Applications of Lévy processes / Oleg Kudryavtsev and Antonino Zanette, editors.
2021
QA274.73 .A67 2021
Formats
| Format | |
|---|---|
| BibTeX | |
| MARCXML | |
| TextMARC | |
| MARC | |
| DublinCore | |
| EndNote | |
| NLM | |
| RefWorks | |
| RIS |
Linked e-resources
Details
Title
Applications of Lévy processes / Oleg Kudryavtsev and Antonino Zanette, editors.
ISBN
9781536198492 electronic book
1536198498 electronic book
9781536195255 hardcover
1536198498 electronic book
9781536195255 hardcover
Published
New York : Nova Science Publishers, [2021]
Language
English
Description
1 online resource.
Call Number
QA274.73 .A67 2021
System Control No.
(OCoLC)1264730485
Summary
"Lévy processes have found applications in various fields, including physics, chemistry, long-term climate change, telephone communication, and finance. The most famous Lévy process in finance is the Black-Scholes model. This book presents important financial applications of Lévy processes. The Editors consider jump-diffusion and pure non-Gaussian Lévy processes, the multi-dimensional Black-Scholes model, and regime-switching Lévy models. This book is comprised of seven chapters that focus on different approaches to solving applied problems under Lévy processes: Monte Carlo simulations, machine learning, the frame projection method, dynamic programming, the Fourier cosine series expansion, finite difference schemes, and the Wiener-Hopf factorization. Various numerical examples are carefully presented in tables and figures to illustrate the methods designed in the book"-- Provided by publisher.
Bibliography, etc. Note
Includes bibliographical references and index.
Formatted Contents Note
Intro
APPLICATIONS OFLÉVY PROCESSES
APPLICATIONS OFLÉVY PROCESSES
CONTENTS
PREFACE
Chapter 1VARIANCE REDUCTION APPLIED TOMACHINE LEARNING FOR PRICINGBERMUDAN/AMERICAN OPTIONSIN HIGH DIMENSION
Abstract
1. INTRODUCTION
2. AMERICAN OPTIONS IN THE MULTI-DIMENSIONAL BLACK-SCHOLES MODEL
3. MACHINE LEARNING FOR AMERICAN OPTIONSIN THE MULTI-DIMENSIONAL BLACK-SCHOLESMODEL
3.1. Gaussian Process Regression
3.2. Machine Learning Exact Integration for European Options
3.3. Machine Learning Control Variate Algorithm for AmericanOptions
3.3.1. The GPR Monte CarloMethod
3.3.2. The GPR Monte Carlo Control Variate Method
3.3.3. The Control Variate for GPR-Tree and GRP-EI
4. NUMERICAL RESULTS
4.1. Geometric and Arithmetic Basket Put Options
4.2. Call on theMaximum Option
4.3. Variance Reduction
CONCLUSION
REFERENCES
Chapter 2A MACHINE LEARNING APPROACH TOOPTION PRICING UNDER LÉ VY PROCESSES
Abstract
1. INTRODUCTION
1.1. Machine Learning in Finance
advance.1.2.
2. OPTION PRICING
2.1. The Applications in Option Pricing
2.2. Lévy Processes
3. MACHINE LEARNING APPROACH
4. CGMY MODEL CALIBRATION WITH GPR
5. ARTIFICIAL NEURAL NETWORKS
5.1. Feedforward ANN
5.2. Recurrent NN
5.3. Long/Short Term
5.4. Gated Recurrent Units
5.5. Bidirectional Recurrent Neural Networks
5.6. BoltzmannMachines
5.7. Restricted BoltzmannMachines
5.8. Convolutional Networks
6. ACTIVATION FUNCTIONS
6.1. Step Function
6.2. Linear Activation Function
6.3. Sigmoid Activation Function
6.4. Hyperbolic Tangent Activation Function
6.5. Softsign Activation Function
6.6. Basic Rectified Linear Unit (ReLU)The
6.7. Leaky (
6.8. Modified Rectifiers (MELU)Numerous attempts have
6.9. Softplus Activation Function
7. APPLYING A FF ANN TO SOLVE THE MODELCALIBRATION PROBLEM
7.1. Historical Data Preparation
7.2. Synthetic Data
7.3. Training the Network
7.4. Market States ClassificationFinancial markets
8. PRICING OPTIONS IN THE CGMY MODEL VIA AFF ANN
CONCLUSION
ACKNOWLEDGMENT
REFERENCES
Chapter 3ON SWING OPTION PRICINGUNDER LÉ VY PROCESS DYNAMICS
Abstract
1. INTRODUCTION
2. SWING OPTIONS
2.1. Policy Constraints
2.1.1. Volume Penalties
2.1.2. Ramping Constraints
2.2. Cash Flows
2.2.1. The Locally Constrained Case
2.3. Swing Rights and Recovery
3. MODELS FOR THE UNDERLYING
3.1. Exponential Lévy Dynamics
3.2. Mean-Reverting
4. PRICING METHODS
4.1. A Discrete Time Formulation
4.1.1. Value Functions
4.1.2. Optimal Swing Policies
4.2. Trees and Grids
4.3. Monte Carlo
4.4. PROJ Method
4.4.1. Value Functions
4.4.2. Pure Fixed Rights
4.4.3. Numerical Examples: Fixed Rights
4.5. A Continuous Time Formulation
4.5.1. Variational Inequalities
4.6. COSMethod
4.7. PROJ: American Contracts
4.7.1. Algorithm Structure
4.7.2. Numerical Example: Constant Recovery
APPLICATIONS OFLÉVY PROCESSES
APPLICATIONS OFLÉVY PROCESSES
CONTENTS
PREFACE
Chapter 1VARIANCE REDUCTION APPLIED TOMACHINE LEARNING FOR PRICINGBERMUDAN/AMERICAN OPTIONSIN HIGH DIMENSION
Abstract
1. INTRODUCTION
2. AMERICAN OPTIONS IN THE MULTI-DIMENSIONAL BLACK-SCHOLES MODEL
3. MACHINE LEARNING FOR AMERICAN OPTIONSIN THE MULTI-DIMENSIONAL BLACK-SCHOLESMODEL
3.1. Gaussian Process Regression
3.2. Machine Learning Exact Integration for European Options
3.3. Machine Learning Control Variate Algorithm for AmericanOptions
3.3.1. The GPR Monte CarloMethod
3.3.2. The GPR Monte Carlo Control Variate Method
3.3.3. The Control Variate for GPR-Tree and GRP-EI
4. NUMERICAL RESULTS
4.1. Geometric and Arithmetic Basket Put Options
4.2. Call on theMaximum Option
4.3. Variance Reduction
CONCLUSION
REFERENCES
Chapter 2A MACHINE LEARNING APPROACH TOOPTION PRICING UNDER LÉ VY PROCESSES
Abstract
1. INTRODUCTION
1.1. Machine Learning in Finance
advance.1.2.
2. OPTION PRICING
2.1. The Applications in Option Pricing
2.2. Lévy Processes
3. MACHINE LEARNING APPROACH
4. CGMY MODEL CALIBRATION WITH GPR
5. ARTIFICIAL NEURAL NETWORKS
5.1. Feedforward ANN
5.2. Recurrent NN
5.3. Long/Short Term
5.4. Gated Recurrent Units
5.5. Bidirectional Recurrent Neural Networks
5.6. BoltzmannMachines
5.7. Restricted BoltzmannMachines
5.8. Convolutional Networks
6. ACTIVATION FUNCTIONS
6.1. Step Function
6.2. Linear Activation Function
6.3. Sigmoid Activation Function
6.4. Hyperbolic Tangent Activation Function
6.5. Softsign Activation Function
6.6. Basic Rectified Linear Unit (ReLU)The
6.7. Leaky (
6.8. Modified Rectifiers (MELU)Numerous attempts have
6.9. Softplus Activation Function
7. APPLYING A FF ANN TO SOLVE THE MODELCALIBRATION PROBLEM
7.1. Historical Data Preparation
7.2. Synthetic Data
7.3. Training the Network
7.4. Market States ClassificationFinancial markets
8. PRICING OPTIONS IN THE CGMY MODEL VIA AFF ANN
CONCLUSION
ACKNOWLEDGMENT
REFERENCES
Chapter 3ON SWING OPTION PRICINGUNDER LÉ VY PROCESS DYNAMICS
Abstract
1. INTRODUCTION
2. SWING OPTIONS
2.1. Policy Constraints
2.1.1. Volume Penalties
2.1.2. Ramping Constraints
2.2. Cash Flows
2.2.1. The Locally Constrained Case
2.3. Swing Rights and Recovery
3. MODELS FOR THE UNDERLYING
3.1. Exponential Lévy Dynamics
3.2. Mean-Reverting
4. PRICING METHODS
4.1. A Discrete Time Formulation
4.1.1. Value Functions
4.1.2. Optimal Swing Policies
4.2. Trees and Grids
4.3. Monte Carlo
4.4. PROJ Method
4.4.1. Value Functions
4.4.2. Pure Fixed Rights
4.4.3. Numerical Examples: Fixed Rights
4.5. A Continuous Time Formulation
4.5.1. Variational Inequalities
4.6. COSMethod
4.7. PROJ: American Contracts
4.7.1. Algorithm Structure
4.7.2. Numerical Example: Constant Recovery
Source of Description
Description based on online resource; title from digital title page (viewed on October 20, 2021).
Added Author
Series
Mathematics research developments
Available in Other Form
Print version: Applications of Lévy processes New York : Nova Science Publishers, [2021]
Linked Resources
Record Appears in