00675 - Financial Mathematics

Course Unit Page

Academic Year 2018/2019

Learning outcomes

At the end of this course, the student can manage the basics on financial capitalization and actualization regimes. More specifically, the student will be able to handle contracts involving money transactions and to manage different cash flow strategies.


Course contents

Theory of Interest. Simple, Compound and Continuous Interest Rates. Present and Future Values of cash flow streams.

Rendite e ammortamenti. Present and Future values of Annuities. Perpetuities (or consols). Continuous cash flows. Loan calculations,Running amortization, annual worth.

Yields. Coupon bond. Yield to maturity. Internal Rate of Return (Net and Gross). Duration and Modified Duration.

Bonds and Term structure of interest rates. Spot and forward rates. Term structure. Yield to maturity. Duration. Forward contracts. IRS and swap rates. Bootstrapping the forward curve.

Uncertainty, risk and choices. Uncertainty and risk. Preferences. The Von-Neuman and Morgenstein setup, Expected utility, Risk-aversion. Worst-case and Minimal Regret preferences. Risk premiums. Arrow-Pratt theorems. Classes of utitility functions: CARA, CRRA and polynomial.  Mean variance criterion.Risk-selling, risk-pooling, risk-sharing and risk-spreading.

Portfolio Theory. Portfolio returns and risk. Volatility and other risk-easures. Mean-variance approach. The 2-asset portfolio. Markowitz mean-variance portfolio theory. The two-fund theorem. Markowitz model with a risk-free asset. Sharpe's index.


D. Luenberger. Investment Science. Oxford University Press, 1998.

Teaching methods

Blackboard lessons and exercises. Computer experiment sessions to show some model performances.

Assessment methods

Written test with exercises.

Teaching tools

Lessons using Blackboard and slides. Exercises. Computer experiments and examples using market quotations.

Office hours

See the website of Paolo Foschi