Table Of ContentSpringer Texts in Business and Economics
Ralf Korn
Bernd Luderer
Money and
Mathematics
A Conversational Approach
to Modern Financial Mathematics
and Insurance
Springer Texts in Business and Economics
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Ralf Korn • Bernd Luderer
Money and Mathematics
A Conversational Approach to Modern
Financial Mathematics and Insurance
RalfKorn BerndLuderer
FachbereichMathematik Fakulta¨tfu¨rMathematik
TUKaiserslautern TUChemnitz
Kaiserslautern,Germany Chemnitz,Germany
ISSN2192-4333 ISSN2192-4341 (electronic)
SpringerTextsinBusinessandEconomics
ISBN978-3-658-34676-8 ISBN978-3-658-34677-5 (eBook)
https://doi.org/10.1007/978-3-658-34677-5
Original German edition has been published with title Mathe, Märkte und Millionen with Springer
FachmedienWiesbadenGmbHin2019.
©SpringerFachmedienWiesbadenGmbH,partofSpringerNature2019,2021
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To thetwo mostcriticalreaders,
ourwives, gratefullydedicated
Preface
Mathematics—abstract, dust-dry, unrealistic, incomprehensible, and not for you?
Wrong,allwrong!Thereisreallynotruthtothisstereotype.Inparticular,applied
mathematics deals with many extremely exciting and practical questions. It is the
intention of this book to show that it is worth studying them. In more than five
dozenstories, you,dearreader,will geta relaxedbutneverthelessmathematically
exact introduction into the colorful world of financial and insurance mathematics
andintothefinancialmarkets.
Mathematical knowledge is often only required at school level; however, for
some stories, basic knowledge of differential calculus and probability theory is
an advantage. For those readers who want to learn more about the mathematical
background,thelastchapterdescribestheassociatedtheory.
The stories are mostly independent of each other, but are grouped by content.
Frequentlyusedformulas,aglossary,andintroductoryliteraturearecompiledatthe
endofthebook,whilemorespecificsourcescanbefoundintheindividualstories.
ThebookisbasedonanearlierGermanedition,buthasbeenexpandedandadapted
fortheEnglish-speakingreader.
We are indebted to Elke Korn for introducing us to many colorfulexpressions
thatenhancedourtext.WearealsogratefultoSpringerVerlagfortheinclusionof
ourworkinthepublishingprogram.
Kaiserslautern,Germany RalfKorn
Chemnitz,Germany BerndLuderer
May2021
vii
Contents
PartI IncomeTaxes,Lottery,andLionHunting—Elementary
Mathematics
1 “WeTakeoverYourVAT!”HowBigIstheActualDiscount? ........ 3
2 MillionsEveryWeek,but NotforMe. SixNumbersinthe
Lottery ...................................................................... 5
3 Where Did My Money Go? Loss
CompensationAfteraPriceDrop ....................................... 9
4 HowDoYouCatchaLion?FindingaZerobyHalving
theInterval.................................................................. 13
Literature..................................................................... 16
5 Upside Down and Up Again. How Many
ZerosDoesaPolynomialHave?........................................... 17
6 “AccordingtoAdamRies,thatComesto...”AboutFusti,
Freight,andCartage....................................................... 21
Literature..................................................................... 24
7 HowtoInvest?TheCost-AverageEffect................................. 25
Literature..................................................................... 27
8 §32a,thePoliticianandtheCoaster.CalculatingtheIncome
TaxofaPerson.............................................................. 29
9 This Makes the Taxpayer Shudder. What Does “Cold
Progression”ActuallyMean?............................................. 33
Literature..................................................................... 37
PartII Interest Rates, Prices, Yields—Classical Financial
Mathematics
10 AFairDeal?Or:There’sNothingLikeStartingYoung ............... 41
Literature..................................................................... 42
ix
x Contents
11 ShouldIPaytheBillQuickly?CashDiscount .......................... 43
12 TheChildrenoftheInterestRateAretheGrand-Childrenof
theCapital.CompoundInterest .......................................... 45
Literature..................................................................... 48
13 WhenWillScroogeMcDuckBeSatisfied?TheDoublingProblem... 49
14 HowRealIsNominal?TheActualRateofReturnonaPrincipal.... 53
Literature..................................................................... 56
15 “HaveILearnedtoCalculateCorrectly?”WhyDr.X.from
GifhornWasWrong........................................................ 57
16 “What,IHavetoPaythatLong?”FullRepaymentofaLoan........ 59
17 TheWidowoftheGeneralandthePainter.ALoanàlaChekhov.... 63
Literature..................................................................... 66
18 WhyDoesNominalnotEqualEffective?TheEffectiveInterest
RateofanImmediateLoan................................................ 67
19 SandwichwithaCarInside.FinancingwithHooksandEyes ........ 69
20 TheAssiduousClerk.CapitalCertificatesandFederalBonds........ 73
21 7500EurosMonthly:ALifetime.OrBetterYet,TwoMillions
RightAway?................................................................. 77
22 FinancingaCarwithZeroPercent:ABargain?........................ 81
Literature..................................................................... 82
23 Interest Payments Anytime: Isn’t That Wonderful?
ContinuousCompoundingofInterest.................................... 83
24 BearerBondsandCoupons.BondPricesandReturnsofBonds ..... 87
25 Oops!ALawContainingFormulasandNumericalMethods?
TheCalculationoftheEffectiveInterestRateAccordingto
theGermanPriceIndicationOrdinance................................. 91
Literature..................................................................... 94
PartIII FinancialProductsandStrategies—ModernFinancial
Mathematics
26 FairPricesandMarketPrices ............................................ 97
27 TheShortEndandtheLongEnd.YieldCurves,SpotRates,
andForwardRates......................................................... 99
Literature..................................................................... 104
28 SimpleasVanillaIceCream.OnStandardFinancialProducts....... 105
Contents xi
29 ExchangesforMutualBenefit.Swaps.................................... 107
Literature..................................................................... 109
30 The Telescope That Has Been Pushed Together. How to
CalculateaSwapRate?.................................................... 111
31 Pull out Yourself of the Swamp by Your Own Hair. The
BootstrappingMethod..................................................... 115
Literature..................................................................... 118
32 NoRisk,NoFun!RiskIndicatorsofFixed-IncomeSecurities........ 119
33 SleepWellDespiteTurbulent Markets?The Immunization
PropertyoftheDuration................................................... 125
34 RisingLikeaPhoenixfromtheAshes.NewShine
forYourDepot?............................................................. 129
Literature..................................................................... 132
35 TheCropofStandingCorn.AreSpeculatorsReallyBadPeople?.... 133
Literature..................................................................... 134
36 OrangeJuiceandPorkBellies.ForwardTransactions................. 135
37 Empty Pockets and No Money. About Short Sales and
No-ArbitragePortfolios.................................................... 137
38 Earning Money Without Capital and Risk. Arbitrage
TransactionsandFairPrices.............................................. 141
Literature..................................................................... 145
39 FibonacciandHisRabbits.AFewWordsAbout
TechnicalAnalysis.......................................................... 147
PartIV OnlyRights,NoObligations—Options
40 ATripAroundtheWorld:DifferentTypesofOptions................. 153
Literature..................................................................... 155
41 TwoTriumvirates:FromArbitragetoSpeculation..................... 157
42 NothingIsforFree:TheArbitragePrinciple ........................... 159
43 HowMuchDoIHavetoPayforMyRight?OptionPricing
AccordingtoBlackandScholes........................................... 161
44 ItTakesTwo:OptionPricingintheBinomialModel .................. 165
Literature..................................................................... 172
45 SafeBehindtheHedge:HedgingofStockPositions.................... 173
