Fixed income mathematics analytical and statistical techniques
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| Sprache: | English |
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McGraw-Hill
2006
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| Ausgabe: | 4. ed. |
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| 100 | 1 | |a Fabozzi, Frank J. |d 1948- |e Verfasser |0 (DE-588)129772054 |4 aut | |
| 245 | 1 | 0 | |a Fixed income mathematics |b analytical and statistical techniques |c Frank J. Fabozzi |
| 250 | |a 4. ed. | ||
| 264 | 1 | |a New York [u.a.] |b McGraw-Hill |c 2006 | |
| 300 | |a XIX, 649 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Taux de rendement | |
| 650 | 4 | |a Valeurs mobilières à revenus fixes - Mathématiques | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Fixed-income securities |x Mathematics | |
| 650 | 4 | |a Rate of return | |
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Datensatz im Suchindex
| DE-BY-TUM_call_number | 0102 WIR 175f 2012 A 7573(4) |
|---|---|
| DE-BY-TUM_katkey | 1875914 |
| DE-BY-TUM_location | 01 |
| DE-BY-TUM_media_number | 040071470163 |
| _version_ | 1820881267239944192 |
| adam_text | CONTENTS
Preface
xvii
Acknowledgments
xix
Chapter
1
Introduction
1
Overview of the Book
2
Chapter
2
Overview of Fixed Income Securities and Derivatives
5
General Features of Bonds
5
Bonds
7
Securitized Products
10
Preferred Stock
13
Interest-Rate Derivatives
14
Credit Derivatives
19
Summary
19
PARTI
TIME VALUE OF MONEY
Chapter
3
Future Value
23
Future Value of an Investment
23
Future Value of an Ordinary Annuity
28
Summary
34
Chapter
4
Present Value
37
Present Value of a Single Amount to Be Received in the Future
37
Present Value for a Fractional Period
40
Properties of Present Value
41
Present Value of a Series of Future Values
41
Present Value of an Ordinary Annuity
43
Present Value When the Frequency Is More Than Once Per Year
46
Pricing Any Financial Instrument
50
Summary
50
Appendix: Continuous Compounding
52
Chapter
5
Yield (Internal Rate of Return)
53
Computing the Yield on Any Investment
53
Yield Calculation When There Is Only One Cash Flow
58
Annualizing Yields
60
Summary
61
PART
2
BOND PRICING FOR OPTION-FREE BONDS AND
CONVENTIONAL YIELD MEASURES
Chapter
6
The Price of a Bond
65
Determining the Cash Flows
65
Determining the Required Yield
66
Pricing a Bond
66
Relationship between Required Yield and Price at a Given Time
71
Relationships among Coupon Rate, Required Yield, and Price
72
Time Path of a Bond
73
Analysis of Bond Price Changes
76
The Price of a Zero-Coupon Bond
78
Price Quotations
79
Determining the Price When the Settlement Date Falls between
Coupon Periods
80
Price Buyer Pays and Price Quotes
87
Tax Treatment of Original-Issue Discount Coupon
87
Summary
90
Chapter
7
Conventional Yield and Spread Measures for Bonds
93
Current Yield
93
Yield to Maturity
94
Yield to Call
102
Yield to Put
104
Yield to Worst
106
Portfolio Yield
106
Yield Spread Measures
108
Summary 111
Chapter
8
The Yield Curve, Spot Rate Curve, and Forward Rates
115
A Bond is a Package of Zero-Coupon Instruments
115
The Yield Curve
116
The Spot Rate Curve
117
Pricing a Bond
122
Drawback of Traditional Yield Spread Analysis
122
Forward Rates
127
Summary
136
PART3
RETURN ANALYSIS
Chapter
9
Potential Sources of Dollar Return
139
Potential Sources of Dollar Return
139
Conventional Measures and the Three Potential Sources
of a Bond s Dollar Return
140
Computation of the Interest-on-Interest Component of a Bond s
Dollar Return
141
Bond Characteristics That Affect the Importance of the Interest-on-Interest
Component
146
Tax Considerations
149
Summary and Investment Implications
151
Chapter
10
Total Return
155
Another Look at the Drawbacks of the Yield to Maturity and Yield to Call
155
Computing
the
Total
Return for a Bond Held to Maturity
157
Computing the Total Return for a Bond to Be Sold Prior to Maturity
163
Analyzing Callable Bonds With the Total Return
167
After-Tax Total Return to Maturity
171
Scenario Analysis
173
Application to Cheapest to Deliver for Futures Contract
176
Summary and Implications
178
Chapter
11
Measuring Historical Performance
179
Portfolio Period Return
179
Averaging Subperiod Returns
181
Annualizing Returns
186
CFA
Institute Performance Presentation Standards
186
Summary
187
PART
4
PRICE VOLATILITY FOR OPTION-FREE BONDS
Chapter
12
Price Volatility of Properties of Option-Free Bonds
193
A Closer Look at the Price/Yield Relationship for Option-Free Bonds
193
The Price Volatility Characteristics of Option-Free Bonds
196
Characteristics of a Bond That Affect Its Price Volatility
203
Measuring Price Volatility Using the Price Value of a Basis Point
205
Summary
212
Chapter
13
Duration as a Measure of Price Volatility
213
Macaulay Duration
213
Link between Duration and Bond Price Volatility
219
Portfolio Duration
226
Approximating Duration
228
Applications
230
Spread Duration
244
Total Risk
245
Final Note on Duration
245
Summary
246
Chapter
14____________________________________________________
Combining Duration and Convexity to Measure Price Volatility
247
Estimating Price with Duration: A Graphical Depiction
247
Measuring Convexity
249
Percentage Price Change Due to Convexity
252
Percentage Price Change Due to Duration and Convexity
253
Convexity as a Measure of the Change in Dollar Duration
260
Summary of Properties of Convexity
263
Value of Convexity
265
Approximating Convexity: Effective Convexity
268
Summary
269
Chapter
15
Duration and the Yield Curve
271
Duration and
Nonparallel
Yield-Curve Shifts
271
Types of Yield-Curve Shifts and Approaches to Measuring Yield-Curve Risk
274
Key Rate Durations
278
Level, Slope, and Curvature Durations
278
Yield-Curve Reshaping Durations
279
Summary
282
PART
5
ANALYZING BONDS WITH EMBEDDED OPTIONS
Chapter
16
Interest-Rate Models
287
Measuring Changes in Interest Rates
287
Historical Movements in Interest Rates
288
Arbitrage-Free versus Equilibrium Interest-Rate Models
290
One-Factor versus Multifactor Models
291
One-Factor Models: Normal versus
Lognormal 292
Applying the Arbitrage-Free Interest-Rate Model
294
Summary
298
Chapter
17
Call Options: Investment and Price Characteristics
301
What Is an Option?
301
Payoffs from Buying and Selling Options
301
The Intrinsic Value and Time Value of an Option
306
The Option Price
308
Sensitivity of the Theoretical Call Option Price to Changes in Factors
311
Duration of an Option
316
Summary
317
Chapter
18
Valuation and Price Volatility of Bonds with Embedded Options
319
Price/Yield Relationship for a Callable Bond
320
The Components of a Bond with an Embedded Option
321
Traditional Valuation Methodology
322
Lattice Model for Valuing Bonds with Embedded Options
323
Option-Adjusted Spread
340
Price Volatility of Bonds with Embedded Options
341
Summary
344
PART
6
CREDIT RISK
Chapter
19
Credit Risk Concepts and Measures for Corporate Bonds
347
Types of Credit Risk
347
Rating Transition Table
350
Measuring Default Rates
352
Recovery Rate and Loss Given Default
353
Approaches to Credit Risk Modeling
354
Financial Ratios Used in Traditional Credit Analysis
358
PART
7
ANALYZING SECURITIZED PRODUCTS
Chapter
20
Measures Used for Securitized Products
365
Structured Finance Transactions and Securitization
365
Illustration of a Securitization
366
Amortizing versus Nonamortizing Assets
368
Information
Used in the Underwriting Process
368
Description of the Pool of Assets
371
Prepayment Measures
373
Defaults and Delinquencies
376
Summary
378
Appendix A: Description of Pool of Assets for CSFB Manufactured Housing
Pass-Through Certificates, Series 2002-MH3 at the Cut-Off Date
380
Appendix B: Composition of the Receivables Pool for Toyota Auto Receivables
1996-
A
Grantor Trust
$722,335,000 6.30%
Asset Backed Certificates, Class A
387
Appendix C: Composition and Historical Performance of the Sears Portfolio for Sears
Credit Account Master Trust II
392
Chapter
21
Cash Flow Characteristics of Amortizing Loans
397
Residential Fixed-Rate, Level-Payment, Fully Amortizing Mortgage Loans
397
Residential Adjustable-Rate Mortgages
408
Other Loan Types
416
Chapter
22
Cash Flow Characteristics of Mortgage-Backed Securities
421
The Prepayment Option and the Cash Flow
421
Overview of Agency Mortgage-Backed Securities
422
Cash Flow for an Agency CMO and Stripped MBS
447
Cash Flow for Credit-Sensitive MBS
448
Summary
450
Chapter
23
Prepayment Models for Mortgage-Backed Securities
453
Agency Prepayment Models
454
Nonagency MBS Prepayment Models
464
Summary
469
Chapter
24
Basics of MBS Structuring
471
Overview of Structuring
471
Structuring for Agency CMOs
472
Agency Mortgage Strips
490
Credit-Sensitive CMOs
490
Summary
496
Chapter
25
Analysis of Agency Mortgage-Backed Securities
497
Static Cash Flow Model
497
Monte Carlo Simulation Model
504
Market-Based Approaches to Duration Estimation for Agency MBS
511
Total Return
513
General Approach to
AB S
Valuation
516
Summary
518
PART
8
STATISTICAL AND OPTIMIZATION TECHNIQUES
Chapter
26
Basics of Probability Theory and Statistics
523
Basic Concepts in Probability Theory
523
Basic Rules of Probability Theory
525
Random Variable and Probability Distribution
526
Discrete versus Continuous Probability Distribution
528
Describing a Probability Distribution Function
529
Discrete Probability Distributions Used in Credit Risk Modeling
534
Continuous Probability Distributions
537
Two Applications to Risk Measurement
548
Summary
555
Chapter
27
Regression Analysis
557
The Simple Linear Regression Model
557
Multiple Linear Regression Model
569
Nonlinear Regressions
570
Applications of Regression Analysis
572
Summary
575
Chapter
28
Statistical Techniques for Credit Scoring and Risk Factor Identification
577
Statistical Techniques for Credit Scoring Models
577
Principal Component Analysis
581
Summary
587
Chapter
29_________________________________
Tracking Error and Multifactor Risk Models
589
Tracking Error
589
Multifactor Risk Models
594
Summary
600
Chapter
30___________
Simulation
603
Monte Carlo Simulation
604
Steps for Monte Carlo Simulation
605
Illustration of the Steps of Monte Carlo Simulation
610
Application to a Mortgage-Backed Securities Portfolio
615
Summary
620
Chapter
31_________________________________________
Optimization Models
621
Mathematical Programming
621
Types of Mathematical Programming Models
622
Applications
624
Summary
628
Index
629
Armed with this trusted, easy-to-understand
reference, readers will be able to make consis¬
tently profitable investment decisions by utilizing
the very latest analytical tools and techniques for
evaluating fixed income securities. Fixed Income
Mathematics offers detailed coverage of the many
new concepts and methodologies that have been
recently introduced to the fixed income market,
particularly for securitized products and credit risk
management. By utilizing these advanced methods,
readers can maximize the accuracy of the numbers
used in decision-making and minimize risk and
potential loss.
More than
30
accessible chapters cover fun-
damental
and all-new aspects of the constantly
evolving fixed income field, including:
•
Time Value of Money
—
How to compute
future value of an investment, present
value of cash flows, and yield
•
Bond Pricjng for Optktti Free Bonds and
Conventional Yield Measures
—
How value
is determined, conventional yield and
spread measures for bonds, the yield curve,
and the determination of spot rates and
forward rates
•
Return Analysis
—
Potential sources of
monetary return, use of total return, and
techniques for measuring the historical
return for a portfolio
•
Price Volatility for Option-Free
Bonds
—
Price volatility of bonds without
embedded options, two measures of price
volatility, how to calculate convexity, and
measures for quantifying the exposure of
a shift in the yield curve
•
Analyzing Bonds with Embedded
Options
—
Interest rate modeling,
investment and price characteristics of
options, and techniques for valuing bonds
with embedded options
•
Credit Risk
—
Credit risk concepts and
measures for corporate bond and credit
analysis
•
Analyzing Securitized Products
—
Measures used for securitized products,
cash flow characteristics of amortizing
loans and MBS, results of recent
prepayment models, the structuring
process, analysis of agency MBS
•
Statistical and Optimization Techniques
—
Basics of probability theory and statistics,
regression analysis, credit scoring and risk
factor identification, tracking error,
Monte Carlo simulation, optimization
techniques
To deal with the complexity of fixed income
instruments, you must embrace new valuation
methodologies, analytical techniques, and
frameworks for credit risk modeling. Fixed Income
Mathematics arms you with these new tools,
explaining how to implement them and success¬
fully integrate them into existing investment
programs.
|
| any_adam_object | 1 |
| author | Fabozzi, Frank J. 1948- |
| author_GND | (DE-588)129772054 |
| author_facet | Fabozzi, Frank J. 1948- |
| author_role | aut |
| author_sort | Fabozzi, Frank J. 1948- |
| author_variant | f j f fj fjf |
| building | Verbundindex |
| bvnumber | BV022423962 |
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| ctrlnum | (OCoLC)61115518 (DE-599)BVBBV022423962 |
| dewey-full | 332.63/2/0151 332.632042 332.6320151 |
| dewey-hundreds | 300 - Social sciences |
| dewey-ones | 332 - Financial economics |
| dewey-raw | 332.63/2/0151 332.632042 332.6320151 |
| dewey-search | 332.63/2/0151 332.632042 332.6320151 |
| dewey-sort | 3332.63 12 3151 |
| dewey-tens | 330 - Economics |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | 4. ed. |
| format | Book |
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| id | DE-604.BV022423962 |
| illustrated | Illustrated |
| indexdate | 2024-12-23T20:04:24Z |
| institution | BVB |
| isbn | 007146073X 9780071460736 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015632242 |
| oclc_num | 61115518 |
| open_access_boolean | |
| owner | DE-1102 DE-739 DE-384 DE-945 DE-634 DE-188 DE-91G DE-BY-TUM DE-1047 |
| owner_facet | DE-1102 DE-739 DE-384 DE-945 DE-634 DE-188 DE-91G DE-BY-TUM DE-1047 |
| physical | XIX, 649 S. graph. Darst. |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | McGraw-Hill |
| record_format | marc |
| spellingShingle | Fabozzi, Frank J. 1948- Fixed income mathematics analytical and statistical techniques Taux de rendement Valeurs mobilières à revenus fixes - Mathématiques Mathematik Fixed-income securities Mathematics Rate of return Finanzmathematik (DE-588)4017195-4 gnd Kapitalmarkt (DE-588)4029578-3 gnd Finanzanalyse (DE-588)4133000-6 gnd Festverzinsliches Wertpapier (DE-588)4121262-9 gnd Mathematik (DE-588)4037944-9 gnd |
| subject_GND | (DE-588)4017195-4 (DE-588)4029578-3 (DE-588)4133000-6 (DE-588)4121262-9 (DE-588)4037944-9 |
| title | Fixed income mathematics analytical and statistical techniques |
| title_auth | Fixed income mathematics analytical and statistical techniques |
| title_exact_search | Fixed income mathematics analytical and statistical techniques |
| title_full | Fixed income mathematics analytical and statistical techniques Frank J. Fabozzi |
| title_fullStr | Fixed income mathematics analytical and statistical techniques Frank J. Fabozzi |
| title_full_unstemmed | Fixed income mathematics analytical and statistical techniques Frank J. Fabozzi |
| title_short | Fixed income mathematics |
| title_sort | fixed income mathematics analytical and statistical techniques |
| title_sub | analytical and statistical techniques |
| topic | Taux de rendement Valeurs mobilières à revenus fixes - Mathématiques Mathematik Fixed-income securities Mathematics Rate of return Finanzmathematik (DE-588)4017195-4 gnd Kapitalmarkt (DE-588)4029578-3 gnd Finanzanalyse (DE-588)4133000-6 gnd Festverzinsliches Wertpapier (DE-588)4121262-9 gnd Mathematik (DE-588)4037944-9 gnd |
| topic_facet | Taux de rendement Valeurs mobilières à revenus fixes - Mathématiques Mathematik Fixed-income securities Mathematics Rate of return Finanzmathematik Kapitalmarkt Finanzanalyse Festverzinsliches Wertpapier |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015632242&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=015632242&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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