
Course unit
MATHEMATICS FOR FINANCIAL RISK AND DERIVATIVES
EPP6077357, A.A. 2017/18
Information concerning the students who enrolled in A.Y. 2017/18
ECTS: details
Type 
ScientificDisciplinary Sector 
Credits allocated 
Core courses 
MAT/06 
Probability and Mathematical Statistics 
9.0 
Mode of delivery (when and how)
Period 
First semester 
Year 
1st Year 
Teaching method 
frontal 
Organisation of didactics
Type of hours 
Credits 
Hours of teaching 
Hours of Individual study 
Shifts 
Lecture 
9.0 
63 
162.0 
No turn 
Start of activities 
02/10/2017 
End of activities 
19/01/2018 
Examination board
Board 
From 
To 
Members of the board 
1 Commissione A.A. 2017/18 
01/10/2017 
30/09/2018 
EDOLI
ENRICO
(Presidente)
BURATTO
ALESSANDRA
(Membro Effettivo)
GALLANA
MARCO
(Membro Effettivo)

Prerequisites:

Mathematics, Probability, Statistics. 
Target skills and knowledge:

This course is ideal for students who want a rigorous introduction to finance. The course covers the following fundamental topics in finance: the time value of money, portfolio theory, capital market theory, security price modeling, and financial derivatives. 
Examination methods:

Written exam. 
Course unit contents:

The Time Value of Money
– Compound interest with fractional compounding
– NPV, IRR, and Descartes’s Rule of Signs
– Annuity and amortization theory
Portfolio Theory
– Markowitz portfolio model
– Twosecurity portfolio
– Nsecurity portfolio
– Investor utility
Capital Market Theory and Portfolio Risk Measures
– The Capital Market Line
– The CAPM Theorem
– The Security Market Line
– The Sharpe ratio
– The Sortino ratio
– VaR
Modeling the Future Value of Risky Securities
– Binomial trees
– Continuoustime limit of the CRR tree
– Stochastic process: Brownian motion and geometric Brownian motion
– Itô’s formula
Forwards, Futures, and Options
– No arbitrage and the Law of One Price
– Forwards
– Futures
– Option type, style, and payoff
– PutCall Parity for European options
– PutCall Parity bounds for American options
The BlackScholesMerton Model
– BlackScholesMerton (BSM) formula
– P.D.E. approach to the BSM formula
– Continuoustime, riskneutral approach to the BSM formula
– Binomialtree approach to the BSM formula
– Delta hedging
– Implied volatility 
Textbooks (and optional supplementary readings) 

Bjork T, Arbitrage theory in continuous time. Oxford: Oxford University Press, 2001.


