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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 |
Scientific-Disciplinary 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)
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Prerequisites:
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Mathematics, Probability, Statistics. |
Target skills and knowledge:
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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:
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Written exam. |
Course unit contents:
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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
– Two-security portfolio
– N-security 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
– Continuous-time 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
– Put-Call Parity for European options
– Put-Call Parity bounds for American options
The Black-Scholes-Merton Model
– Black-Scholes-Merton (BSM) formula
– P.D.E. approach to the BSM formula
– Continuous-time, risk-neutral approach to the BSM formula
– Binomial-tree approach to the BSM formula
– Delta hedging
– Implied volatility |
Textbooks (and optional supplementary readings) |
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Bjork T, Arbitrage theory in continuous time. Oxford: Oxford University Press, 2001.
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