This course presents the basic models for the analysis and evaluation of financial operations, both under conditions of certainty and randomness. The main goal of the course is to equip the student with the ability to model and solve some basic mathematical problems, commonly encountered in the financial practice.
1. Financial operations. Present and future value. Simple and compound interest. Spot and forward rates. Market rates.
2. Present value of a cash flow. Amortizement of a debt. Computation of the instalments. Choice criteria among cash flows: Net Present Value and Internal Rate of Return. Fixed and floating rate mortgages. Coupon bonds and term structure. Immunization, duration and convexity.
3. Portfolio selection. Investing in stocks. Expected return and volatility of a portfolio. Risk aversion and Markowitz criterium. Efficient portfolios when investing in: a stock and a bond, two stocks, two stocks and a bond. Constrained optimization techniques (Lagrange) Covariance matrix and efficient portfolios with N stocks. The Capital Market Line and the Capital Asset Pricing Model.
Books:
- Matematica finanziaria, P. Bortot, U. Magnani, G. Olivieri, F. A. Rossi, M. Torrigiani, Monduzzi, BO, ultima edizione.
- Matematica finanziaria, G. Scandolo, Amon Edizioni
Written, 2 hours, exercises
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