EVALUATION OF CONTINGENT CLAIMS IN THE CONTINUOUS TIME. ELEMENTS OF PROBABILITY THEORY. RANDOM VARIABLES. PROBABILITY DISTRIBUTIONS. STOCHASTIC PROCESSES. WIENER PROCESS. BROWNIAN MOTION. ITO PROCESS. ITO'S LEMMA. STOCHASTIC MODELS IN CONTINUOUS TIME. BLACK AND SCHOLES MODEL. BLACK AND SCHOLES EQUATION. FEYNMANN-KAC REPRESENTATION. RISK-NEUTRAL MEASURE. THE APPLICATION OF FINANCIAL EVALUATION MODELS. THE CAPM MODEL AS A FACTORIAL MARKET MODEL. THE ESTIMATE OF BETA. EMPIRICAL CHECK OF CAPM. THE ALFA OF JENSEN. THE MARKET EMPIRICAL LINE. ARMA MODEL FOR THE ANALYSIS OF FINANCIAL DATA. MODELS FOR VOLATILITY: ARCH AND GARCH MODELS. STOCHASTIC MODELS FOR VOLATILITY. MONTECARLO SIMULATION.

MATERIAL PROVIDED BY THE TEACHER

THE MULTIPLE LINEAR REGRESSION MODEL. INTERPRETATION AND COMPARISON OF REGRESSION MODELS. HETEROSCHEDASTICITY AND AUTOCORRELATION. ENDOGENITY AND INSTRUMENTAL VARIABLES.

MODELS WITH LIMITED DEPENDENT VARIABLES. BINARY CHOICE MODELS: PROBIT AND LOGIT MODELS. MULTIPLE-CHOICE MODELS: PROBIT AND LOGIT MODELS ORDERED, LOGIT MODEL MULTINOMIAL. MODELS FOR COUNTING DATA. TOBIT MODELS.
Seemingly Unrelated Regression (SUR): ESTIMATION AND TESTING METHODS.
SIMULTANEOUS EQUATIONS Model (SEM).
MODELS FOR PANEL DATA. THE STATIC LINEAR MODEL: FIXED EFFECT MODELS; RANDOM EFFECT MODELS. ESTIMATORS WITHIN AND BETWEEN. HETEROSCHEDASTICITY AND AUTOCORRELATION TESTS. DYNAMIC MODELS FOR PANEL DATA: THE ARELLANO-BOND ESTIMATOR.
MODELS WITH LAGGED VARIABLES: DYNAMIC REGRESSION MODELS, MODELS WITH DISTRIBUTED LAGS (DL, ARDL).

For the course program students can consult the following texts (the first three can be considered alternative among them)
1) Introduzione all'Econometria, J. H. Stock, M. W. Watson, Ed. Pearson
2) Econometrica, J. Johnston, Ed. Franco Angeli
3) Econometria, M. Verbeek, Ed. Zanichelli
4) Lectures on advanced econometrics, L. Pieraccini, Ed. Aracne
5) Introduction to Time Series Analysis and Forecasting, D. C. Montgomery, C. L. Jennings, M. Kulahci, Ed. Wiley

Some of the topics in the course can also be found in
Introductory Econometrics for Finance, C. Brooks, Cambridge University Press

For introductory references of statistical inference and algebra of matrices students can consult:
Fondamenti di Inferenza Statistica, L. Pieraccini, Ed. Giappichelli
Matrix Differential Calculus in Statistics and Econometrics, J. R. Magnus, H. Neudecker, Ed. Wiley Series in Probability and Statistics

For the laboratory course with R, students can consult one of the following texts:
Introductory Statistics with R, P. Dalgaard, Ed. Springer
An Introduction to Applied Multivariate Analysis with R, B. Everitt, T. Hothorn, Ed. Springer

1 – FINANCIAL VALUATION METHODS AND MODELS
The value and risk categories. Financial valuation methods. Discounted certainty equivalent approach. Discounted certainty equivalent models. On the choice between risky alternatives. Expected utility hypothesis. Option pricing theory. Risk-adjusted discounting method. Risk-adjusted discounting models. Mixed methods.

2 – RISK MANAGEMENT: CRITERIA AND RULES
Formal scheme. Sources and forms of risk. Market risk and credit risk. Stochastic models for market risk: (a brief review of) equity and currency risk, interest rate risk. Interest rate risk management and control. Semi-deterministic financial immunization theory. Stochastic financial immunization theory and hedging logic. Risk measures for the maximum potential loss (VAR, Risk Capital). Banking and insurance regulation and supervision, and risk culture: Basilea 2 and Solvency 2.

Handouts from teacher.

The international monetary system
Money functions in international transactions. Monetary systems and exchange rates. Exchange rate regimes and monetary unions: from the Gold Standard to the EMU. Costs and benefits of a single currency. The theory of optimal currency areas. Fragility of incomplete monetary unions. Inflation, monetary stability and capital movements.
The institutions of the EMU
The Maastricht Treaty. The European Central Bank. The principle of independence and the governance of the ECB. The European System of Central Banks. The Stability and Growth Pact. Operating procedures of the Eurosystem. Banking supervision and financial stability in the Eurozone.

European monetary policy
Central banks and asymmetric shocks. The ECB's strategy. Intervention instruments: minimum reserve, main and long-term refinancing, fine-tuning, structural operations and open market operations. Transmission mechanisms: interest rates, exchange rates, asset prices and credit conditions. Credit risk and credit crunch regulation: from Basel 1 to Basel 3. Benefits and constraints of a common monetary policy. Monetary policies compared: United States, United Kingdom and European Union.

Tax policies in monetary unions
Tax policies and theory of optimal currency areas. The sustainability of public deficits. Need for fiscal discipline in monetary unions. Effectiveness of the Stability and Growth Pact. National defaults and systems of guarantees in monetary unions. The European Financial Stability Fund. The Fiscal Compact.

The euro, the financial markets and the crisis
Single currency and financial markets. The stability of the financial markets. Currency and effective demand. Credit cycle and financial crises. The financial crisis of 2007 - 2009: from the speculative bubble of the American real estate sector to the economic crisis. The rescue of banks and the sovereign debt crisis. Risks of national default and euro crisis.

DE GRAUWE P., ECONOMIA DELL’UNIONE MONETARIA, IL MULINO, 2010.

EVALUATION OF CONTINGENT CLAIMS IN THE CONTINUOUS TIME. ELEMENTS OF PROBABILITY THEORY. RANDOM VARIABLES. PROBABILITY DISTRIBUTIONS. STOCHASTIC PROCESSES. WIENER PROCESS. BROWNIAN MOTION. ITO PROCESS. ITO'S LEMMA. STOCHASTIC MODELS IN CONTINUOUS TIME. BLACK AND SCHOLES MODEL. BLACK AND SCHOLES EQUATION. FEYNMANN-KAC REPRESENTATION. RISK-NEUTRAL MEASURE. THE APPLICATION OF FINANCIAL EVALUATION MODELS. THE CAPM MODEL AS A FACTORIAL MARKET MODEL. THE ESTIMATE OF BETA. EMPIRICAL CHECK OF CAPM. THE ALFA OF JENSEN. THE MARKET EMPIRICAL LINE. ARMA MODEL FOR THE ANALYSIS OF FINANCIAL DATA. MODELS FOR VOLATILITY: ARCH AND GARCH MODELS. STOCHASTIC MODELS FOR VOLATILITY. MONTECARLO SIMULATION.

MATERIAL PROVIDED BY THE TEACHER

THE MULTIPLE LINEAR REGRESSION MODEL. INTERPRETATION AND COMPARISON OF REGRESSION MODELS. HETEROSCHEDASTICITY AND AUTOCORRELATION. ENDOGENITY AND INSTRUMENTAL VARIABLES.

MODELS WITH LIMITED DEPENDENT VARIABLES. BINARY CHOICE MODELS: PROBIT AND LOGIT MODELS. MULTIPLE-CHOICE MODELS: PROBIT AND LOGIT MODELS ORDERED, LOGIT MODEL MULTINOMIAL. MODELS FOR COUNTING DATA. TOBIT MODELS.
Seemingly Unrelated Regression (SUR): ESTIMATION AND TESTING METHODS.
SIMULTANEOUS EQUATIONS Model (SEM).
MODELS FOR PANEL DATA. THE STATIC LINEAR MODEL: FIXED EFFECT MODELS; RANDOM EFFECT MODELS. ESTIMATORS WITHIN AND BETWEEN. HETEROSCHEDASTICITY AND AUTOCORRELATION TESTS. DYNAMIC MODELS FOR PANEL DATA: THE ARELLANO-BOND ESTIMATOR.
MODELS WITH LAGGED VARIABLES: DYNAMIC REGRESSION MODELS, MODELS WITH DISTRIBUTED LAGS (DL, ARDL).

For the course program students can consult the following texts (the first three can be considered alternative among them)
1) Introduzione all'Econometria, J. H. Stock, M. W. Watson, Ed. Pearson
2) Econometrica, J. Johnston, Ed. Franco Angeli
3) Econometria, M. Verbeek, Ed. Zanichelli
4) Lectures on advanced econometrics, L. Pieraccini, Ed. Aracne
5) Introduction to Time Series Analysis and Forecasting, D. C. Montgomery, C. L. Jennings, M. Kulahci, Ed. Wiley

Some of the topics in the course can also be found in
Introductory Econometrics for Finance, C. Brooks, Cambridge University Press

For introductory references of statistical inference and algebra of matrices students can consult:
Fondamenti di Inferenza Statistica, L. Pieraccini, Ed. Giappichelli
Matrix Differential Calculus in Statistics and Econometrics, J. R. Magnus, H. Neudecker, Ed. Wiley Series in Probability and Statistics

For the laboratory course with R, students can consult one of the following texts:
Introductory Statistics with R, P. Dalgaard, Ed. Springer
An Introduction to Applied Multivariate Analysis with R, B. Everitt, T. Hothorn, Ed. Springer

1 – FINANCIAL VALUATION METHODS AND MODELS
The value and risk categories. Financial valuation methods. Discounted certainty equivalent approach. Discounted certainty equivalent models. On the choice between risky alternatives. Expected utility hypothesis. Option pricing theory. Risk-adjusted discounting method. Risk-adjusted discounting models. Mixed methods.

2 – RISK MANAGEMENT: CRITERIA AND RULES
Formal scheme. Sources and forms of risk. Market risk and credit risk. Stochastic models for market risk: (a brief review of) equity and currency risk, interest rate risk. Interest rate risk management and control. Semi-deterministic financial immunization theory. Stochastic financial immunization theory and hedging logic. Risk measures for the maximum potential loss (VAR, Risk Capital). Banking and insurance regulation and supervision, and risk culture: Basilea 2 and Solvency 2.

Handouts from teacher.

The international monetary system
Money functions in international transactions. Monetary systems and exchange rates. Exchange rate regimes and monetary unions: from the Gold Standard to the EMU. Costs and benefits of a single currency. The theory of optimal currency areas. Fragility of incomplete monetary unions. Inflation, monetary stability and capital movements.
The institutions of the EMU
The Maastricht Treaty. The European Central Bank. The principle of independence and the governance of the ECB. The European System of Central Banks. The Stability and Growth Pact. Operating procedures of the Eurosystem. Banking supervision and financial stability in the Eurozone.

European monetary policy
Central banks and asymmetric shocks. The ECB's strategy. Intervention instruments: minimum reserve, main and long-term refinancing, fine-tuning, structural operations and open market operations. Transmission mechanisms: interest rates, exchange rates, asset prices and credit conditions. Credit risk and credit crunch regulation: from Basel 1 to Basel 3. Benefits and constraints of a common monetary policy. Monetary policies compared: United States, United Kingdom and European Union.

Tax policies in monetary unions
Tax policies and theory of optimal currency areas. The sustainability of public deficits. Need for fiscal discipline in monetary unions. Effectiveness of the Stability and Growth Pact. National defaults and systems of guarantees in monetary unions. The European Financial Stability Fund. The Fiscal Compact.

The euro, the financial markets and the crisis
Single currency and financial markets. The stability of the financial markets. Currency and effective demand. Credit cycle and financial crises. The financial crisis of 2007 - 2009: from the speculative bubble of the American real estate sector to the economic crisis. The rescue of banks and the sovereign debt crisis. Risks of national default and euro crisis.

DE GRAUWE P., ECONOMIA DELL’UNIONE MONETARIA, IL MULINO, 2010.