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Nonlinear Models in Mathematical Finance : New Research Trends in Option Pricing.

By: Material type: TextTextPublisher: New York : Nova Science Publishers, Incorporated, 2008Copyright date: ©2008Edition: 1st edDescription: 1 online resource (374 pages)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9781608764211
Subject(s): Genre/Form: Additional physical formats: Print version:: Nonlinear Models in Mathematical FinanceDDC classification:
  • 332.64/53
LOC classification:
  • HG6024.A3 -- N66 2008eb
Online resources:
Contents:
Intro -- NONLINEAR MODELSIN MATHEMATICAL FINANCE:NEW RESEARCH TRENDSIN OPTION PRICING -- NONLINEAR MODELSIN MATHEMATICAL FINANCE:NEW RESEARCH TRENDSIN OPTION PRICING -- CONTENTS -- PREFACE NONLINEAR MODELS IN OPTION PRICING -- ABSTRACT -- INTRODUCTION -- PART I: NONLINEAR BLACK-SCHOLES MODELS -- PART II: ANALYTIC SOLUTIONS -- PART III: NUMERICAL TREATMENT OF NONLINEAR BLACK-SCHOLES EQUATIONS -- PART IV: PARAMETER IDENTIFICATION (INVERSE PROBLEMS) -- NONLINEAR MODELS IN OPTION PRICING - AN INTRODUCTION -- Abstract -- 1.Introduction -- 2.Financial Derivatives -- 3.Linear Black-Scholes Equations -- 4.Nonlinear Black-Scholes Equations -- 5.Terminal and Boundary Conditions -- 6.Volatility Models -- Conclusion -- Acknowledgements -- Appendix -- A.Stochastics -- B.Pricing Formulae -- References -- PART I. NONLINEAR BLACK-SCHOLES MODELS -- OPTION PRICING AND HEDGING IN THE PRESENCE OF TRANSACTION COSTS AND NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS -- Abstract -- 1.Introduction -- 2.Modelling the Transaction Costs -- 3.The Leland's Approach to Option Pricing and Hedging -- 4.Utility-Based Option Pricing and Hedging -- 5.Conclusion -- Acknowledgements -- References -- UTILITY INDIFFERENCE PRICING WITH MARKET INCOMPLETENESS -- Abstract -- 1.Introduction -- 2.Utility-Based Pricing and Hedging: The General Set-up -- 3.Basis Risk Model -- 4.Partial Information Basis Risk Model -- Conclusion -- Acknowledgements -- References -- PART II. ANALYTIC SOLUTIONS -- PRICING OPTIONS IN ILLIQUID MARKETS: SYMMETRY REDUCTIONS AND EXACT SOLUTIONS -- Abstract -- 1.Introduction -- 2.Illiquid Markets and Nonlinear Black-Scholes Equations -- 3.Invariant Solutions for a Nonlinear Black-Scholes Equation -- 4.Properties of Solutions and Parameter-Sensitivity -- Conclusion -- Acknowledgements -- References.
DISTRIBUTIONAL SOLUTIONS TO AN INTEGRO-DIFFERENTIAL PARABOLIC PROBLEM ARISING IN FINANCIAL MATHEMATICS -- Abstract -- 1.Introduction -- 2.Solutions for the Integro-Differential Problem (3) -- 3.Solutions for the Convolution Problem (8) -- Acknowledgements -- References -- PART III. NUMERICAL TREATMENT OF NONLINEARBLACK-SCHOLES EQUATIONS -- A SEMIDISCRETIZATION METHOD FOR SOLVING NONLINEAR BLACK-SCHOLES EQUATIONS: NUMERICAL ANALYSIS AND COMPUTING -- Abstract -- 1.Introduction -- 2.Numerical Schemes Construction -- 3.Numerical Analysis about Local in Time Models -- 4.Numerical Analysis about Global in Time Models -- Conclusion -- Acknowledgements -- References -- TRANSFORMATION METHODS FOR EVALUATING APPROXIMATIONS TO THE OPTIMAL EXERCISE BOUNDARY FOR LINEAR AND NONLINEAR BLACK-SCHOLES EQUATIONS -- Abstract -- 1.Introduction -- 2.Risk Adjusted Methodology Model -- 3.Transformation Method for a Linear Black-Scholes Equa-tion -- 4.Transformation Method for a Nonlinear Black-Scholes Equation -- 5.Transformation Methods for Asian Call Options -- Conclusion -- Acknowledgements -- References -- GLOBAL IN SPACE NUMERICAL COMPUTATION FOR THE NONLINEAR BLACK-SCHOLES EQUATION -- Abstract -- 1.Introduction -- 2.Transaction Costs Model -- 3.Global in Space Computation -- 4.Optimal Investment Problem -- Conclusion -- Acknowledgements -- References -- FIXED DOMAIN TRANSFORMATIONS AND SPLIT-STEP FINITE DIFFERENCE SCHEMES FOR NONLINEAR BLACK-SCHOLES EQUATIONS FOR AMERICAN OPTIONS -- Abstract -- 1.Introduction -- 2.Volatility Models -- 3.The Fixed Domain Transformation -- 4.Numerical Solution -- 5.Comparison Study -- Conclusion -- Acknowledgements -- Appendix -- References -- PRICING HYDROELECTRIC POWER PLANTS WITH/WITHOUT OPERATIONAL RESTRICTIONS: A STOCHASTIC CONTROL APPROACH -- Abstract -- 1.Introduction -- 2.Hydroelectric Power Plant Valuation Problem.
3.Numerical Algorithms -- 4.Properties of the Numerical Schemes -- 5.Numerical Results -- Conclusion -- Acknowledgements -- References -- NUMERICAL SOLUTIONS OF CERTAIN NONLINEAR MODELS IN EUROPEAN OPTIONS ON A DISTRIBUTED COMPUTING ENVIRONMENT -- Abstract -- 1.Introduction -- 2.The Black-Scholes Equation -- 3.Numerical Solutions of the Black-Scholes Equation with Lin-ear Volatility -- 4.Nonlinear Volatility -- 5.Numerical Solutions of the Black-Scholes Equation with Non-linear Volatility -- 6.The Two Level Time-Domain Algorithm -- 7.Conclusion -- References -- PART IV.PARAMETER IDENTIFICATION(INVERSE PROBLEMS) -- CALIBRATION PROBLEMS IN OPTION PRICING -- Abstract -- 1.Introduction -- 2.The Calibration Problem -- 3.Analysis of the Optimal Control Problem -- 4.A Sequential Quadratic Programming Algorithm -- 5.Numerical Experiments -- Conclusion -- Acknowledgements -- References -- INDEX.
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Intro -- NONLINEAR MODELSIN MATHEMATICAL FINANCE:NEW RESEARCH TRENDSIN OPTION PRICING -- NONLINEAR MODELSIN MATHEMATICAL FINANCE:NEW RESEARCH TRENDSIN OPTION PRICING -- CONTENTS -- PREFACE NONLINEAR MODELS IN OPTION PRICING -- ABSTRACT -- INTRODUCTION -- PART I: NONLINEAR BLACK-SCHOLES MODELS -- PART II: ANALYTIC SOLUTIONS -- PART III: NUMERICAL TREATMENT OF NONLINEAR BLACK-SCHOLES EQUATIONS -- PART IV: PARAMETER IDENTIFICATION (INVERSE PROBLEMS) -- NONLINEAR MODELS IN OPTION PRICING - AN INTRODUCTION -- Abstract -- 1.Introduction -- 2.Financial Derivatives -- 3.Linear Black-Scholes Equations -- 4.Nonlinear Black-Scholes Equations -- 5.Terminal and Boundary Conditions -- 6.Volatility Models -- Conclusion -- Acknowledgements -- Appendix -- A.Stochastics -- B.Pricing Formulae -- References -- PART I. NONLINEAR BLACK-SCHOLES MODELS -- OPTION PRICING AND HEDGING IN THE PRESENCE OF TRANSACTION COSTS AND NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS -- Abstract -- 1.Introduction -- 2.Modelling the Transaction Costs -- 3.The Leland's Approach to Option Pricing and Hedging -- 4.Utility-Based Option Pricing and Hedging -- 5.Conclusion -- Acknowledgements -- References -- UTILITY INDIFFERENCE PRICING WITH MARKET INCOMPLETENESS -- Abstract -- 1.Introduction -- 2.Utility-Based Pricing and Hedging: The General Set-up -- 3.Basis Risk Model -- 4.Partial Information Basis Risk Model -- Conclusion -- Acknowledgements -- References -- PART II. ANALYTIC SOLUTIONS -- PRICING OPTIONS IN ILLIQUID MARKETS: SYMMETRY REDUCTIONS AND EXACT SOLUTIONS -- Abstract -- 1.Introduction -- 2.Illiquid Markets and Nonlinear Black-Scholes Equations -- 3.Invariant Solutions for a Nonlinear Black-Scholes Equation -- 4.Properties of Solutions and Parameter-Sensitivity -- Conclusion -- Acknowledgements -- References.

DISTRIBUTIONAL SOLUTIONS TO AN INTEGRO-DIFFERENTIAL PARABOLIC PROBLEM ARISING IN FINANCIAL MATHEMATICS -- Abstract -- 1.Introduction -- 2.Solutions for the Integro-Differential Problem (3) -- 3.Solutions for the Convolution Problem (8) -- Acknowledgements -- References -- PART III. NUMERICAL TREATMENT OF NONLINEARBLACK-SCHOLES EQUATIONS -- A SEMIDISCRETIZATION METHOD FOR SOLVING NONLINEAR BLACK-SCHOLES EQUATIONS: NUMERICAL ANALYSIS AND COMPUTING -- Abstract -- 1.Introduction -- 2.Numerical Schemes Construction -- 3.Numerical Analysis about Local in Time Models -- 4.Numerical Analysis about Global in Time Models -- Conclusion -- Acknowledgements -- References -- TRANSFORMATION METHODS FOR EVALUATING APPROXIMATIONS TO THE OPTIMAL EXERCISE BOUNDARY FOR LINEAR AND NONLINEAR BLACK-SCHOLES EQUATIONS -- Abstract -- 1.Introduction -- 2.Risk Adjusted Methodology Model -- 3.Transformation Method for a Linear Black-Scholes Equa-tion -- 4.Transformation Method for a Nonlinear Black-Scholes Equation -- 5.Transformation Methods for Asian Call Options -- Conclusion -- Acknowledgements -- References -- GLOBAL IN SPACE NUMERICAL COMPUTATION FOR THE NONLINEAR BLACK-SCHOLES EQUATION -- Abstract -- 1.Introduction -- 2.Transaction Costs Model -- 3.Global in Space Computation -- 4.Optimal Investment Problem -- Conclusion -- Acknowledgements -- References -- FIXED DOMAIN TRANSFORMATIONS AND SPLIT-STEP FINITE DIFFERENCE SCHEMES FOR NONLINEAR BLACK-SCHOLES EQUATIONS FOR AMERICAN OPTIONS -- Abstract -- 1.Introduction -- 2.Volatility Models -- 3.The Fixed Domain Transformation -- 4.Numerical Solution -- 5.Comparison Study -- Conclusion -- Acknowledgements -- Appendix -- References -- PRICING HYDROELECTRIC POWER PLANTS WITH/WITHOUT OPERATIONAL RESTRICTIONS: A STOCHASTIC CONTROL APPROACH -- Abstract -- 1.Introduction -- 2.Hydroelectric Power Plant Valuation Problem.

3.Numerical Algorithms -- 4.Properties of the Numerical Schemes -- 5.Numerical Results -- Conclusion -- Acknowledgements -- References -- NUMERICAL SOLUTIONS OF CERTAIN NONLINEAR MODELS IN EUROPEAN OPTIONS ON A DISTRIBUTED COMPUTING ENVIRONMENT -- Abstract -- 1.Introduction -- 2.The Black-Scholes Equation -- 3.Numerical Solutions of the Black-Scholes Equation with Lin-ear Volatility -- 4.Nonlinear Volatility -- 5.Numerical Solutions of the Black-Scholes Equation with Non-linear Volatility -- 6.The Two Level Time-Domain Algorithm -- 7.Conclusion -- References -- PART IV.PARAMETER IDENTIFICATION(INVERSE PROBLEMS) -- CALIBRATION PROBLEMS IN OPTION PRICING -- Abstract -- 1.Introduction -- 2.The Calibration Problem -- 3.Analysis of the Optimal Control Problem -- 4.A Sequential Quadratic Programming Algorithm -- 5.Numerical Experiments -- Conclusion -- Acknowledgements -- References -- INDEX.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

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