The specific objectives are to prove the necessary quantitative knowledge for understanding the patterns underlying the risk management of financial intermediaries. Consistent with these objectives will be presented simple mathematical models for measuring and controlling market, credit and operational risk. The main purpose of the course is that the student approaches a number of sophisticated techniques and concepts in a simple way.
1.The evolution of the price of a stock: binomial tree. Risk neutral evaluation.
2. Volatility, correlations and copulas,
3. Value at risk and Expected shortfall,
4.Parametric VaR, Historical simulation, Monte carlo simulation,EVT.
4. Evaluating VaR Models: backtesting
1. Introduction: exposure at default, event of default, severity and recovery rate. Conditional and unconditional default probabilities. Intensity of default. Bernoullian approach: expected loss, unexpected loss and Economic capital.
2. Default probability: how to derive historical and risk neutral default probability from market data.
3. Structural models and reduced form models: Merton, KMV, Jarrow e Turnbull, Jarrow, Lando e Turnbull.
4. Portfolio models: default correlation Gaussian copula Credit Metrics Portfolio Manager Credit Portfolio View Credit Risk Plus.
5. Credit derivatives : definition and pricing . Credit default products. Basket products; the k-to default CDS, Collateralized Debt Obligation, CDS indices: CDX and iTRAXX .
1.Characteristics of operational risk data.
2. Basic indicator approach, Standardized method and AMA- LDA ( Loss Distribution Approach) and the Standardized Measurement Approach (SMA) .
