American-style derivatives: valuation and computation
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton, Fla. [u.a.]
Chapman & Hall /CRC
2006
|
| Series: | Chapman & Hall/CRC financial mathematics series
|
| Subjects: | |
| Online Access: | Table of contents only Publisher description Klappentext Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references (p. 217-228) and index Includes bibliographical references (p. 217-228) and index |
| Physical Description: | 232 S. graph. Darst. 25 cm |
| ISBN: | 9781584885672 158488567X |
Staff View
MARC
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| 264 | 1 | |a Boca Raton, Fla. [u.a.] |b Chapman & Hall /CRC |c 2006 | |
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| 500 | |a Includes bibliographical references (p. 217-228) and index | ||
| 650 | 4 | |a Derivative securities |z United States | |
| 650 | 4 | |a Derivative securities |x Valuation | |
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Record in the Search Index
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|---|---|
| adam_text | While the valuation of standard American option contracts has now
achieved a fair degree of maturity, much work remains to be done regarding
the new contractual forms that are constantly emerging in response to
evolving economic conditions and regulations. Focusing on recent
developments in the field, American-Style Derivatives provides an
extensive treatment of option pricing with an emphasis on the valuation
of American options on dividend-paying assets.
The book begins with a review of valuation principles for European
contingent claims in a financial market in which the underlying asset price
follows an
Ito
process and the interest rate is stochastic and then extends
the analysis to American contingent claims. In this context the author lays
out the basic valuation principles for American claims and describes
instructive representation formulas for their prices. The results are applied
to standard American options in the Black-Scholes market setting as well
as to a variety of exotic contracts such as barrier, capped, and mutiiple
asset options. He also reviews numerical methods for option pricing and
compares their relative performance.
The author explains all the concepts using standard financial terms and
intuitions and relegates proofs to appendices that can be found at the
end of each chapter. The book is written so that the material is easily
accessible not only to those with a background in stochastic processes
and/or derivative securities, but also to those with a more limited exposure
to those areas.
CONTENTS 1 INTRODUCTION . 1 2 EUROPEAN CONTINGENT CLAIMS 7 2.1
DEFINITIONS 7 2.2 THE ECONOMY 8 2.3 ATTAINABLE CONTINGENT CLAIMS 10 2.4
VALUATION OF ATTAINABLE CLAIMS 14 2.5 CLAIMS INVOLVING NEGATIVE PAYOFFS
16 2.6 THE STRUCTURE OF CONTINGENT CLAIMS PRICES 18 2.7 CHANGES OF
NUMERAIRE AND VALUATION 19 2.8 OPTION AND FORWARD CONTRACTS 21 2.9
MARKETS WITH DETERMINISTIC COEFFICIENTS 24 2.10 MARKETS WITH MULTIPLE
ASSETS 28 2.11 APPENDIX: PROOFS 29 3 AMERICAN CONTINGENT CLAIMS 37 3.1
CONTINGENT CLAIMS WITH RANDOM MATURITY 37 3.2 AMERICAN CONTINGENT CLAIMS
39 3.3 EXERCISE PREMIUM REPRESENTATIONS 41 3.4 A DUALITY FORMULA: UPPER
PRICE BOUNDS 44 3.5 AMERICAN OPTIONS AND FORWARD CONTRACTS 45 3.6
MULTIPLE UNDERLYING ASSETS 47 3.7 APPENDIX: PROOFS 48 4 STANDARD
AMERICAN OPTIONS 55 4.1 THE IMMEDIATE EXERCISE REGION 55 4.2 THE CALL
PRICE FUNCTION 57 4.3 EARLY EXERCISE PREMIUM REPRESENTATION 59 4.4 A
ONE-DIMENSIONAL INTEGRAL EQUATION 61 4.5 HEDGING 62 4.6 DIFFUSION
PROCESSES 63 4.7 FLOATING STRIKE ASIAN OPTIONS 67 4.8 AMERICAN FORWARD
CONTRACTS 69 4.9 APPENDIX: PROOFS 71 CONTENTS 5 BARRIER AND CAPPED
OPTIONS 85 5.1 BARRIER OPTIONS 85 5.1.1 DEFINITIONS AND LITERATURE 85
5.1.2 VALUATION 86 5.2 CAPPED OPTIONS 89 5.2.1 DEFINITIONS, EXAMPLES AND
LITERATURE 89 5.2.2 CONSTANT CAP 89 5.2.3 CAPPED OPTIONS WITH GROWING
CAPS 93 5.2.4 STOCHASTIC CAP, INTEREST RATE AND VOLATILITY 96 5.3
DIFFUSION PROCESSES 97 5.4 APPENDIX: PROOFS 98 6 OPTIONS ON MULTIPLE
ASSETS 107 6.1 DEFINITIONS, EXAMPLES AND LITERATURE 107 6.2 THE
FINANCIAL MARKET 109 6.3 CALL OPTIONS ON THE MAXIMUM OF 2 PRICES 109
6.3.1 EXERCISE REGION OF A MAX-CALL OPTION 110 6.3.2 VALUATION OF
MAX-CALL OPTIONS . . 114 6.3.3 DUAL STRIKE MAX-OPTIONS 119 6.3.4 PUT
OPTIONS ON THE MINIMUM OF 2 PRICES 120 6.3.5 ECONOMIC IMPLICATIONS 120
6.4 AMERICAN SPREAD OPTIONS 121 6.4.1 EXERCISE REGION AND VALUATION 121
6.4.2 OPTIONS TO EXCHANGE ONE ASSET FOR ANOTHER 123 6.4.3 EXCHANGE
OPTIONS WITH PROPORTIONAL CAPS 124 6.5 OPTIONS ON AN AVERAGE OF 2 PRICES
125 6.5.1 GEOMETRIC AVERAGING 125 6.5.2 ARITHMETIC AVERAGING 126 6.6
CALL OPTIONS ON THE MINIMUM OF 2 PRICES 129 6.6.1 EXERCISE REGION OF A
MIN-CAIL OPTION 129 6.6.2 THE EEP REPRESENTATION 132 6.6.3 INTEGRAL
EQUATIONS FOR THE BOUNDARY COMPONENTS 135 6.7 APPENDIX A: DERIVATIVES ON
MULTIPLE ASSETS 135 6.8 APPENDIX B: PROOFS 143 7 OCCUPATION TIME
DERIVATIVES 155 7.1 BACKGROUND AND LITERATURE . . . . ; . . . . . .
155 7.2 DEFINITIONS 156 7.3 SYMMETRY PROPERTIES 157 7.4 QUANTILE OPTIONS
158 7.4.1 CONTRACTUAL SPECIFICATION . . ** 158 7.4.2 THE DISTRIBUTION OF
AN A-QUANTILE 159 7.4.3 PRICING QUANTILE OPTIONS 159 7.4.4 A REDUCTION
IN DIMENSIONALITY 162 7.4.5 QUANTILE CONTINGENT CLAIMS 163 7.5 PARISIAN
OPTIONS 163 CONTENTS 7.5.1 CONTRACTUAL SPECIFICATION 164 7.5.2 PARITY
AND SYMMETRY RELATIONS 165 7.5.3 PRICING PARISIAN OPTIONS 166 7.5.4
PARISIAN CONTINGENT CLAIMS 169 7.6 CUMULATIVE PARISIAN CONTINGENT CLAIMS
170 7.6.1 DEFINITIONS AND PARITY/SYMMETRY RELATIONS 170 7.6.2 PRICING
CUMULATIVE BARRIER CLAIMS 171 7.6.3 STANDARD AND EXOTIC CUMULATIVE
BARRIER OPTIONS 172 7.7 STEP OPTIONS 173 7.7.1 CONTRACTUAL SPECIFICATION
173 7.7.2 PRICING EUROPEAN-STYLE STEP OPTIONS 174 7.8 AMERICAN
OCCUPATION TIME DERIVATIVES 175 7.8.1 EARLY EXERCISE PREMIUM
REPRESENTATION 175 7.8.2 VALUATION IN THE STANDARD MODEL 176 7.9
MULTIASSET CLAIMS 179 7.9.1 SYMMETRY PROPERTIES 179 7.9.2 VALUATION 181
7.10 APPENDIX: PROOFS 181 8 NUMERICAL METHODS 195 8.1 NUMERICAL METHODS
FOR AMERICAN OPTIONS 195 8.2 INTEGRAL EQUATION METHODS 197 8.3 EXERCISE
TIME APPROXIMATIONS: LBA-LUBA 199 8.3.1 A LOWER BOUND FOR THE OPTION
PRICE 199 8.3.2 A LOWER BOUND FOR THE EXERCISE BOUNDARY 200 8.3.3 AN
UPPER BOUND FOR THE OPTION PRICE 201 8.3.4 PRICE APPROXIMATIONS 202 8.4
DIFFUSION PROCESSES 202 8.4.1 INTEGRAL EQUATION METHODS 203 8.4.2
STOPPING TIME APPROXIMATIONS: LBA AND LUBA 203 8.5 OTHER RECENT
APPROACHES 204 8.5.1 LATTICE METHODS: BINOMIAL BLACK-SCHOLES ALGORITHM .
. . 204 8.5.2 INTEGRAL EQUATION: NON-LINEAR APPROXIMATIONS 204 8.5.3
MONTE CARLO SIMULATION 205 8.6 PERFORMANCE EVALUATION 205 8.6.1
EXPERIMENT DESIGN 206 8.6.2 RESULTS AND DISCUSSION 206 8.7 METHODS FOR
MULTIASSET OPTIONS 207 8.7.1 LATTICE METHODS 207 8.7.2 MONTE CARLO
SIMULATION 209 8.7.3 MONTE CARLO SIMULATION AND DUALITY 211 8.8 METHODS
FOR OCCUPATION TIME DERIVATIVES 212 8.8.1 LAPLACE TRANSFORMS 212 8.8.2
PDE-BASED METHODS 212 8.8.3 BINOMIAL/TRINOMIAL LATTICES 213 8.9
APPENDIX: PROOFS 215 CONTENTS BIBLIOGRAPHY 217 INDEX 229
|
| adam_txt |
While the valuation of standard American option contracts has now
achieved a fair degree of maturity, much work remains to be done regarding
the new contractual forms that are constantly emerging in response to
evolving economic conditions and regulations. Focusing on recent
developments in the field, American-Style Derivatives provides an
extensive treatment of option pricing with an emphasis on the valuation
of American options on dividend-paying assets.
The book begins with a review of valuation principles for European
contingent claims in a financial market in which the underlying asset price
follows an
Ito
process and the interest rate is stochastic and then extends
the analysis to American contingent claims. In this context the author lays
out the basic valuation principles for American claims and describes
instructive representation formulas for their prices. The results are applied
to standard American options in the Black-Scholes market setting as well
as to a variety of exotic contracts such as barrier, capped, and mutiiple
asset options. He also reviews numerical methods for option pricing and
compares their relative performance.
The author explains all the concepts using standard financial terms and
intuitions and relegates proofs to appendices that can be found at the
end of each chapter. The book is written so that the material is easily
accessible not only to those with a background in stochastic processes
and/or derivative securities, but also to those with a more limited exposure
to those areas.
CONTENTS 1 INTRODUCTION . 1 2 EUROPEAN CONTINGENT CLAIMS 7 2.1
DEFINITIONS 7 2.2 THE ECONOMY 8 2.3 ATTAINABLE CONTINGENT CLAIMS 10 2.4
VALUATION OF ATTAINABLE CLAIMS 14 2.5 CLAIMS INVOLVING NEGATIVE PAYOFFS
16 2.6 THE STRUCTURE OF CONTINGENT CLAIMS'PRICES 18 2.7 CHANGES OF
NUMERAIRE AND VALUATION 19 2.8 OPTION AND FORWARD CONTRACTS 21 2.9
MARKETS WITH DETERMINISTIC COEFFICIENTS 24 2.10 MARKETS WITH MULTIPLE
ASSETS 28 2.11 APPENDIX: PROOFS 29 3 AMERICAN CONTINGENT CLAIMS 37 3.1
CONTINGENT CLAIMS WITH RANDOM MATURITY 37 3.2 AMERICAN CONTINGENT CLAIMS
39 3.3 EXERCISE PREMIUM REPRESENTATIONS 41 3.4 A DUALITY FORMULA: UPPER
PRICE BOUNDS 44 3.5 AMERICAN OPTIONS AND FORWARD CONTRACTS 45 3.6
MULTIPLE UNDERLYING ASSETS 47 3.7 APPENDIX: PROOFS 48 4 STANDARD
AMERICAN OPTIONS 55 4.1 THE IMMEDIATE EXERCISE REGION 55 4.2 THE CALL
PRICE FUNCTION 57 4.3 EARLY EXERCISE PREMIUM REPRESENTATION 59 4.4 A
ONE-DIMENSIONAL INTEGRAL EQUATION 61 4.5 HEDGING 62 4.6 DIFFUSION
PROCESSES 63 4.7 FLOATING STRIKE ASIAN OPTIONS 67 4.8 AMERICAN FORWARD
CONTRACTS 69 4.9 APPENDIX: PROOFS 71 CONTENTS 5 BARRIER AND CAPPED
OPTIONS 85 5.1 BARRIER OPTIONS 85 5.1.1 DEFINITIONS AND LITERATURE 85
5.1.2 VALUATION 86 5.2 CAPPED OPTIONS 89 5.2.1 DEFINITIONS, EXAMPLES AND
LITERATURE 89 5.2.2 CONSTANT CAP 89 5.2.3 CAPPED OPTIONS WITH GROWING
CAPS 93 5.2.4 STOCHASTIC CAP, INTEREST RATE AND VOLATILITY 96 5.3
DIFFUSION PROCESSES 97 5.4 APPENDIX: PROOFS 98 6 OPTIONS ON MULTIPLE
ASSETS 107 6.1 DEFINITIONS, EXAMPLES AND LITERATURE 107 6.2 THE
FINANCIAL MARKET 109 6.3 CALL OPTIONS ON THE MAXIMUM OF 2 PRICES 109
6.3.1 EXERCISE REGION OF A MAX-CALL OPTION 110 6.3.2 VALUATION OF
MAX-CALL OPTIONS . . 114 6.3.3 DUAL STRIKE MAX-OPTIONS 119 6.3.4 PUT
OPTIONS ON THE MINIMUM OF 2 PRICES 120 6.3.5 ECONOMIC IMPLICATIONS 120
6.4 AMERICAN SPREAD OPTIONS 121 6.4.1 EXERCISE REGION AND VALUATION 121
6.4.2 OPTIONS TO EXCHANGE ONE ASSET FOR ANOTHER 123 6.4.3 EXCHANGE
OPTIONS WITH PROPORTIONAL CAPS 124 6.5 OPTIONS ON AN AVERAGE OF 2 PRICES
125 6.5.1 GEOMETRIC AVERAGING 125 6.5.2 ARITHMETIC AVERAGING 126 6.6
CALL OPTIONS ON THE MINIMUM OF 2 PRICES 129 6.6.1 EXERCISE REGION OF A
MIN-CAIL OPTION 129 6.6.2 THE EEP REPRESENTATION 132 6.6.3 INTEGRAL
EQUATIONS FOR THE BOUNDARY COMPONENTS 135 6.7 APPENDIX A: DERIVATIVES ON
MULTIPLE ASSETS 135 6.8 APPENDIX B: PROOFS 143 7 OCCUPATION TIME
DERIVATIVES 155 7.1 BACKGROUND AND LITERATURE . . . . ; . . . ' . . .
155 7.2 DEFINITIONS 156 7.3 SYMMETRY PROPERTIES 157 7.4 QUANTILE OPTIONS
158 7.4.1 CONTRACTUAL SPECIFICATION . . ** 158 7.4.2 THE DISTRIBUTION OF
AN A-QUANTILE 159 7.4.3 PRICING QUANTILE OPTIONS 159 7.4.4 A REDUCTION
IN DIMENSIONALITY 162 7.4.5 QUANTILE CONTINGENT CLAIMS 163 7.5 PARISIAN
OPTIONS 163 CONTENTS 7.5.1 CONTRACTUAL SPECIFICATION 164 7.5.2 PARITY
AND SYMMETRY RELATIONS 165 7.5.3 PRICING PARISIAN OPTIONS 166 7.5.4
PARISIAN CONTINGENT CLAIMS 169 7.6 CUMULATIVE PARISIAN CONTINGENT CLAIMS
170 7.6.1 DEFINITIONS AND PARITY/SYMMETRY RELATIONS 170 7.6.2 PRICING
CUMULATIVE BARRIER CLAIMS 171 7.6.3 STANDARD AND EXOTIC CUMULATIVE
BARRIER OPTIONS 172 7.7 STEP OPTIONS 173 7.7.1 CONTRACTUAL SPECIFICATION
173 7.7.2 PRICING EUROPEAN-STYLE STEP OPTIONS 174 7.8 AMERICAN
OCCUPATION TIME DERIVATIVES 175 7.8.1 EARLY EXERCISE PREMIUM
REPRESENTATION 175 7.8.2 VALUATION IN THE STANDARD MODEL 176 7.9
MULTIASSET CLAIMS 179 7.9.1 SYMMETRY PROPERTIES 179 7.9.2 VALUATION 181
7.10 APPENDIX: PROOFS 181 8 NUMERICAL METHODS 195 8.1 NUMERICAL METHODS
FOR AMERICAN OPTIONS 195 8.2 INTEGRAL EQUATION METHODS 197 8.3 EXERCISE
TIME APPROXIMATIONS: LBA-LUBA 199 8.3.1 A LOWER BOUND FOR THE OPTION
PRICE 199 8.3.2 A LOWER BOUND FOR THE EXERCISE BOUNDARY 200 8.3.3 AN
UPPER BOUND FOR THE OPTION PRICE 201 8.3.4 PRICE APPROXIMATIONS 202 8.4
DIFFUSION PROCESSES 202 8.4.1 INTEGRAL EQUATION METHODS 203 8.4.2
STOPPING TIME APPROXIMATIONS: LBA AND LUBA 203 8.5 OTHER RECENT
APPROACHES 204 8.5.1 LATTICE METHODS: BINOMIAL BLACK-SCHOLES ALGORITHM .
. . 204 8.5.2 INTEGRAL EQUATION: NON-LINEAR APPROXIMATIONS 204 8.5.3
MONTE CARLO SIMULATION 205 8.6 PERFORMANCE EVALUATION 205 8.6.1
EXPERIMENT DESIGN 206 8.6.2 RESULTS AND DISCUSSION 206 8.7 METHODS FOR
MULTIASSET OPTIONS 207 8.7.1 LATTICE METHODS 207 8.7.2 MONTE CARLO
SIMULATION 209 8.7.3 MONTE CARLO SIMULATION AND DUALITY 211 8.8 METHODS
FOR OCCUPATION TIME DERIVATIVES 212 8.8.1 LAPLACE TRANSFORMS 212 8.8.2
PDE-BASED METHODS 212 8.8.3 BINOMIAL/TRINOMIAL LATTICES 213 8.9
APPENDIX: PROOFS 215 CONTENTS BIBLIOGRAPHY 217 INDEX 229 |
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| geographic | USA |
| geographic_facet | USA |
| id | DE-604.BV023100692 |
| illustrated | Illustrated |
| index_date | 2024-07-02T19:44:37Z |
| indexdate | 2024-07-09T21:11:02Z |
| institution | BVB |
| isbn | 9781584885672 158488567X |
| language | English |
| lccn | 2005052861 |
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| record_format | marc |
| series2 | Chapman & Hall/CRC financial mathematics series |
| spelling | Detemple, Jérôme Verfasser aut American-style derivatives valuation and computation Jérôme Detemple Boca Raton, Fla. [u.a.] Chapman & Hall /CRC 2006 232 S. graph. Darst. 25 cm txt rdacontent n rdamedia nc rdacarrier Chapman & Hall/CRC financial mathematics series Includes bibliographical references (p. 217-228) and index Derivative securities United States Derivative securities Valuation USA http://www.loc.gov/catdir/toc/fy0605/2005052861.html Table of contents only http://www.loc.gov/catdir/enhancements/fy0648/2005052861-d.html Publisher description Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016303420&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Klappentext SWB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016303420&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Detemple, Jérôme American-style derivatives valuation and computation Derivative securities United States Derivative securities Valuation |
| title | American-style derivatives valuation and computation |
| title_auth | American-style derivatives valuation and computation |
| title_exact_search | American-style derivatives valuation and computation |
| title_exact_search_txtP | American-style derivatives valuation and computation |
| title_full | American-style derivatives valuation and computation Jérôme Detemple |
| title_fullStr | American-style derivatives valuation and computation Jérôme Detemple |
| title_full_unstemmed | American-style derivatives valuation and computation Jérôme Detemple |
| title_short | American-style derivatives |
| title_sort | american style derivatives valuation and computation |
| title_sub | valuation and computation |
| topic | Derivative securities United States Derivative securities Valuation |
| topic_facet | Derivative securities United States Derivative securities Valuation USA |
| url | http://www.loc.gov/catdir/toc/fy0605/2005052861.html http://www.loc.gov/catdir/enhancements/fy0648/2005052861-d.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016303420&sequence=000002&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=016303420&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT detemplejerome americanstylederivativesvaluationandcomputation |