Mathematical finance:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Bologna
Societa Editrice Esculapi
September 2015
|
| Edition: | First edition |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 288 Seiten Illustrationen |
| ISBN: | 9788874887811 |
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MARC
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Record in the Search Index
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| adam_text | Contents
Preface 11
1 Main instruments of the Mathematical Finance 13
1.1 Elementary spot financial transactions........................ 13
1.2 Elementary forward financial transactions .................... 15
1.3 The complex spot/forward financial transactions............... 15
1.4 The financial function and its properties..................... 16
2 The Financial Conventions 23
2.1 Simple convention............................................. 25
2.1.1 The accumulation law................................... 25
2.1.2 The discount law........................................ 28
2.1.3 Inverse problems........................................ 30
2.1.4 Equivalent interest rates............................. 30
2.2 Commercial convention....................................... 31
2.2.1 The discount law....................................... 31
2.2.2 The accumulation law ................................... 34
2.2.3 Equivalent discount rates............................. 35
2.2.4 Inverse problems....................................... 35
2.2.5 Rational versus commercial discount..................... 35
2.3 Compound convention: multiple case............................ 36
2.3.1 The accumulation law................................... 37
2.3.2 The discount law........................................ 40
2.3.3 Inverse problems........................................ 42
2.3.4 Equivalent interest rates............................. 42
2.4 Compound convention: not multiple case....................... 46
2.4.1 A comparison between the accumulation laws in compound
convention (not multiple case).......................... 47
2.5 Instantaneous convention...................................... 49
3 Annuities 55
3.1 Classification of annuities . .............................. 55
3.2 General discrete annuities................................... 57
3.3 Periodic annuities........................................... 58
3.4 Continuous annuities........................................ 62
3.5 Perpetual annuities........................................... 63
3.6 Annuities in simple financial convention...................... 64
3.6.1 General discrete annuities.............................. 64
6
3.6.2 Periodic annuities........................................ 65
3.6.3 Periodic and constant annuities........................... 65
3.6.4 Continuous annuities.................................... 66
3.7 Annuities in commercial financial convention.................. 68
3.7.1 General discrete annuities................................ 68
3.7.2 Periodic annuities........................................ 68
3.7.3 Periodic and constant annuities........................... 69
3.7.4 Continuous annuities...................................... 70
3.8 Annuities in compound convention.............................. 72
3.8.1 General discrete annuities................................ 72
3.8.2 Periodic annuities........................................ 72
3.8.3 Periodic and constant annuities.......................... 73
3.8.4 Periodic arithmetic progression annuities................. 78
3.8.5 Periodic geometric progression annuities.................. 81
3.8.6 Periodic and fractional annuities......................... 83
3.8.7 Annuities with multiple period ......................... 86
3.8.8 Periodic and constant annuities in compound-linear conven-
tion .......................................................... 87
3.8.9 Continuous annuities...................................... 91
3.8.10 Perpetuities: constant, arithmetic and geometric progres-
sion payments.................................................. 94
3.9 Annuities in instantaneous convention....................... 96
3.9.1 General discrete annuities.............................. 96
3.9.2 Periodic annuities ..................................... 97
3.9.3 Periodic and constant annuities.......................... 98
3.9.4 Continuous annuities......................................100
3.9.5 Constant perpetuities................................... 102
4 Time-indexes 103
4.1 Arithmetic mean maturity........................................103
4.2 Financial mean maturity or average maturity ..................103
4.2.1 Financial mean maturity in simple convention............105
4.2.2 Financial mean maturity in commercial convention ..... 105
4.2.3 Financial mean maturity in compound convention..........105
4.2.4 Financial mean maturity in instantaneous convention . . . 106
4.3 Duration...................................................... 107
5 Fairness condition for financial transactions 111
5.1 Fairness condition..............................................Ill
6 Sinking Funds 113
6.1 Sinking Funds.................................................113
6.2 Sinking Funds: simple financial convention .....................115
6.2.1 Elementary financial transaction........................ 115
6.2.2 Complex financial transaction: general payments...........115
6.2.3 Complex financial transaction: periodic payments..........115
Mathematical Finance
7
6.2.4 Complex financial transaction: constant and periodic pay-
ments . ........................................... 116
6.3 Sinking Funds: compound financial convention..................124
6.3.1 Elementary financial transaction...................... 124
6.3.2 Complex financial transaction: general payments....... 124
6.3.3 Complex financial transaction: periodic payments........125
6.3.4 Complex financial transaction: periodic and constant pay-
ments ........................................................125
6.3.5 Complex financial transaction: periodic payments that are
variable in arithmetic progression.......................129
6.3.6 Complex financial transaction: periodic payments that are
variable in geometric progression...................... . 135
6.4 Sinking Funds with variable conditions........................141
6.4.1 Variable interest rates: a revaluation logic............142
6.4.2 Variable final goal: an indexation logic................143
7 Unshared loan amortization 147
7.1 Unshared loan amortization: simple financial convention.......152
7.1.1 Single settlement repayment.............................152
7.1.2 Multiple settlement repayments: general weak amortiza-
tion installments...............................................155
7.1.3 Multiple settlement repayments: periodic weak amortiza-
tion installments...............................................156
7.1.4 Multiple settlement repayments: periodic and constant weak
amortization installments............................ 158
7.2 Unshared loan amortization: compound financial convention . . . 161
7.2.1 Single settlement repayment.............................161
7.2.2 Multiple settlement repayments: general weak amortiza-
tion installments .......................................... 163
7.2.3 Several interest repayments and sigle repayment of the prin-
cipal: general case........................................... 167
7.2.4 Several interest repayments and single repayment of the
principal: periodic case............................. 169
7.2.5 Several interest repayments and sigle repayment of the prin-
cipal with collateral funding of the principal: general case . 171
7.2.6 American amortization ..................................174
7.2.7 Strict amortization................................. 177
7.2.8 Cession’s value of rights concerning a loan’s amortization . . 183
7.2.9 Italian amortization ...................................185
7.2.10 French amortization ....................................187
7.2.11 German amortization................................... 189
8 Shared loan amortization 193
8.1 Basic concepts ..............................................193
8.2 Constant number of reimbursed share per period................196
8
8.3 Constant number of reimbursed share per period, constant reim-
bursement price and constant or null bonus (italian case) ...... 197
8.4 Constant net theoretical amortization installments, constant reim-
bursement price and constant or null bonus (french net case).... 198
8.5 Constant gross theoretical amortization installments, constant re-
imbursement price and constant or null bonus (french gross case) . 201
8.6 The effective rate for the group of bondholders................203
8.7 Effective rate for the issuer..................................204
8.8 The cession’s values of the credit.............................206
8.9 The effective rate of a bondholder.............................209
8.10 Survival and death probability of a bond......................212
8.11 The residual life of a bond...................................214
8.11.1 The mean life of a bond.................................214
8.11.2 The median life of a bond ..............................216
8.11.3 The mathematical life of a bond.........................217
8.12 The cession’s values of a bond................................219
8.12.1 The bare ownership of a bond............................219
8.12.2 The usufruct of a bond ................................223
8.12.3 The value of a bond . ..................................229
8.12.4 Achard formula............................................230
9 Bonds* market 233
9.1 The structure of the market.................................... 233
9.2 From prices to rates/yields.................................... 239
9.3 Instantaneous rates..............................................242
9.4 Coupon bonds: fixed and index linked coupons.....................244
9.4.1 Fixed coupon bonds . ...................................244
9.4.2 Index-linked coupon bonds.................................245
9.4.3 Swap contracts ...........................................248
9.5 Immunization: basic principles...................................252
9.6 The time of immunization....................................... 258
9.7 Theorems of immunization: parallel and not-parallel shifts ..... 262
9.8 Theorems of immunization: more complex shifts....................264
9.9 Defaultable bond ................................................265
9.9.1 Credit derivatives........................................266
10 Appendix I: Basic concepts of probability theory 269
10.1 Probability spaces . .........................................269
10.2 Random variables and vectors..................................271
10.2.1 Expectation of a random variable........................274
10.2.2 Independent random variables............................ 275
10.2.3 Gaussian random variables and vectors.....................276
Mathematical Finance
9
11 Appendix II; Methods of approximated calculous 279
11.1 Linear interpolation................................... 279
11.2 Newton-Fourier interpolation............................. . 280
11.3 Iterative method...........................................282
Bibliography 287
|
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| isbn | 9788874887811 |
| language | English |
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| spelling | Romagnoli, Silvia Verfasser aut Mathematical finance Silvia Romagnoli First edition Bologna Societa Editrice Esculapi September 2015 288 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Finanzmathematik (DE-588)4017195-4 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Finanzmathematik (DE-588)4017195-4 s b DE-604 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028362387&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
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| subject_GND | (DE-588)4017195-4 (DE-588)4123623-3 |
| title | Mathematical finance |
| title_auth | Mathematical finance |
| title_exact_search | Mathematical finance |
| title_full | Mathematical finance Silvia Romagnoli |
| title_fullStr | Mathematical finance Silvia Romagnoli |
| title_full_unstemmed | Mathematical finance Silvia Romagnoli |
| title_short | Mathematical finance |
| title_sort | mathematical finance |
| topic | Finanzmathematik (DE-588)4017195-4 gnd |
| topic_facet | Finanzmathematik Lehrbuch |
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