Mathematical finance:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Hoboken [u.a.]
Wiley
2012
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | Incl. bibliogr. references and index |
| Beschreibung: | XVIII, 536 S. graph. Darst. |
| ISBN: | 9780470641842 |
Internformat
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| 100 | 1 | |a Alhabeeb, Musaddak J. |d 1954- |e Verfasser |0 (DE-588)171213726 |4 aut | |
| 245 | 1 | 0 | |a Mathematical finance |c M. J. Alhabeeb |
| 264 | 1 | |a Hoboken [u.a.] |b Wiley |c 2012 | |
| 300 | |a XVIII, 536 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Incl. bibliogr. references and index | ||
| 650 | 0 | 7 | |a Finanzmathematik |0 (DE-588)4017195-4 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1804148559095791616 |
|---|---|
| adam_text | CONTENTS
Preface
xv
UNIT I MATHEMATICAL INTRODUCTION
1
1
Numbers, Exponents, and Logarithms
3
1.1.
Numbers,
3
1.2.
Fractions,
3
1.3.
Decimals,
5
1.4.
Repetends,
6
1.5.
Percentages,
7
1.6.
Base Amount, Percentage Rate, and Percentage Amount,
8
1.7.
Ratios,
9
1.8.
Proportions,
10
1.9.
Aliquots,
10
1.10.
Exponents,
11
1.11.
Laws of Exponents,
11
1.12.
Exponential Function,
12
1.13.
Natural Exponential Function,
13
1.14.
Laws of Natural Exponents,
14
1.15.
Scientific Notation,
15
1.16.
Logarithms,
15
1.17.
Laws of Logarithms,
16
1.18.
Characteristic, Mantissa, and Antilogarithm,
16
1.19.
Logarithmic Function,
18
2
Mathematical Progressions
20
2.1.
Arithmetic Progression,
20
2.2.
Geometric Progression,
23
2.3.
Recursive Progression,
26
2.4.
Infinite Geometric Progression,
28
2.5.
Growth and Decay Curves,
29
2.6.
Growth and Decay Functions with a Natural
Logarithmic Base,
34
viii CONTENTS
3
Statistical Measures
35
3.1.
Basic Combinatorial Rules and Concepts,
35
3.2.
Permutation,
37
3.3.
Combination,
40
3.4.
Probability,
41
3.5.
Mathematical Expectation and Expected Value,
44
3.6.
Variance,
46
3.7.
Standard Deviation,
48
3.8.
Covariance,
49
3.9.
Correlation,
50
3.10.
Normal Distribution,
52
Unit I Summary
54
List of Formulas
55
Exercises for Unit I
60
UNIT II MATHEMATICS OF THE TIME VALUE OF MONEY
63
Introduction
65
1
Simple Interest
67
1.1.
Total Interest,
67
1.2.
Rate of Interest,
67
1.3.
Term of Maturity,
68
1.4.
Current Value,
68
1.5.
Future Value,
69
1.6.
Finding
η
and
r
When the Current and Future Values are
Both Known,
69
1.7.
Simple Discount,
70
1.8.
Calculating the Term in Days,
72
1.9.
Ordinary Interest and Exact Interest,
73
1.10.
Obtaining Ordinary Interest and Exact Interest in Terms of Each
Other,
73
1.11.
Focal Date and Equation of Value,
75
1.12.
Equivalent Time: Finding an Average due Date,
78
1.13.
Partial Payments,
80
1.14.
Finding the Simple Interest Rate by the Dollar-Weighted Method,
81
2
Bank Discount
83
2.1.
Finding FV Using the Discount Formula,
84
2.2.
Finding the Discount Term and the Discount Rate,
84
CONTENTS ix
2.3.
Difference Between a Simple Discount and a
Bank Discount,
85
2.4.
Comparing the Discount Rate to the Interest Rate,
87
2.5.
Discounting a Promissory Note,
88
2.6.
Discounting a Treasury Bill,
90
3
Compound Interest
93
3.1.
The Compounding Formula,
94
3.2.
Finding the Current Value,
97
3.3.
Discount Factor,
98
3.4.
Finding the Rate of Compound Interest,
100
3.5.
Finding the Compounding Term,
100
3.6.
The Rule of
72
and Other Rules,
101
3.7.
Effective Interest Rate,
102
3.8.
Types of Compounding,
104
3.9.
Continuous Compounding,
105
3.10.
Equations of Value for a Compound Interest,
106
3.11.
Equated Time For a Compound Interest,
108
4
Annuities
110
4.1.
Types of Annuities,
110
4.2.
Future Value of an Ordinary Annuity, 111
4.3.
Current Value of an Ordinary Annuity,
114
4.4.
Finding the Payment of an Ordinary Annuity,
116
4.5.
Finding the Term of an Ordinary Annuity,
118
4.6.
Finding the Interest Rate of an Ordinary Annuity,
120
4.7.
Annuity Due: Future and Current Values,
121
4.8.
Finding the Payment of an Annuity Due,
123
4.9.
Finding the Term of an Annuity Due,
124
4.10.
Deferred Annuity,
126
4.11.
Future and Current Values of a Deferred Annuity,
127
4.12.
Perpetuities,
128
Unit II Summary
130
List of Formulas
132
Exercises for Unit II
138
UNIT III MATHEMATICS OF DEBT AND LEASING
145
1
Credit and Loans
147
1.1.
Types of Debt,
147
12.
Dynamics of Interest-Principal Proportions,
148
1.3.
Premature Payoff,
152
χ
CONTENTS
1.4.
Assessing Interest and Structuring Payments,
154
1.5.
Cost of Credit,
158
1.6.
Finance Charge and Average Daily Balance,
160
1.7.
Credit Limit vs. Debt Limit,
162
2
Mortgage Debt
164
2.1.
Analysis of Amortization,
164
2.2.
Effects of Interest Rate, Term, and Down Payment on the
Monthly Payment,
170
2.3.
Graduated Payment Mortgage,
172
2.4.
Mortgage Points and the Effective Rate,
176
2.5.
Assuming a Mortgage Loan,
176
2.6.
Prepayment Penalty on a Mortgage Loan,
177
2.7.
Refinancing a Mortgage Loan,
178
2.8.
Wraparound and Balloon Payment Loans,
180
2.9.
Sinking Funds,
182
2.10.
Comparing Amortization to Sinking Fund Methods,
187
3
Leasing
189
3.1.
For the Lessee,
189
3.2.
For the Lessor,
196
Unit III Summary
198
List of Formulas
199
Exercises for Unit III
202
UNIT
IV
MATHEMATICS OF CAPITAL BUDGETING AND
DEPRECIATION
205
1
Capital Budgeting
207
1.1.
Net Present Value,
207
1.2.
Internal Rate of Return,
210
1.3.
Profitability Index,
212
1.4.
Capitalization and Capitalized Cost,
213
1.5.
Other Capital Budgeting Methods,
216
2
Depreciation and Depletion
219
2.1.
The Straight-Line Method,
220
2.2.
The Fixed-Proportion Method,
223
2.3.
The Sum-of-Digits Method,
226
CONTENTS xi
2.4.
The Amortization Method,
229
2.5.
The Sinking Fund Method,
231
2.6.
Composite Rate and Composite Life,
233
2.7.
Depletion,
235
Unit IV Summary
239
List of Formulas
240
Exercises for Unit IV
243
UNIT V MATHEMATICS OF THE BREAK-EVEN POINT
AND LEVERAGE
247
1
Break-Even Analysis
249
1.1.
Deriving BEQ and
BER,
249
1.2.
BEQ and
BER
Variables,
251
1.3.
Cash Break-Even Technique,
254
1.4.
The Break-even Point and the Target Profit,
256
1.5.
Algebraic Approach to the Break-Even Point,
257
1.6.
The Break-Even Point When Borrowing,
261
1.7.
Dual Break-Even Points,
264
1.8.
Other Applications of the Break-Even Point,
267
1.9.
BEQ and
BER
Sensitivity to their Variables,
272
1.10.
Uses and Limitations of Break-Even Analysis,
272
2
Leverage
274
2.1.
Operating Leverage,
274
2.2.
Operating Leverage, Fixed Cost, and Business Risk,
277
2.3.
Financial Leverage,
278
2.4.
Total or Combined Leverage,
284
Unit V Summary
287
List of Formulas
289
Exercises for Unit V
291
UNIT VI MATHEMATICS OF INVESTMENT
295
1
Stocks
297
1.1.
Buying and Selling Stocks,
298
1.2.
Common Stock Valuation,
300
1.3.
Cost of New Issues of Common Stock,
306
xii CONTENTS
1.4. Stock
Value with Two-Stage Dividend Growth,
307
1.5.
Cost of Stock Through the CAPM,
307
1.6.
Other Methods for Common Stock Valuation,
308
1.7.
Valuation of Preferred Stock,
309
1.8.
Cost of Preferred Stock,
310
2
Bonds
311
2.1.
Bond Valuation,
311
2.2.
Premium and Discount Prices,
315
2.3.
Premium Amortization,
317
2.4.
Discount Accumulation,
319
2.5.
Bond Purchase Price Between Interest Days,
321
2.6.
Estimating the Yield Rate,
324
2.7.
Duration,
328
3
Mutual Funds
330
3.1.
Fund Evaluation,
331
3.2.
Loads,
332
3.3.
Performance Measures,
332
3.4.
The Effect of Systematic Risk
(β),
338
3.5.
Dollar-Cost Averaging,
340
4
Options
341
4.1.
Dynamics of Making Profits With Options,
343
4.2.
Intrinsic Value of Calls and Puts,
344
4.3.
Time Value of Calls and Puts,
347
4.4.
The Delta Ratio,
348
4.5.
Determinants of Option Value,
350
4.6.
Option Valuation,
351
4.7.
Combined Intrinsic Values of Options,
353
5
Cost of Capital and Ratio Analysis
357
5.1.
Before- and After-Tax Cost of Capital,
357
5.2.
Weighted-Average Cost of Capital,
358
5.3.
Ratio Analysis,
359
5.4.
The DuPont Model,
374
5.5.
A Final Word About Ratios,
376
Unit VI Summary
377
List of Formulas
379
Exercises for Unit VI
384
CONTENTS xiii
UNIT
VII
MATHEMATICS OF RETURN AND RISK
387
1
Measuring Return and Risk
389
1.1.
Expected Rate of Return,
389
1.2.
Measuring the Risk,
390
1.3.
Risk Aversion and Risk Premium,
394
1.4.
Return and Risk at the Portfolio Level,
394
1.5.
Markowitz s Two-Asset Portfolio,
405
1.6.
Lending and Borrowing at a Risk-Free Rate of Return,
408
1.7.
Types of Risk,
409
2
The Capital Asset Pricing Model (CAPM)
411
2.1.
The Financial Beta
(β),
411
2.2.
The CAPM Equation,
414
2.3.
The Security Market Line,
416
2.4.
SML Swing by Risk Aversion,
418
Unit
VII
Summary
422
List of Formulas
423
Exercises for Unit
VII
425
UNIT
VIII
MATHEMATICS OF INSURANCE
429
1
Life Annuities
431
1.1.
Mortality Table,
431
1.2.
Commutation Terms,
436
1.3.
Pure Endowment,
438
1.4.
Types of Life Annuities,
439
2
Life Insurance
448
2.1.
Whole Life Insurance Policy,
448
2.2.
Annual Premium: Whole Life Basis,
449
2.3.
Annual Premium:
/η
-Payment Basis,
450
2.4.
Deferred Whole Life Policy,
451
2.5.
Deferred Annual Premium: Whole Life Basis,
452
2.6.
Deferred Annual Premium: m-Payment Basis,
453
2.7.
Term Life Insurance Policy,
454
2.8.
Endowment Insurance Policy,
456
2.9.
Annual Premium for the Endowment Policy,
457
2.10.
Less than Annual Premiums,
458
xiv CONTENTS
2.11.
Natural Premium vs. the Level Premium,
459
2.12.
Reserve and Terminal Reserve Funds,
461
2.13.
Benefits of the Terminal Reserve,
465
2.14.
How Much Life Insurance Should You Buy?,
465
3
Property and Casualty Insurance
470
3.1.
Déductibles
and Co-Insurance,
472
3.2.
Health Care Insurance,
473
3.3.
Policy Limit,
476
Unit
VIII
Summary
477
List of Formulas
478
Exercises for Unit
VIII 482
References
485
Appendix
487
Index
515
An introduction to the mathematical skills needed to
understand finance and make better financial decisions
туїЯ
зјТЗЕшјННДЖ
ЕяИУТпїі
Mati
unders
operations
to large corporations, and to also make better personal financial decisions. Despite
the availability of automated tools to perform financial calculations, the author demon
that a basic grasp of the underlying mathematical formulas and tables is essential to nun
understand finance.
The book begins with an introduction to the most fundamental mathematical concepts,
including numbers, exponents, and logarithms; mathematical progressions; and statistical
measures. Next, the author explores the mathematics of the time value of money through
*
discussion of simple interest, bank discount, compound interest, and annuities. Subseque
chapters explore the mathematical aspects of various financial scenarios, including:
•
Mortgage debt, leasing, and credit and loans
Capital budgeting, depreciation, and depletion
•
Break-even analysis and leverage
-
Investing, with coverage of stocks, bonds, mutual funds, options, cost
of capital, and ratio analysis
Return and risk, along with a discussion of the Capital Asset Pricing
Model (CAPM)
•
Life annuities as well as life, property, and casualty insurance
Throughout the book, numerous examples and exercises present realistic financial sce~~
that aid readers in applying their newfound mathematical skills to devise solution
author does not promote the use of financial calculators and computers, bur rather
readers through problem solving using formulas and tables with little emphasis on
dem
and proofs.
Extensively class-tested to ensure an easy-to-rollow presentation, Mathematical F,
is an excellent book for courses in business, economics, and mathematics of finance at the
upper-undergraduate and graduate levels. The book is also appropriate for consumers and
entrepreneurs who need to build their mathematical skills in order to better
unde
financial problems and make better financial choices.
ML J. ALHABEEB, PhD, is Professor of Economics and Finance at the Univen
Massachusetts Amherst. A recipient of the Academy of Educational Leadership s Outsn
Teaching Award for Innovative and Creative Teaching, Dr. Alhabeeb has been teaching
f
and various courses in economics for more than thirtv vears.
I Visit wiley com/mathematics
WILEY
wilev.com
Alto available
as an e-book
9ll780 f70ll6A1842l
|
| any_adam_object | 1 |
| author | Alhabeeb, Musaddak J. 1954- |
| author_GND | (DE-588)171213726 |
| author_facet | Alhabeeb, Musaddak J. 1954- |
| author_role | aut |
| author_sort | Alhabeeb, Musaddak J. 1954- |
| author_variant | m j a mj mja |
| building | Verbundindex |
| bvnumber | BV039690339 |
| classification_rvk | QP 890 SK 980 |
| ctrlnum | (OCoLC)753309789 (DE-599)BVBBV039690339 |
| dewey-full | 332.015195 |
| dewey-hundreds | 300 - Social sciences |
| dewey-ones | 332 - Financial economics |
| dewey-raw | 332.015195 |
| dewey-search | 332.015195 |
| dewey-sort | 3332.015195 |
| dewey-tens | 330 - Economics |
| discipline | Mathematik Wirtschaftswissenschaften |
| format | Book |
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| id | DE-604.BV039690339 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:09:03Z |
| institution | BVB |
| isbn | 9780470641842 |
| language | English |
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| physical | XVIII, 536 S. graph. Darst. |
| publishDate | 2012 |
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| publisher | Wiley |
| record_format | marc |
| spelling | Alhabeeb, Musaddak J. 1954- Verfasser (DE-588)171213726 aut Mathematical finance M. J. Alhabeeb Hoboken [u.a.] Wiley 2012 XVIII, 536 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Incl. bibliogr. references and index Finanzmathematik (DE-588)4017195-4 gnd rswk-swf Finanzmathematik (DE-588)4017195-4 s DE-604 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024539141&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024539141&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Alhabeeb, Musaddak J. 1954- Mathematical finance Finanzmathematik (DE-588)4017195-4 gnd |
| subject_GND | (DE-588)4017195-4 |
| title | Mathematical finance |
| title_auth | Mathematical finance |
| title_exact_search | Mathematical finance |
| title_full | Mathematical finance M. J. Alhabeeb |
| title_fullStr | Mathematical finance M. J. Alhabeeb |
| title_full_unstemmed | Mathematical finance M. J. Alhabeeb |
| title_short | Mathematical finance |
| title_sort | mathematical finance |
| topic | Finanzmathematik (DE-588)4017195-4 gnd |
| topic_facet | Finanzmathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024539141&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024539141&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT alhabeebmusaddakj mathematicalfinance |