Nonlinear models in mathematical finance : new research trends in option pricing / Matthias Ehrhardt, editor.

Format:

Book

Contributor:

Ehrhardt, Matthias.

Language:

English

Subjects (All):

Options (Finance)--Prices--Mathematical models.

Options (Finance).

Investments--Mathematical models.

Investments.

Physical Description:

1 online resource (374 p.)

Edition:

1st ed.

Place of Publication:

New York : Nova Science Publishers, c2008.

Language Note:

English

Summary:

Contents: Introduction: Option Pricing and Hedging in the Presence of Transaction Costs and Nonlinear Partial Differential Equations; Utility indifference pricing with market incompleteness; Pricing options in illiquid markets: symmetry reductions and exact solutions; Distributional solutions to an integro-differential parabolic problem arising on Financial Mathematics; A semidiscretisation method for solving nonlinear Black-Scholes equations: numerical analysis and computing; Transformation methods for evaluating approximations to the optimal exercise boundary for a linear and nonlinear Black-Scholes equation; Global in space numerical computation for the nonlinear Black-Scholes equation; Fixed domain transformations and Split-Step Finite Difference schemes for Nonlinear Black-Scholes equations for American Options; Pricing Hydroelectric Power Plants with/without Operational Restrictions: a Stochastic Control Approach; Numerical solutions of certain nonlinear models in European options on a distributed computing environment; Calibration problems in option pricing; A semi-discretisation method for solving nonlinear Black-Scholes equations: numerical analysis and computing.

Contents:

Intro

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

2.Modelling the Transaction Costs

3.The Leland's Approach to Option Pricing and Hedging

4.Utility-Based Option Pricing and Hedging

5.Conclusion

UTILITY INDIFFERENCE PRICING WITH MARKET INCOMPLETENESS

2.Utility-Based Pricing and Hedging: The General Set-up

3.Basis Risk Model

4.Partial Information Basis Risk Model

PART II. ANALYTIC SOLUTIONS

PRICING OPTIONS IN ILLIQUID MARKETS: SYMMETRY REDUCTIONS AND EXACT SOLUTIONS

2.Illiquid Markets and Nonlinear Black-Scholes Equations

3.Invariant Solutions for a Nonlinear Black-Scholes Equation

4.Properties of Solutions and Parameter-Sensitivity

References.

DISTRIBUTIONAL SOLUTIONS TO AN INTEGRO-DIFFERENTIAL PARABOLIC PROBLEM ARISING IN FINANCIAL MATHEMATICS

2.Solutions for the Integro-Differential Problem (3)

3.Solutions for the Convolution Problem (8)

PART III. NUMERICAL TREATMENT OF NONLINEARBLACK-SCHOLES EQUATIONS

A SEMIDISCRETIZATION METHOD FOR SOLVING NONLINEAR BLACK-SCHOLES EQUATIONS: NUMERICAL ANALYSIS AND COMPUTING

2.Numerical Schemes Construction

3.Numerical Analysis about Local in Time Models

4.Numerical Analysis about Global in Time Models

TRANSFORMATION METHODS FOR EVALUATING APPROXIMATIONS TO THE OPTIMAL EXERCISE BOUNDARY FOR LINEAR AND NONLINEAR BLACK-SCHOLES EQUATIONS

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

GLOBAL IN SPACE NUMERICAL COMPUTATION FOR THE NONLINEAR BLACK-SCHOLES EQUATION

2.Transaction Costs Model

3.Global in Space Computation

4.Optimal Investment Problem

FIXED DOMAIN TRANSFORMATIONS AND SPLIT-STEP FINITE DIFFERENCE SCHEMES FOR NONLINEAR BLACK-SCHOLES EQUATIONS FOR AMERICAN OPTIONS

2.Volatility Models

3.The Fixed Domain Transformation

4.Numerical Solution

5.Comparison Study

PRICING HYDROELECTRIC POWER PLANTS WITH/WITHOUT OPERATIONAL RESTRICTIONS: A STOCHASTIC CONTROL APPROACH

2.Hydroelectric Power Plant Valuation Problem.

3.Numerical Algorithms

4.Properties of the Numerical Schemes

5.Numerical Results

NUMERICAL SOLUTIONS OF CERTAIN NONLINEAR MODELS IN EUROPEAN OPTIONS ON A DISTRIBUTED COMPUTING ENVIRONMENT

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

PART IV.PARAMETER IDENTIFICATION(INVERSE PROBLEMS)

CALIBRATION PROBLEMS IN OPTION PRICING

2.The Calibration Problem

3.Analysis of the Optimal Control Problem

4.A Sequential Quadratic Programming Algorithm

5.Numerical Experiments

INDEX.

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

1-60876-421-4

OCLC:

844071137