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2021 | Buch

Classical Financial Mathematics

Basic Ideas, Central Formulas and Terms at a Glance

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This essential teaches basic formulas, methods and ideas of classical financial mathematics. Since classical financial mathematics makes do with elementary mathematical tools, any interested reader with average mathematical school knowledge can easily follow this text. The core of the text is the calculation of interest and compound interest, annuity calculation, amortization calculation and price calculation. A large number of practical examples illustrate the mathematical questions.

This Springer essential is a translation of the original German 1st edition essentials, Klassische Finanzmathematik by Bernd Luderer, published by Springer Fachmedien Wiesbaden GmbH, part of Springer Nature in 2019. The translation was done with the help of artificial intelligence (machine translation by the service DeepL.com). A subsequent human revision was done primarily in terms of content, so that the book will read stylistically differently from a conventional translation. Springer Nature works continuously to further the development of tools for the production of books and on the related technologies to support the authors.

Inhaltsverzeichnis

Frontmatter
Chapter 1. Introduction
Abstract
Classical financial mathematics traditionally covers the areas of interest and compound interest calculation, annuity, redemption, and  price calculation. At the same time, it forms the basis for modern financial mathematics, whose models require in-depth stochastic results.
Bernd Luderer
Chapter 2. Time is Decisive
Abstract
Time plays a special role in financial mathematics because the value of a payment depends on the time at which it is due.
Bernd Luderer
Chapter 3. How to Pay Interest?
Abstract
The calculation of interest is not clearly defined, it depends on the practical setting. The two most important types of interest calculation are the linear and the geometric interest calculation.
Bernd Luderer
Chapter 4. Reaching Your Goal Through Regular Saving
Abstract
Regular payments can often be usefully combined into a single payment, both within one interest period and over several interest periods.
Bernd Luderer
Chapter 5. Annuity Calculation—Not Only for Pensioners
Abstract
The main purpose of the annuity calculation is to combine several regular payments into a single payment. Depending on the point in time under consideration, this involves the present and the final value of an annuity.
Bernd Luderer
Chapter 6. Would You Rather Be a Debtor or Creditor?
Abstract
The amortization calculation is about determining the repayment rates for interest and repayment of a loan that a debtor has taken out with a creditor. The two main forms are repayment by installments and annuity amortization.
Bernd Luderer
Chapter 7. Short and Long Periods
Abstract
If the interest period does not coincide with the (usually shorter) periods of installment payments or interest payments, one must determine how the interest rates of the short periods relate to those of the original interest period.
Bernd Luderer
Chapter 8. Bonds, Coupons, and Yields
Abstract
Bonds are a widespread financial product. The determination of the parameters fair value and rate of return (yield rate) are central concerns in price calculation.
Bernd Luderer
Chapter 9. The Cherry on the Cake is the Rate of Return
Abstract
The calculation of the rate of return or effective interest rate of financial products or financial investments is a recurrent theme in all areas of financial mathematics. The equivalence principle plays an important role here. Several examples illustrate the procedure for determining the rate of return.
Bernd Luderer
Chapter 10. What Else is Important?
Abstract
Questions going beyond classical financial mathematics are discussed.
Bernd Luderer
Backmatter
Metadaten
Titel
Classical Financial Mathematics
verfasst von
Prof. Dr. Bernd Luderer
Copyright-Jahr
2021
Electronic ISBN
978-3-658-32038-6
Print ISBN
978-3-658-32037-9
DOI
https://doi.org/10.1007/978-3-658-32038-6

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