Academic Year 2015/2016 - 2° Year

SECS-S/06 - 9 CFU - 1° Semester

**Model prices in the financial markets **

**The cardinal utility theory; axiomatic structure. fundamental theorem.**

**Intensity of preference. Absolute and relative risk measures. **

**The certainty equivalent. Applications equivalent course. Risk premium. **

**Main families of utility functions and their properties. ****Paradoxes of Allais and Ellsberg. ****Some experiments by Kahneman and Tversky .**

**First and second order stochastic dominance.**

**Portfolio Theory. Mean-variance models. ****Risk indices.**

** Only two risky assets. Efficient Frontier: possible cases particularly interesting. **

**Contraction risk. Portfolio of minimum risk. **

**Model mean-variance with the most risky assets. **

**Main theorems on the efficient frontier. Feasible set and shape of the border. **

**Diversification and risk reduction. Systematic risk. **

**Diversification and risk reduction. Systematic risk. Minimization of the variance of the portfolio. **

**Maximizing the risk premium and the consequences on the efficient frontier. The Chapital Market Line. Portfolio Market. Separation theorem. **

**CAPM assumptions and mathematical derivations of the model. SML. Systematic risk and specific risk. The coefficient '' beta ''. Diversification and risk reduction in the CAPM. **

**Non-standard versions of the CAPM.**

**Single Index Model. Multifactorial models.**

**Options: first definitions and payoffs. Using options for basic risk management.**

**Hedging strategies by combining options and below. **

**The spreads. Combinations of options. ****Put-call parity. Minimum and maximum limits for the value of a put and a call. **

**Risk-neutral pricing model.**

**Fixed-Income Market Models and Derivatives.**

1. J. Cvitanic, F. Zapatero, “Introduction to the Economics and Mathematics of Financial Markets.’’The MIT Press Cambridge, Massachusetts London, England, 2004.

2. D. Luenberger , “Finanza e Investimenti’’, Apogeo, Milano 2006.

3. J. Berck , P. DeMarzo, “Chapital budgeting”, Addison Wesley (Pearson International Ed.), Milano 2009.

4. J. Berck, P. DeMarzo, “Finanza aziendale 2”, Addison Wesley (Pearson International Ed.), Milano 2008.

5. S. Benninga , “Modelli finanziari”, McGraw-Hill, Milano 2010.

6. E. J. Elton, M. J. Gruber ,“Modern portfolio theory and investment analysis”, Wiley, 2002.