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The Resource Saddlepoint approximation methods in financial engineering, Yue Kuen Kwok, Wendong Zheng

Saddlepoint approximation methods in financial engineering, Yue Kuen Kwok, Wendong Zheng

Label
Saddlepoint approximation methods in financial engineering
Title
Saddlepoint approximation methods in financial engineering
Statement of responsibility
Yue Kuen Kwok, Wendong Zheng
Creator
Contributor
Author
Subject
Language
eng
Summary
This book summarizes recent advances in applying saddlepoint approximation methods to financial engineering. It addresses pricing exotic financial derivatives and calculating risk contributions to Value-at-Risk and Expected Shortfall in credit portfolios under various default correlation models. These standard problems involve the computation of tail probabilities and tail expectations of the corresponding underlying state variables.  The text offers in a single source most of the saddlepoint approximation results in financial engineering, with different sets of ready-to-use approximation formulas. Much of this material may otherwise only be found in original research publications. The exposition and style are made rigorous by providing formal proofs of most of the results. Starting with a presentation of the derivation of a variety of saddlepoint approximation formulas in different contexts, this book will help new researchers to learn the fine technicalities of the topic. It will also be valuable to quantitative analysts in financial institutions who strive for effective valuation of prices of exotic financial derivatives and risk positions of portfolios of risky instruments.  
Member of
Cataloging source
N$T
http://library.link/vocab/creatorDate
1957-
http://library.link/vocab/creatorName
Kwok, Y. K.
Dewey number
512.7/3
Illustrations
illustrations
Index
index present
LC call number
QA221
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
http://library.link/vocab/relatedWorkOrContributorName
Zheng, Wendong
Series statement
SpringerBriefs in quantitative finance,
http://library.link/vocab/subjectName
  • Method of steepest descent (Numerical analysis)
  • Financial engineering
  • Mathematics
  • Quantitative Finance
Label
Saddlepoint approximation methods in financial engineering, Yue Kuen Kwok, Wendong Zheng
Instantiates
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • Intro; Preface; Objectives and Audience; Guide to the Chapters; Acknowledgements; Contents; 1 Cumulant Generating Functions and Steepest Descent Method; 1.1 Characteristic Functions and Cumulant Generating Functions; 1.1.1 Generalized Fourier Transform and Characteristic Functions; 1.1.2 Laplace Transform and Cumulant Generating Functions; 1.2 Steepest Descent Method; 1.2.1 Saddlepoint and Steepest Descent Path; 1.2.2 Asymptotic Expansion of Complex Integrals; 2 Saddlepoint Approximations to Density Functions, Tail Probabilities and Tail Expectations; 2.1 Density Functions
  • 2.1.1 Exponentially Tilted Edgeworth Expansion2.1.2 Extension to the Non-Gaussian Base; 2.2 Tail Probabilities; 2.2.1 Extension to Non-Gaussian Base; 2.2.2 Lattice Variables; 2.3 Tail Expectations; 2.3.1 Change of Measure Approach; 2.3.2 Esscher Exponential Tilting and Edgeworth Expansion; 2.3.3 Laplace Inversion Representation; 3 Extended Saddlepoint Approximation Methods; 3.1 Small Time Expansion; 3.1.1 Pure Diffusion Processes; 3.1.2 Jump-Diffusion Processes; 3.2 Affine Jump-Diffusion Processes; 4 Saddlepoint Approximation Formulas for Pricing Options
  • 4.1 Option Prices as Complementary Probabilities4.1.1 Extension to Stochastic Volatility and Interest Rate; 4.1.2 Non-Gaussian Base; 4.2 VIX Derivatives; 4.2.1 Pricing VIX Futures; 4.2.2 Pricing VIX Options; 4.3 Options on Discrete Realized Variance; 4.3.1 Small Time Approximation; 4.3.2 Sample Calculations; 5 Saddlepoint Approximation for Credit Portfolios; 5.1 Default Correlation Models; 5.1.1 CreditRisk+; 5.1.2 Gaussian Copula Models; 5.2 Risk Measures and Risk Contributions; 5.2.1 Value-at-Risk and Expected Shortfall; 5.2.2 Risk Contributions
  • 5.2.3 Risk Measures Calculations for Default Correlation Models5.3 Pricing of Collateralized Debt Obligations; 5.3.1 Cashflows in Different Tranches; 5.3.2 Fair Spread Rates for Tranches; Appendix References; ; Index
Control code
SPR1023628337
Dimensions
unknown
Extent
1 online resource
File format
unknown
Form of item
online
Isbn
9783319741017
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-3-319-74101-7
Other physical details
illustrations
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
  • on1023628337
  • (OCoLC)1023628337
Label
Saddlepoint approximation methods in financial engineering, Yue Kuen Kwok, Wendong Zheng
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • Intro; Preface; Objectives and Audience; Guide to the Chapters; Acknowledgements; Contents; 1 Cumulant Generating Functions and Steepest Descent Method; 1.1 Characteristic Functions and Cumulant Generating Functions; 1.1.1 Generalized Fourier Transform and Characteristic Functions; 1.1.2 Laplace Transform and Cumulant Generating Functions; 1.2 Steepest Descent Method; 1.2.1 Saddlepoint and Steepest Descent Path; 1.2.2 Asymptotic Expansion of Complex Integrals; 2 Saddlepoint Approximations to Density Functions, Tail Probabilities and Tail Expectations; 2.1 Density Functions
  • 2.1.1 Exponentially Tilted Edgeworth Expansion2.1.2 Extension to the Non-Gaussian Base; 2.2 Tail Probabilities; 2.2.1 Extension to Non-Gaussian Base; 2.2.2 Lattice Variables; 2.3 Tail Expectations; 2.3.1 Change of Measure Approach; 2.3.2 Esscher Exponential Tilting and Edgeworth Expansion; 2.3.3 Laplace Inversion Representation; 3 Extended Saddlepoint Approximation Methods; 3.1 Small Time Expansion; 3.1.1 Pure Diffusion Processes; 3.1.2 Jump-Diffusion Processes; 3.2 Affine Jump-Diffusion Processes; 4 Saddlepoint Approximation Formulas for Pricing Options
  • 4.1 Option Prices as Complementary Probabilities4.1.1 Extension to Stochastic Volatility and Interest Rate; 4.1.2 Non-Gaussian Base; 4.2 VIX Derivatives; 4.2.1 Pricing VIX Futures; 4.2.2 Pricing VIX Options; 4.3 Options on Discrete Realized Variance; 4.3.1 Small Time Approximation; 4.3.2 Sample Calculations; 5 Saddlepoint Approximation for Credit Portfolios; 5.1 Default Correlation Models; 5.1.1 CreditRisk+; 5.1.2 Gaussian Copula Models; 5.2 Risk Measures and Risk Contributions; 5.2.1 Value-at-Risk and Expected Shortfall; 5.2.2 Risk Contributions
  • 5.2.3 Risk Measures Calculations for Default Correlation Models5.3 Pricing of Collateralized Debt Obligations; 5.3.1 Cashflows in Different Tranches; 5.3.2 Fair Spread Rates for Tranches; Appendix References; ; Index
Control code
SPR1023628337
Dimensions
unknown
Extent
1 online resource
File format
unknown
Form of item
online
Isbn
9783319741017
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-3-319-74101-7
Other physical details
illustrations
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
  • on1023628337
  • (OCoLC)1023628337

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