30560 - MATHEMATICAL MODELLING FOR FINANCE
Course taught in English
Go to class group/s: 27
Class-group lessons delivered on campus
The course equips students with mathematical models to deal with core problems of finance. Students will develop a unique combination of financial intuition and rigorous mathematical reasoning to tackle and to solve fundamental questions in finance with a meticulous mathematical approach.
- Financial markets, risk and return;
- Law of One Price: linear pricing functionals, Stochatisc Discount Factors, Risk-Neutral probabilites;
- No Arbitrage and the 1st Fundamental Theorem of Asset Pricing;
- No Arbitrage, completeness and the Fundamental Theorem of Asset Pricing;
- Optimal portfolio consumption and equilibrium asset pricing;
- Stochatisc Discount Factors, the mean variance fronteer and beta models;
- The Capital Asset Pricing Model, CAPM.
- Information and conditional expectation;
- Financial securities, investment strategies, cashflows;
- Dynamic no-arbitrage and completeness: the 1st and the 2nd Fundamental Theorem of Asset Pricing;
- No-Arbitrage valutation of derivatives;
- Dynamic programming and applications to finance: American options and portfolio optimization;
- Equilibrium in multiperiod financial markets.
- Recognize the main features of financial markets both in a static and in a dynamic framework.
- Identify the necessary conditions for financial equilibrium in the one-period and in the multiperiod case.
- Discuss absence of arbitrage and market completeness.
- Identify optimal portfolio strategies and the mean-variance fronteer in the one-period setting.
- Define the hedging strategy and the derivatives' prices in no-arbitrage complete markets.
- Describe the optimal portfolio problem in a multi-period setting.
- Discuss the main features of asset prices in equilibrium markets.
- Verify the absence of arbitrage and the completeness of one-period and multiperiod financial market models.
- Hedge and evaluate derivatives securities in no-arbitrage complete markets, both in the one-period and in the multiperiod case.
- Solve optimal portolio problems in the one-period and in the multi-period case.
- Face-to-face lectures
- Exercises (exercises, database, software etc.)
Some lectures will be dedicated to the solution of exercises. Students will be trained to deal with core problems of finance applying rigorous mathematical reasoning.
No distinction between attending and non-attending students.
The exam consists of a written individual exam with open-ended questions and closed-ended questions. The open-ended questions require substantiated answers and check the ability to describe key features of the theoretical models presented (e.g. the absence of arbitrage and the completeness of one-period and multiperiod financial market models) and to apply mathematical methods to solve financial problems (e.g. hedging and evaluating derivatives securities in no-arbitrage complete markets, or solving optimal portfolio problems in the one-period and in the multi-period case).
The closed-ended questions with "multiple choice questions" verify the ability to recognize basic knowledge and concepts regarding the most important features of the mathematical modelling of core financial problems discussed in the lectures.
Slides and lecture notes prepared by Instructors. All teaching materials will be distributed via BBoard.