Laurea Magistrale in Matematica
Salta il menu di secondo livelloMETODI STOCASTICI PER LA FINANZA - 7 CFU
Mutuato da STOCHASTIC METHODS FOR FINANCE (CORSO DI LAUREA MAGISTRALE IN MATHEMATICAL ENGINEERING - INGEGNERIA MATEMATICA)
Insegnante
Martino Grasselli
Periodo
I Anno - 2 Semestre | 02/03/2020 - 12/06/2020
Ore: 56 (56 lezione)
Prerequisiti
Analisi stocastica (Propedeutico per gli studenti della laurea in matematica)
Conoscenze e abilità da acquisire
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
Modalità di esame
Final examination based on: Written and oral examination.
Criteri di valutazione
Critical knowledge of the course topics. Ability to present the studied material.
contenuti
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.
Change of numeraire and Forward Risk Neutral measure.
Attività di apprendimento previste e metodologie di insegnamento
Lecture supported by tutorial, exercises and laboratory activities.
Eventuali indicazioni sui materiali di studio
Lecture notes and reference books will be given by the lecturer.
Testi di riferimento
- 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
- J. Hull, Options, Futures and Other Derivatives, Pearson, 8th edition, 2012. Suggested for: General introduction of option markets, Greeks, financial institutions
- 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