Presentazione

Organizzazione della Didattica

DM270
MATEMATICA ORD. 2011


7

Curriculum Generale

 

Frontali Esercizi Laboratorio Studio Individuale
ORE: 32 24 0 102

Periodo

AnnoPeriodo
I anno2 semestre

Frequenza

Facoltativa

Erogazione

Convenzionale

Lingua

Inglese

Calendario Attività Didattiche

InizioFine
27/02/201709/06/2017

Tipologia

TipologiaAmbitoSSDCFU
affine/integrativo Nessun ambitoSECS-S/063
affine/integrativo Nessun ambitoMAT/064


Responsabile Insegnamento

ResponsabileSSDStruttura
Prof. GRASSELLI MARTINOSECS-S/06Dipartimento di Matematica

Altri Docenti

Non previsti.

Attività di Supporto alla Didattica

Non previste.

Bollettino

Analisi stocastica (Propedeutico per gli studenti della laurea in matematica)

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

Lecture supported by tutorial, exercises and laboratory activities.

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. Feynman-Kac formula and risk neutral pricing in continuous time. Pur Call parity, dividends and static vs dynamic hedging. The Greeks and the Delta-Gamma hedging. Delta-Gamma-Vega 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 multi-asset 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. Pre-crisis and multiple-curve frameworks. Short rate models, Vasicek, CIR, Hull-White models, affine models. Cap&Floor pricing in the short rate approaches. The pricing of swaptions. Forward rate models: HJM approach, the drift condition and BGM models. Change of numeraire and Forward Risk Neutral measure. LIBOR and Swap models.

Final examination based on: Written and oral examination.

Critical knowledge of the course topics. Ability to present the studied material.

D. Lamberton and B. Lapeyre, Introduction to stochastic calculus applied to finance.. : Cambridge University Press., 2000 J. Hull, Options, Futures and Other Derivatives. : Pearson, 8th edition, 2012 T. Bjork, Arbitrage theory in continuous time. : Oxford Univ. Press, Second Edition, 2004

Lecture notes and reference books will be given by the lecturer.