
Course unit
STOCHASTIC METHODS FOR FINANCE
INP5070417, A.A. 2019/20
Information concerning the students who enrolled in A.Y. 2019/20
ECTS: details
Type 
ScientificDisciplinary Sector 
Credits allocated 
Educational activities in elective or integrative disciplines 
SECSS/06 
Mathematics for Economics, Actuarial Studies and Finance 
9.0 
Course unit organization
Period 
Second semester 
Year 
1st Year 
Teaching method 
frontal 
Type of hours 
Credits 
Teaching hours 
Hours of Individual study 
Shifts 
Lecture 
9.0 
72 
153.0 
No turn 
Examination board
Board 
From 
To 
Members of the board 
2 2019 
01/10/2019 
15/03/2021 
GRASSELLI
MARTINO
(Presidente)
VARGIOLU
TIZIANO
(Membro Effettivo)
CALLEGARO
GIORGIA
(Supplente)

1 2018 
01/10/2018 
15/03/2020 
GRASSELLI
MARTINO
(Presidente)
VARGIOLU
TIZIANO
(Membro Effettivo)
CALLEGARO
GIORGIA
(Supplente)

Prerequisites:

Stochastic analysis 
Target skills and knowledge:

The course presents some important models that are typically used in the banking industry.
The students at the end should be familiar with pricing and hedging in both discrete and continuous time and they should be able to apply stochastic methods to the pricing of equity/forex/fixed income products 
Examination methods:

Final examination based on: Written and oral examination. 
Assessment criteria:

Critical knowledge of the course topics. Ability to present the studied material. 
Course unit contents:

The pricing problem in the binomial models
Risk neutral pricing in the discrete time world
European and American options in the binomial model.
Arbitrage and risk neutral pricing in continuous time.
Pricing of contingent claims in continuous time: the Black&Scholes formula.
Black&Sholes via PDE and via Girsanov.
Hedging and completeness in the Black&Scholes framework.
FeynmanKac formula and risk neutral pricing in continuous time.
Pur Call parity, dividends and static vs dynamic hedging.
The Greeks and the DeltaGamma hedging. DeltaGammaVega neutral portfolios.
Barrier options pricing in the Black&Scholes model.
Quanto option pricing in the Black&Scholes model.
Multi asset markets, pricing and hedging.
Exchange options pricing in the multiasset Black&Scholes model.
Incomplete markets: quadratic hedging.
Smile and skew stylized facts.
Beyond the Black&Scholes model: stochastic volatility.
The Heston model.
Bonds and interest rates. Precrisis and multiplecurve frameworks.
Short rate models, Vasicek, CIR, HullWhite models, affine models.
Cap&Floor pricing in the short rate approaches.
Change of numeraire and Forward Risk Neutral measure. 
Planned learning activities and teaching methods:

Lecture supported by tutorial, exercises and laboratory activities. 
Additional notes about suggested reading:

Lecture notes and reference books will be given by the lecturer. 
Textbooks (and optional supplementary readings) 

T. Bjork, Arbitrage theory in continuous time. : Oxford Univ. Press, Second Edition, 2004. Suggested for: Pricing products in the Black&Scholes framework, arbitrage, barrier options, forex, interest rates

D. Lamberton and B. Lapeyre, Introduction to stochastic calculus applied to finance.. : Cambridge University Press., 2000. Suggested for: Discrete time binomial models, Black&Scholes formula, Girsanov methodology

J. Hull, Options, Futures and Other Derivatives. : Pearson, 8th edition, 2012. Suggested for: General introduction of option markets, Greeks, financial institutions


