Numerical methods for finance and risk management
A.A. 2018/2019
Obiettivi formativi
Non definiti
Risultati apprendimento attesi
Non definiti
Periodo: Secondo trimestre
Modalità di valutazione: Esame
Giudizio di valutazione: voto verbalizzato in trentesimi
Corso singolo
Questo insegnamento non può essere seguito come corso singolo. Puoi trovare gli insegnamenti disponibili consultando il catalogo corsi singoli.
Programma e organizzazione didattica
Edizione unica
Responsabile
Periodo
Secondo trimestre
STUDENTI FREQUENTANTI
STUDENTI NON FREQUENTANTI
Propedeuticità
Elementary Probability Theory, Statistics and Integration.
Prerequisiti
Risk Management module
Written and Oral examination
Written and Oral examination
Metodi didattici
Risk Management module
Lectures with real-time applications in R.
Lectures with real-time applications in R.
Module Numerical Methods for Finance
Programma
Sigma algebra and filtration
Convergences
Introduction to continuous time stochastic processes
Simple and quadratic variations
Wiener process
Stochastic differential equations
Ito stochastic integral and Ito formula
Martingales
Principles of options pricing and the Black&Scholes market
Contingent T-Claims and derivation of the general Black&Scholes pricing formula
Derivation of explicit formula for European call/put options under the Black&Scholes market
Martingale measures and their relations to pricing
Fundamental theorem of option pricing
Simulation of stochastic differential equations
Monte Carlo approach to option pricing
Variance-reduction techniques
Parameter estimation from discretely observed stochastic differential equations
Historical and implied volatility
Monitoring volatility though change point analysis
Explorative data analysis: clustering and lead-lag estimation
Quasi MLE, AIC and Lasso model selection
Introduction to Lévy processes: properties, simulation and parametric estimation
Estimated (MC) expected payoffs under different physical measures
Pricing for the multidimensional Black&Scholes model
Convergences
Introduction to continuous time stochastic processes
Simple and quadratic variations
Wiener process
Stochastic differential equations
Ito stochastic integral and Ito formula
Martingales
Principles of options pricing and the Black&Scholes market
Contingent T-Claims and derivation of the general Black&Scholes pricing formula
Derivation of explicit formula for European call/put options under the Black&Scholes market
Martingale measures and their relations to pricing
Fundamental theorem of option pricing
Simulation of stochastic differential equations
Monte Carlo approach to option pricing
Variance-reduction techniques
Parameter estimation from discretely observed stochastic differential equations
Historical and implied volatility
Monitoring volatility though change point analysis
Explorative data analysis: clustering and lead-lag estimation
Quasi MLE, AIC and Lasso model selection
Introduction to Lévy processes: properties, simulation and parametric estimation
Estimated (MC) expected payoffs under different physical measures
Pricing for the multidimensional Black&Scholes model
Metodi didattici
classroom and laboratories
Materiale di riferimento
Iacus, S.M., Yoshida, N. (2018) Simulation and Inference for Stochastic Processes with YUIMA, Springer, New York
Iacus, S.M. (2011) Option Pricing and Estimation of Financial Models with R, John Wiley & Sons, Ltd., Chichester, 472 page, ISBN: 978-0-470-74584-7
Iacus, S.M. (2008) Simulation and Inference for Stochastic Differential Equations: with R examples, Springer Series in Statistics, Springer NY, 300 pages, ISBN: 978-0-387-75838-1
Iacus, S.M. (2011) Option Pricing and Estimation of Financial Models with R, John Wiley & Sons, Ltd., Chichester, 472 page, ISBN: 978-0-470-74584-7
Iacus, S.M. (2008) Simulation and Inference for Stochastic Differential Equations: with R examples, Springer Series in Statistics, Springer NY, 300 pages, ISBN: 978-0-387-75838-1
Module Risk Management
Programma
Prerequisites.
Overview of Basel 2, Basel 3 and Solvency 2. Basic Concept in Risk Management: Risk Measures (VaR and ES).
Light tailed versus Heavy tailed distributions. Regularly varying distributions, EVT: the POT method.
Modeling dependence with copulas.
Multivariate Modelling: ''if Only the World Were Elliptical'' - Coherent Measures of Risk .
Standard methods for Market Risk .
Risk Aggregation and Model Uncertainty.
Operational Risk: some case studies.
Overview of Basel 2, Basel 3 and Solvency 2. Basic Concept in Risk Management: Risk Measures (VaR and ES).
Light tailed versus Heavy tailed distributions. Regularly varying distributions, EVT: the POT method.
Modeling dependence with copulas.
Multivariate Modelling: ''if Only the World Were Elliptical'' - Coherent Measures of Risk .
Standard methods for Market Risk .
Risk Aggregation and Model Uncertainty.
Operational Risk: some case studies.
Metodi didattici
Lectures with real-time applications in R.
Materiale di riferimento
TEXTBOOK:
AJ McNeil, R Frey and P Embrechts,
Quantitative Risk Management: Concepts, Techniques, Tools. Revised Edition.
Princeton University Press, Princeton, 2015;
ADDITIONAL MATERIAL:
Set of slides provided by the instructor
AJ McNeil, R Frey and P Embrechts,
Quantitative Risk Management: Concepts, Techniques, Tools. Revised Edition.
Princeton University Press, Princeton, 2015;
ADDITIONAL MATERIAL:
Set of slides provided by the instructor
Prerequisiti
Risk Management module
PREREQUISITES: Elementary Probability Theory, Statistics and Integration.
EXAM: Written and Oral examination
PREREQUISITES: Elementary Probability Theory, Statistics and Integration.
EXAM: Written and Oral examination
Module Numerical Methods for Finance
Programma
Sigma algebra and filtration
Convergences
Introduction to continuous time stochastic processes
Simple and quadratic variations
Wiener process
Stochastic differential equations
Ito stochastic integral and Ito formula
Martingales
Principles of options pricing and the Black&Scholes market
Contingent T-Claims and derivation of the general Black&Scholes pricing formula
Derivation of explicit formula for European call/put options under the Black&Scholes market
Martingale measures and their relations to pricing
Fundamental theorem of option pricing
Simulation of stochastic differential equations
Monte Carlo approach to option pricing
Variance-reduction techniques
Parameter estimation from discretely observed stochastic differential equations
Historical and implied volatility
Monitoring volatility though change point analysis
Explorative data analysis: clustering and lead-lag estimation
Quasi MLE, AIC and Lasso model selection
Introduction to Lévy processes: properties, simulation and parametric estimation
Estimated (MC) expected payoffs under different physical measures
Pricing for the multidimensional Black&Scholes model
Convergences
Introduction to continuous time stochastic processes
Simple and quadratic variations
Wiener process
Stochastic differential equations
Ito stochastic integral and Ito formula
Martingales
Principles of options pricing and the Black&Scholes market
Contingent T-Claims and derivation of the general Black&Scholes pricing formula
Derivation of explicit formula for European call/put options under the Black&Scholes market
Martingale measures and their relations to pricing
Fundamental theorem of option pricing
Simulation of stochastic differential equations
Monte Carlo approach to option pricing
Variance-reduction techniques
Parameter estimation from discretely observed stochastic differential equations
Historical and implied volatility
Monitoring volatility though change point analysis
Explorative data analysis: clustering and lead-lag estimation
Quasi MLE, AIC and Lasso model selection
Introduction to Lévy processes: properties, simulation and parametric estimation
Estimated (MC) expected payoffs under different physical measures
Pricing for the multidimensional Black&Scholes model
Materiale di riferimento
Iacus, S.M., Yoshida, N. (2018) Simulation and Inference for Stochastic Processes with YUIMA, Springer, New York
Iacus, S.M. (2011) Option Pricing and Estimation of Financial Models with R, John Wiley & Sons, Ltd., Chichester, 472 page, ISBN: 978-0-470-74584-7
Iacus, S.M. (2008) Simulation and Inference for Stochastic Differential Equations: with R examples, Springer Series in Statistics, Springer NY, 300 pages, ISBN: 978-0-387-75838-1
Iacus, S.M. (2011) Option Pricing and Estimation of Financial Models with R, John Wiley & Sons, Ltd., Chichester, 472 page, ISBN: 978-0-470-74584-7
Iacus, S.M. (2008) Simulation and Inference for Stochastic Differential Equations: with R examples, Springer Series in Statistics, Springer NY, 300 pages, ISBN: 978-0-387-75838-1
Module Risk Management
Programma
Prerequisites.
Overview of Basel 2, Basel 3 and Solvency 2. Basic Concept in Risk Management: Risk Measures (VaR and ES).
Light tailed versus Heavy tailed distributions. Regularly varying distributions, EVT: the POT method.
Modeling dependence with copulas.
Multivariate Modelling: ''if Only the World Were Elliptical'' - Coherent Measures of Risk .
Standard methods for Market Risk .
Risk Aggregation and Model Uncertainty.
Operational Risk: some case studies.
Overview of Basel 2, Basel 3 and Solvency 2. Basic Concept in Risk Management: Risk Measures (VaR and ES).
Light tailed versus Heavy tailed distributions. Regularly varying distributions, EVT: the POT method.
Modeling dependence with copulas.
Multivariate Modelling: ''if Only the World Were Elliptical'' - Coherent Measures of Risk .
Standard methods for Market Risk .
Risk Aggregation and Model Uncertainty.
Operational Risk: some case studies.
Materiale di riferimento
TEXTBOOK:
AJ McNeil, R Frey and P Embrechts,
Quantitative Risk Management: Concepts, Techniques, Tools. Revised Edition.
Princeton University Press, Princeton, 2015;
ADDITIONAL MATERIAL:
Set of slides provided by the instructor
AJ McNeil, R Frey and P Embrechts,
Quantitative Risk Management: Concepts, Techniques, Tools. Revised Edition.
Princeton University Press, Princeton, 2015;
ADDITIONAL MATERIAL:
Set of slides provided by the instructor
Moduli o unità didattiche
Module Numerical Methods for Finance
SECS-S/01 - STATISTICA - CFU: 6
Lezioni: 40 ore
Docente:
Iacus Stefano Maria
Module Risk Management
SECS-S/06 - METODI MATEMATICI DELL'ECONOMIA E DELLE SCIENZE ATTUARIALI E FINANZIARIE - CFU: 6
Lezioni: 40 ore
Docente:
Puccetti Giovanni
Docente/i