Option prices as probabilities: a new look at generalized Black-Scholes formulae
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2010
|
| Schriftenreihe: | Springer finance
|
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | XXI, 270 S. graph. Darst. |
| ISBN: | 9783642103940 |
Internformat
MARC
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| 100 | 1 | |a Profeta, Christophe |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Option prices as probabilities |b a new look at generalized Black-Scholes formulae |c Christophe Profeta ; Bernard Roynette ; Marc Yor |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2010 | |
| 300 | |a XXI, 270 S. |b graph. Darst. | ||
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Datensatz im Suchindex
| _version_ | 1805093898801905664 |
|---|---|
| adam_text |
2.1.1 HYPOTHESES AND NOTATION 21 CONTENTS 1 READING THE BLACK-SCHOLES
FORMULA IN TERMS OF FIRST AND LAST PASSAGE TIMES 1 1.1 INTRODUCTION AND
NOTATION 1 1.1.1 BASIC NOTATION 1 1.1.2 EXPONENTIAL MARTINGALES AND THE
CAMERON-MARTIN FORMULA . 2 1.1.3 FIRST AND LAST PASSAGE TIMES 2 1.1.4
THE CLASSICAL BLACK-SCHOLES FORMULA 3 1.2 THE BLACK-SCHOLES FORMULA IN
TERMS OF FIRST AND LAST PASSAGE TIMES 5 1.2.1 A NEW EXPRESSION FOR THE
BLACK-SCHOLES FORMULA 5 1.2.2 COMMENTS 6 1.2.3 PROOF OF THEOREM 1.2 7
1.2.4 ON THE AGREEMENT BETWEEN THE CLASSICAL BLACK-SCHOLES FORMULA
(THEOREM 1.1 ) AND OUR RESULT (THEOREM 1.2) 10 1.2.5 A REMARK ON THEOREM
1.2 AND TIME INVERSION 11 1.3 EXTENSION OF THEOREM 1.2 TO AN ARBITRARY
INDEX V 13 1.3.1 STATEMENT OF THE MAIN RESULT 13 1.3.2 SOME COMMENTS ON
THEOREM 1.3 14 1.3.3 A SHORT PROOF OF THEOREM 1.3 15 1.4 ANOTHER
FORMULATION OF THE BLACK-SCHOLES FORMULA 16 1.4.1 STATEMENT OF THE
RESULT 16 1.4.2 FIRST PROOF OF THEOREM 1.4 16 1.4.3 A SECOND PROOF OF
THEOREM 1.4 17 1.5 NOTES AND COMMENTS 19 2 GENERALIZED BLACK-SCHOLES
FORMULAE FOR MARTINGALES, IN TERMS OF LAST PASSAGE TIMES 21 2.1
EXPRESSION OF THE EUROPEAN PUT PRICE IN TERMS OF LAST PASSAGE TIMES 21
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1000035417 DIGITALISIERT
DURCH CONTENTS 2.1.2 EXPRESSION OF N(K,T) IN TERMS OF SF M) 22 2.1.3
PROOF OF THEOREM 2.1 22 2.2 EXPRESSION OF THE EUROPEAN CALL PRICE IN
TERMS OF LAST PASSAGE TIMES 24 2.2.1 HYPOTHESES 24 2.2.2 PRICE OF A
EUROPEAN CALL IN TERMS OF LAST PASSAGE TIMES . 25 2.2.3 PROOF OF
THEOREM 2.2 26 2.3 SOME EXAMPLES OF COMPUTATIONS OF THE LAW OF &% 27 2.4
A MORE GENERAL FORMULA FOR THE COMPUTATION OF THE LAW OF ^ ' . 32 2.4.1
HYPOTHESES 32 2.4.2 DESCRIPTION OF THE LAW OF $4 M) 33 2.4.3 SOME
EXAMPLES OF APPLICATIONS OF THEOREM 2.3 34 2.5 COMPUTATION OF THE LAW OF
EFR IN THE FRAMEWORK OF TRANSIENT DIFFUSIONS 37 2.5.1 GENERAL FRAMEWORK
37 2.5.2 A GENERAL FORMULA FOR THE LAW OF 4 X) 38 2.5.3 CASE WHERE THE
INFINITESIMAL GENERATOR IS GIVEN BY ITS DIFFUSION COEFFICIENT AND ITS
DRIFT 39 2.6 COMPUTATION OF THE PUT ASSOCIATED TO A CADLAG MARTINGALE
WITHOUT POSITIVE JUMPS 41 2.6.1 NOTATION 41 2.6.2 COMPUTATION OF THE PUT
ASSOCIATED TO THE MARTINGALE (M U) ,A 0) 42 2.6.3 COMPUTATION OF THE
LAW OF E^"^ 44 2.6.4 A MORE PROBABILISTIC APPROACH OF PROPOSITION 2.2 45
2.6.5 AN APPLICATION OF PROPOSITION 2.1 TO THE LOCAL TIMES OF THE
MARTINGALE (S T CONTENTS XV 3 REPRESENTATION OF SOME PARTICULAR AZEMA
SUPERMARTINGALES 65 3.1 A GENERAL REPRESENTATION THEOREM 65 3.1.1
INTRODUCTION 65 3.1.2 GENERAL FRAMEWORK 66 3.1.3 STATEMENT OF THE
REPRESENTATION THEOREM 66 3.1.4 APPLICATION OF THE REPRESENTATION
THEOREM 3.1 TO THE SUPERMARTINGALE (P(FR T\& T ) ,T 0), WHEN A/ M =
0 67 3.1.5 A REMARK ON THEOREM 3.2 69 3.2 STUDY OF THE PRE %*- AND POST
^-PROCESSES, WHEN M* = 0 70 3.2.1 ENLARGEMENT OF FILTRATION FORMULAE 70
3.2.2 STUDY OF THE POST ^--PROCESS 71 3.2.3 STUDY OF THE PRE ^-PROCESS
72 3.2.4 SOME PREDICTABLE COMPENSATORS 73 3.2.5 EXPRESSION OF THE AZEMA
SUPERMARTINGALE (P(%* T\&T), T 0) WHEN M, JI 0 76 3.2.6 COMPUTATION
OF THE AZEMA SUPERMARTINGALE 77 3.3 A WIDER FRAMEWORK: THE SKOROKHOD
SUBMARTINGALES 78 3.3.1 INTRODUCTION 78 3.3.2 SKOROKHOD SUBMARTINGALES
79 3.3.3 A COMPARATIVE ANALYSIS OF THE THREE CASES 81 3.3.4 TWO
SITUATIONS WHERE THE MEASURE Q EXISTS 82 3.4 NOTES AND COMMENTS 87 4 AN
INTERESTING FAMILY OF BLACK-SCHOLES PERPETUITIES 89 4.1 INTRODUCTION 89
4.1.1 A FIRST EXAMPLE 89 4.1.2 OTHER PERPETUITIES 90 4.1.3 A FAMILY OF
PERPETUITIES ASSOCIATED TO THE BLACK-SCHOLES FORMUL CONTENTS STUDY OF
LAST PASSAGE TIMES UP TO A FINITE HORIZON 115 5.1 STUDY OF LAST PASSAGE
TIMES UP TO A FINITE HORIZON FOR THE BROWNIAN MOTION WITH DRIFT 115
5.1.1 INTRODUCTION AND NOTATION 115 5.1.2 STATEMENT OF OUR MAIN RESULT
116 5.1.3 AN EXPLICIT EXPRESSION FOR THE LAW OF G^\T) 123 5.2
PAST-FUTURE (SUB)-MARTINGALES 127 5.2.1 DEFINITIONS 127 5.2.2 PROPERTIES
AND CHARACTERIZATION OF PFH-FUNCTIONS 128 5.2.3 TWO CLASSES OF
PFH-FUNCTIONS 131 5.2.4 ANOTHER CHARACTERIZATION OF PFH-FUNCTIONS 131
5.2.5 DESCRIPTION OF EXTREMAL PFH-FUNCTIONS 133 5.3 NOTES AND COMMENTS
141 PUT OPTION AS JOINT DISTRIBUTION FUNCTION IN STRIKE AND MATURITY .
143 6.1 PUT OPTION AS A JOINT DISTRIBUTION FUNCTION AND EXISTENCE OF
PSEUDO-INVERSES 143 6.1.1 INTRODUCTION 143 6.1.2 SEEING N M (K,T) AS A
FUNCTION OF 2 VARIABLES 144 6.1.3 GENERAL PATTERN OF THE PROOF 144 6.1.4
A USEFUL CRITERION 145 6.1.5 OUTLINE OF THE FOLLOWING SECTIONS 145 6.2
THE BLACK-SCHOLES PARADIGM 146 6.2.1 STATEMENT OF THE MAIN RESULT 146
6.2.2 DESCRIPTIONS OF THE PROBABILITY Y 149 6.2.3 AN EXTENSION OF
THEOREM 6.1 155 6.2.4 Y AS A SIGNED MEASURE ONK + XK+ 157 6.3 NOTES AND
COMMENTS 159 EXISTENC CONTENTS 7.4 TWO EXTENSIONS OF BESSEL PROCESSES
WITH INCREASING PSEUDO-INVERSES 192 7.4.1 BESSEL PROCESSES WITH INDEX
V *- AND DRIFT A 0 192 7.4.2 SQUARES OF GENERALIZED ORNSTEIN-UHLENBECK
PROCESSES, ALSO CALLED CIR PROCESSES IN MATHEMATICAL FINANCE 193 7.4.3 A
THIRD EXAMPLE 195 7.5 THEMOREGENERALFAMILY(RI,Y' A) ;A:0,AE[0,L]) 196
7.5.1 SOME USEFUL FORMULAE 196 7.5.2 DEFINITION OF (G^ +E ' V) ,Y
0,V,9 0) AND {T$ V+E ' V \Y 0,U,E 0) 197 7.5.3 EXISTENCE AND
PROPERTIES OF (Y^' A) ; X Y, V 0, A * [0,1]) 199 7.6 NOTES AND
COMMENTS 201 EXISTENCE OF PSEUDO-INVERSES FOR DIFFUSIONS 203 8.1
INTRODUCTION 203 8.2 PSEUDO-INVERSE FOR A BROWNIAN MOTION WITH A CONVEX,
DECREASING, POSITIVE DRIFT 205 8.3 STUDY OF A FAMILY OF K + -VALUED
DIFFUSIONS 210 8.3.1 DEFINITION OF THE OPERATOR T 210 8.3.2 STUDY OF THE
FAMILY (X (OR) CONTENTS A.2.3 COMPUTATIONS OF SEVERAL EXAMPLES OF
FUNCTIONS MI(T) 244 A.3 SOME CONNEXIONS WITH DUPIRE'S FORMULA 246 A.3.1
DUPIRE'S FORMULA (SEE [20, F]) 246 A.3.2 EXTENSION OF DUPIRE'S FORMULA
TO A GENERAL MARTINGALE IN J^ C 246 A.3.3 A FORMULA RELATIVE TO LEVY
PROCESSES WITHOUT POSITIVE JUMPS 248 B BESSEL FUNCTIONS AND BESSEL
PROCESSES 251 B.I BESSEL FUNCTIONS (SEE [46], P. 108-136) 251 B.2
SQUARED BESSEL PROCESSES (SEE [70] CHAPTER XI, OR [26]) 253 B.2.1
DEFINITION OF SQUARED BESSEL PROCESSES 253 B.2.2 BESQ AS A DIFFUSION 254
B.2.3 BROWNIAN LOCAL TIMES AND BESQ PROCESSES 254 B.3 BESSEL PROCESSES
(SEE [70] CHAPTER XI, OR [26]) 255 B.3.1 DEFINITION 255 B.3.2 AN
IMPLICIT REPRESENTATION IN TERMS OF GEOMETRIC BROWNIAN MOTIONS 256
REFERENCES 259 FURTHER READINGS 265 INDEX 269 |
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| dewey-ones | 519 - Probabilities and applied mathematics |
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| discipline | Mathematik Wirtschaftswissenschaften |
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| spelling | Profeta, Christophe Verfasser aut Option prices as probabilities a new look at generalized Black-Scholes formulae Christophe Profeta ; Bernard Roynette ; Marc Yor Berlin [u.a.] Springer 2010 XXI, 270 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer finance Diffusionsprozess (DE-588)4274463-5 gnd rswk-swf Martingal (DE-588)4126466-6 gnd rswk-swf Black-Scholes-Modell (DE-588)4206283-4 gnd rswk-swf Black-Scholes-Modell (DE-588)4206283-4 s Martingal (DE-588)4126466-6 s Diffusionsprozess (DE-588)4274463-5 s b DE-604 Roynette, Bernard Verfasser (DE-588)108971090 aut Yor, Marc 1949-2014 Verfasser (DE-588)120628635 aut Erscheint auch als Online-Ausgabe 978-3-642-10395-7 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3423945&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020195385&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Profeta, Christophe Roynette, Bernard Yor, Marc 1949-2014 Option prices as probabilities a new look at generalized Black-Scholes formulae Diffusionsprozess (DE-588)4274463-5 gnd Martingal (DE-588)4126466-6 gnd Black-Scholes-Modell (DE-588)4206283-4 gnd |
| subject_GND | (DE-588)4274463-5 (DE-588)4126466-6 (DE-588)4206283-4 |
| title | Option prices as probabilities a new look at generalized Black-Scholes formulae |
| title_auth | Option prices as probabilities a new look at generalized Black-Scholes formulae |
| title_exact_search | Option prices as probabilities a new look at generalized Black-Scholes formulae |
| title_full | Option prices as probabilities a new look at generalized Black-Scholes formulae Christophe Profeta ; Bernard Roynette ; Marc Yor |
| title_fullStr | Option prices as probabilities a new look at generalized Black-Scholes formulae Christophe Profeta ; Bernard Roynette ; Marc Yor |
| title_full_unstemmed | Option prices as probabilities a new look at generalized Black-Scholes formulae Christophe Profeta ; Bernard Roynette ; Marc Yor |
| title_short | Option prices as probabilities |
| title_sort | option prices as probabilities a new look at generalized black scholes formulae |
| title_sub | a new look at generalized Black-Scholes formulae |
| topic | Diffusionsprozess (DE-588)4274463-5 gnd Martingal (DE-588)4126466-6 gnd Black-Scholes-Modell (DE-588)4206283-4 gnd |
| topic_facet | Diffusionsprozess Martingal Black-Scholes-Modell |
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