Computational Modeling of Derivative Products


The objective of this discipline is to introduce and analyze a diverse set of financial products, completing the necessary development for a total qualification of the students with the necessary tools for their study. The mathematical models underlying the pricing and coverage problems will be revisited and contextualized.

General characterization





Responsible teacher

Pedro José dos Santos Palhinhas Mota


Weekly - 4

Total - 68

Teaching language



Knowledge of Measurement Theory, Stochastic Processes and Stochastic Calculus.


  • Bjork T. Arbitrage, Theory in Continuous Time. Oxford University Press, 2009.
  • Brigo, D. and Mercurio, F., Interest Rate Models – Theory and Practice, 2nd ed. Springer, 2007.
  • Elliott, R.J. and Kopp, P.E., Mathematics of Financial Markets, 2nd ed. Springer, 2005.
  • Iacus, S.M., Simulation and Inference for Stochastic Differential Equations (with R examples). Springer, 2008.
  • Musiela, M. and Rutkowski, M., Martingale Methods in Financial Modelling, 2nd ed. Springer, 2005.
  • Oksendal B. Stochastic Differential Equations: An Introduction with Applications, 6th ed. Springer (2003).
  • Robert C.P. e Casella G. Introducing Monte Carlo Methods with R, Springer, 2010.
  • Ross, S.M., An Elementary Introduction to Mathematical Finance, 3rd ed. Cambridge University Press, 2011.
  • Wilmott, P. Paul Wilmott Introduces Quantitative Finance, 2nd ed. John Wiley & Sons, 2007.

Teaching method

Classes work in a practical theoretical regime.

In the classes the theoretical concepts are exposed, some demonstrations are carried out simultaneously illustrating their application through examples and exercises.

A substantial part of the study is done in the student''s autonomy, with the aid of notes and other bibliographical supports, and with the support of teachers to clarify doubts at pre-established times.

Evaluation method

There is a continuous assessment in the course. It is composed of 2 moments, either tests or written reports; the continuous assessment grade is the average of both results. For those who fail there is still the possibility of a global exam.

Subject matter

  1. Monte Carlo Simulation and Numerical Integration
  2. Numerical Solution of Stochastic Differential Equations
  3. Black-Scholes Model and European Options
  4. Complete Markets and Hedging
  5. Dividends, Foreign Exchange Rates and Exotic Options
  6. Bonds and Interest Rates
  7. Short Rate Models


Programs where the course is taught: