Course 2026-2027 a.y.

Simple interest. Invers formulas. Simple interest and floating interest rates. Compound interest. Discrete capitalization. Interest capitalization axiom. Inverse formulas. Compound interest and floating interest rates. Decomposability property. Equivalent interest rates in compound interest. Annual nominal interest rate. Continuous interest. Annuities. Ordinary annuities. An important financial symbol. Perpetuities. Inverse formulas. Annuities increasing according to a geometric sequence. Zero coupon bonds. Coupon bonds. Dirty and clean prices. Accrued interest. Ordinary Italian Treasury Bonds. Gross and net simple yield to maturity. Treasury Bills. Discounted Cash Flow. Net Present value. Internal Rate of Return. Investments and loans. Net Present Value rules. Basic review of probability calculus. Random variables. Exprected value and variance. Properties. Valuation of an ordinary share. Gordon-Shapiro formula. Introduction to derivative contracts. Forwards. Futures. Options. Call and put options. Payoff of a call and put options. Exotic options. Evolution of a stock price in discrete time. Risk-neutral probability measure. One-period pricing model in discrete time for European options. Replication portfolio. No-arbitrage condition. Fair price of a call/put option. Profit function of a call/put option. CRR pricing model. Two-period pricing model in discrete time for European call/put option with dividends and without dividends. An example of pricing of an exotic option (asian option) and a barrier option.

The main knowledge topics of the course will refer to:

1. Understanding which economic or financial variables are important in a decision problem.
2. Explaining the right procedurs to apply to answer a decision problem.
3. Identifying different ways to solve a decision problem and understanding which one can give the best answer.

At the end of the course students will be able to:

1. move amounts of money back and forth in time using different financial mathematics models.
2. mvaluate the price of non-quoted shares using different assumptions about share dividends.
3. find and justify the fair price of a financial derivative.
4. build and interpret different ratios from the balance sheet.

• Lectures
• Practical Exercises
• Individual works / Assignments
• Collaborative Works / Assignments

Practical exercises are coherent with the programme and will help students to better understand the theory in practical situations. Assignments (individual and collaborative) are applications of the quantitative analysis to real-life decision problems.

The final grade is determined as follows: active class partecipation (10% final grade), assignments (30% final grade) and general exam (60% final grade). The general exam consists of open and/or closed questions.

The final grade is determined by a general exam. The general exam consists of open and/or closed questions.

• Slide Sets
• Exercises