SECS-P/01 (ECONOMIA POLITICA)
DIPARTIMENTO DI SCIENZE ECONOMICHE E AZIENDALI
Corso di studio
ECONOMICS, FINANCE AND INTERNATIONAL INTEGRATION - ECONOMIA, FINANZA E INTEGRAZIONE INTERNAZIONALE
Secondo Semestre (18/02/2019 - 18/05/2019)
44 ore di attività frontale
No specific prerequisite is needed. Nevertheless, familiarity with the basic concepts of Advanced Calculus, Probability and Statistics will be helpful.
This is a course in the applied aspects of mathematical finance, in particular derivative pricing. The theory of stochastic differential equations is the main mathematical tool used in this course. We cover the basic Black-Scholes-Merton theory and we extend it to the case of several underlying assets (including stochastic interest rates) as well as to dividend paying assets. Interest rate theory constitues a substantial part of the course.
Following a practical risk management approach to derivatives, various exercises will be discussed. MATLAB/R tools will be used for the computational works.
It is expected the learning of the fundamental elements of quantitative finance to understand how financial markets work and how complex financial instruments can be assessed.
At the end of the course, students will be able to handle the main techniques employed to price derivatives and a vast array of other financial contracts, evaluating the accuracy of the results economically and/or in business settings.
Programma e contenuti
- Option markets and contracts: basic definitions and illustrations of option contracts, types of options (financial options, options on futures,
commodity options, other types of options)
- Discrete time option pricing: the Binomial Model
- Stochastic calculus (Itô integral, martingales, Itô formula)
- Stochastic Differential Equations: Geometric Brownian Motion, Kolmogorov equations (backward and forward)
- Continuous time option pricing: the Black-Scholes-Merton formula, inputs to the Black-Scholes-Merton model, the critical role of volatility (historic and implied volatility)
- Option strategies for equity portfolios: standard long and short positions, risk management strategies with options and the underlying, money spreads, combinations of calls and puts
- Interest rate option strategies
- Option portfolio risk management strategies: the Greeks, Delta and Gamma hedging
- Some aspects of derivative pricing in incomplete markets
- Forward markets: types of forwards contracts, pricing and valuation
- Futures markets: types of futures contracts, pricing and valuation
- Swap markets: types of swaps, pricing and valuation
- Bonds and interest rates
- Short rate models; martingale models for the short rate, forward rate models
- In-class practice exercises
- Suggested exercises will be uploaded on the platform KIRO on a weekly basis. These exercises should be done individually and will be explained during the following week’s tutorial.
- Team projects
Testi di riferimento
- T. Bjork, Arbitrage Theory in Continuous Time, 3rd ed., Oxford University Press, 2009
- Don M. Chance, Analysis of Derivatives for the CFA® Program, AIMR, United Book Press Inc., 2003
Modalità verifica apprendimento
An overall written exam or two partial written exams (one half-way through the course and the other one at the end).
Compulsory team projects.
Further material and information are available at