the "principal page" of annuncements ]


Discrete time models
Contingent claims, value process, hedging strategies, completness, arbitrage
Fundamental theorems of Asset Pricing (in discrete time)

The Binomial model for Assset Pricing
One period / multiperiod Binomial model
A Random Walk (RW) interludio (scaled RW, symmetric RW, martingale property and quadratic variation of the symmetric RW, limiting distribution)
Derivation of the Black-Scholes formula (continuous-time limit)

Brownian Motion (BM)
review of the main properties of the BM: filtration generated by BM, martingale property, quadratic variation, volatility, reflection properties, etc.

Stochastic Calculus
Itȏ's integral
Itȏ-Döblin formula
Black-Scholes-Merton Equation
Evolution of Portfolio/Option Value
Solution to the Black-Scholes-Merton Equation
Sensitiveness analysis

Risk-Neutral Pricing
Risk-Neutral Measure and Girsanov's Theorem
Pricing under the Risk-Neutral Measure
Fundamental Theorems of Asset Pricing
Existence/uniqueness of the Risk-Neutral Measure
Forwards and Futures

Stochastic Differential Equations
The Markov Property
Interest Rate Models
Multidimensional Feynman-Kac Theorems
Lookback, asian, amaerican Option

Term structure models
Affine-Yield Models
Two-Factor Vasicek Model
Two-Factor CIR Model
Heath-Jarrow-Morton (HJM) Model
HJM Under Risk-Neutral Measure

Assessment methods and criteria

Written exam