6 ECTS credits
150 h study time
Offer 1 with catalog number 4006946FNR for all students in the 1st semester at a (F) Master - specialised level.
Using mathematical tools, we treat the valorisation and hedging of financial instruments.
We start with the study of static models in discrete time and binomial trees, and in particular with the model of Cox-Ross-Rubenstein (1979). Notions like “arbitrage-free”, “completeness”, “hedging-portfolio” … are introduced. Several applications are explained and different exercises are made to practice the notions of completeness and arbitrage-opportunities; and to price and hedge European and American options.
Afterwards, we concentrate upon dynamic financial models in discrete time, and in particular upon the theory of Harrison & Kreps (1979).
Next, we pass to dynamic financial models in continuous time, based on the theory of stochastic processes and of the Brownian motion in particular. We derive the famous formulae for European options in the model of Black & Scholes (1973) and some generalizations and applications.
Finally, we study stochastic interest rate models in order to evaluate some interest rate derivatives. As an example, we focus upon the model of Vasicek (1977).
Several applications of the different models in the professional world of banking and insurance are mentioned.
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The goal of this course is to present probabilistic techniques used in financial models to price and hedge financial products.
After following this course, the student knows stochastic interest rate models like Vasicek (1977) and the famous basic financial models of Cox-Ross-Rubenstein (1979), Harrison & Kreps (1979) and Black & Scholes (1973), together with a lot of applications in the financial and insurance business. Since the course stresses the general mathematical methods in these models, the student understands also more recent results in the domain of “Mathematical Finance”.
The different basic models which are explained in detail during this course, are extensively used in practice, originally only in the financial world but nowadays more and more in the insurance business. The professional world stimulates research of more realistic models and more precisely pricing- and hedging techniques.
The final grade is composed based on the following categories:
Written Exam determines 30% of the final mark.
SELF Presentation determines 70% of the final mark.
Within the Written Exam category, the following assignments need to be completed:
Within the SELF Presentation category, the following assignments need to be completed:
written project + presentation 70 % of the final mark
written exam 30 % of the final mark
This offer is part of the following study plans:
Master of Mathematics: Financial and Applied Mathematics (only offered in Dutch)
Master of Mathematics: Fundamental Mathematics (only offered in Dutch)
Master of Teaching in Science and Technology: wiskunde (120 ECTS, Etterbeek) (only offered in Dutch)