Fundamentals of Financial Mathematics (B-KUL-G0Q20C)

4 ECTSEnglish26 First termCannot be taken as part of an examination contract
POC Master in statistiek

The aim of the course is to give a rigorous yet accesible introduction to the modern theory of financial mathematics.

  • Sound mathematics, statistics and probability theory knowledge
  • Finance (Financial Markets)

Activities

4 ects. Fundamentals of Financial Mathematics (B-KUL-G0Q20a)

4 ECTSEnglishFormat: Lecture26 First term
POC Master in de actuariële en financiële wetenschappen

The aim of the course is to give a rigorous yet accessible introduction to the modern theory of financial mathematics. The student should already be comfortable with calculus and probability theory. Prior knowledge of basic notions of finance is useful.
We start with providing some background on the financial markets and the instruments traded. We will look at different kinds of derivative securities, the main group of underlying assets, the markets where derivative securities are traded and the financial agents involved in these activities. The fundamental problem in the mathematics of financial derivatives is that of pricing and hedging. The pricing is based on the no-arbitrage assumptions. We start by discussing option pricing in the simplest idealised case: the Single-Period Market. Next, we turn to Binomial tree models. Under these models we price European and American options and discuss pricing methods for the more involved exotic options. Monte-Carlo issues come into play here.
Next, we set up general discrete-time models and look in detail at the mathematical counterpart of the economic principle of no-arbitrage: the existence of equivalent martingale measures. We look when the models are complete, i.e. claims can be hedged perfectly. We discuss the Fundamental theorem of asset pricing in a discrete setting.
To conclude the course, we make a bridge to continuous-time models. We introduce and study the Black-Scholes model in detail.

Evaluation

Evaluation: Fundamentals of Financial Mathematics (B-KUL-G2Q20c)

Type : Partial or continuous assessment with (final) exam during the examination period
Description of evaluation : Written, Paper/Project
Type of questions : Open questions


Features of the evaluation

* The evaluation consists of:

•an assignment
•an written exam
* The deadline for the assignment will be determined by the lecturer and communicated via Toledo.

Determination of the final grade

* The grades are determined by the lecturer as communicated via Toledo and stated in the examination schedule. The result is calculated and communicated as a whole number on a scale of 20.

* The final grade is a weighted score and consists of:

•the assignment: 25% of the final grade
•the exam: 75% of the final grade
* If the student does not participate in the assignment and/or the exam, the grades for that part of the evaluation will be a 0-grade within the calculations of the final grade.

*If the set deadline for the assignment was not respected, the grade for that respective part will be a 0-grade in the final grade, unless the student asked the lecturer to arrange a new deadline. This request needs to be motivated by grave circumstances.

Second examination opportunity

* The features of the evaluation and determination of grades are similar to those of the first examination opportunity, as described above.