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Erschienen in:
Household Expenditure Kapitel lesen Erstes Kapitel lesen

2014 | OriginalPaper | Buchkapitel

12. Mathematics of Interest Rates and Finance

verfasst von : Shapoor Vali

Erschienen in: Principles of Mathematical Economics

Verlag: Atlantis Press

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Abstract

A sequence is an ordered set of numbers. Consider the sequence of real numbers expressed as

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Vorheriges Kapitel Economic Dynamics
Nächstes Kapitel Matrices and Their Applications
Anhänge
Nur mit Berechtigung zugänglich
Fußnoten
1
Actually the notation used to indicate repeating decimal is putting a \(-\), called overline or overbar, over the repeating decimal, like \(3.4\overline{35}\).
 
2
To be mathematically correct, (12.13) must be expressed as \(P(t) = P e^{it}\) to indicate \(P\) as a function of the continuous variable \(t\) (time). We are ignoring these subtleties.
 
3
The interest paying bonds are called coupon bonds.
 
4
The par or face value of a bond is its denomination. Bonds are issued with various denominations, generally with increments of $1,000, like $1,000, $2,000, and so on.
 
5
Interests are commonly paid semiannually. We ignore this twist here.
 
6
We are treating the subject of fixed income (bond) valuation rather casually here. In the real world bond valuation is much more complex and involves many different variables and factors. One very important factor is the financial health and creditworthiness of the bond issuing entity. Perception of investors of potential default risk by issuers of bond (or any other financial debt instrument, for that matter) plays a major role in shaping demand for these papers and their prices in the financial market. The financial crisis of 2008 proved, once again, that the investors’ trust and confidence in the financial health of a company trumps all other factors. This manifested itself vividly when bonds issued by faltering corporations like GM and AIG were offered at a fraction of their face values and nobody was buying.
Our exposition of the subject here is elementary, providing a first approximation method for investment evaluation.
 
7
A basis point is one hundredth of a percentage point, that is 0.01 percentage point is equal to 1 basis point. It is used in the financial industry to denote a rate change or the difference (spread) between two rates.
 
8
To avoid disrupting the flow of our discussion, the technical detail of estimating \(t\) is deferred to the Appendix.
 
9
The definition of “jumbo mortgage” changes over time. It is generally a loan amount above the industry standard conventional loan. Currently in some real estate markets loans larger than $417,000 are considered jumbo loans.
 
10
Again, to avoid disrupting our discussion, the technical details of estimating \(i'\) are presented in the Appendix.
 
11
Points (a point equals one percent of the amount of the mortgage loan) are fees that the mortgage lender charges for making the loan. Points are prepaid interest, or interest that is due when the loan is taken out. Lenders offer lower rates with the payment of more points.
 
12
I assume that deposits are made at the beginning of each period. This type of annuity is called Annuity-due.
 
13
College funds are known as 529 Plans. A 529 plan is a tax-advantaged savings plan designed to encourage saving for future college costs. 529 plans, legally known as “qualified tuition plans,” are sponsored by states, state agencies, or educational institutions and are authorized by Sect. 529 of the Internal Revenue Code (See U.S. Securities and Exchange Commission at www.​sec.​gov/​investor/​pubs/​intro529.​htm).
 
Metadaten
Titel
Mathematics of Interest Rates and Finance
verfasst von
Shapoor Vali
Copyright-Jahr
2014
Buch
Principles of Mathematical Economics

Print ISBN: 978-94-6239-035-5

Electronic ISBN: 978-94-6239-036-2

Copyright-Jahr: 2014

DOI
https://doi.org/10.2991/978-94-6239-036-2_12