Mathematics of Finance

Students will learn about and apply the fundamental methods of the mathematics of finance, as well as its application in business administration. The lecture covers two basic problems. First, we will value a payment flow (interests, dividends, bond investment). For that, specific interest models will be introduced. Second, the interest yield of different investments will be defined. In addition, the mathematics of bonds and annuities will be thoroughly analyzed.

  • Presentation of different interest models
  • Valuation of payments
  • Mathematics of annuities
  • Valuation of assets and rate of returns

Learning outcomes
Students learn about the time value of money. After learning basic concepts of financial mathematics, the main goal of this course is to apply concepts in daily decision making. For how long can I pay myself a yearly annuity? How to finance real estate? Is a given investment profitable?

Necessary prerequisites

Recommended prerequisites

Forms of teaching and learningContact hoursIndependent study time
Lecture2 SWS1 SWS
Exercise class2 SWS1 SWS
Tutorial2 SWS1 SWS
ECTS credits3
Graded yes
Form of assessmentWritten exam (45 min)
Restricted admissionno
Further information
Performing lecturer
Prof. Dr. Simon Rother
Prof. Dr. Simon Rother
Frequency of offeringFall semester
Duration of module 0.5 semesters
Preliminary course workPassing of at least 3 of 5 exercise sheets
Course outline1. Basics
1.1 Introduction
1.1.1 Mathematics of finance: asset classes
1.1.2 Payment flows
1.1.3 Central assumption: certain payments
1.2 Interest rates
1.2.1 Introduction
1.2.2 Compound interest (geometric interest)
1.2.4 Interest computation
1.2.5 Higher frequency and continuous compounding
1.2.6 Mixed compounding
1.3 Valuing payment flows: present value
1.4 Net present value
2. Annuities
2.1 Annuities and pensions
2.2 Annuity repayment
3. Asset pricing and rate of return
3.1 Asset pricing
3.2 Rate of return
3.2.2 One period investment
3.2.3 Final maturity investment
3.2.4 Many period investment