Applications of Lévy processes /edited by Oleg Kudryavtsev, Southern Federal University, Rostov-on-Don, Russia; Rostov Branch of the Russian Customs Academy, Rostov-on-Don, Russia, Antonino Zanette, Department of Economics and Statistics, University of Udine, Udine, Italy.

Contributor(s):

Kudryavtsev, Oleg []

Material type: Text

TextSeries: Mathematics research developmentsDescription: 1 online resourceContent type:

text

Media type:

computer

Carrier type:

online resource

ISBN:

9781536198492

Subject(s):

Lévy processes

Genre/Form:

Electronic Books.

LOC classification:

QA274 .A675 2021

Online resources:

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Available additional physical forms:

Contents:

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

3.3.3. 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

5.1. 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

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

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

Subject: "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"--

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Holdings
Item type	Current library	Collection	Call number	URL	Status	Date due	Barcode
Online Book (LOGIN USING YOUR MY CIU LOGIN AND PASSWORD)	G. Allen Fleece Library ONLINE	Non-fiction	QA274.73 (Browse shelf(Opens below))	Link to resource	Available		on1264730485

Includes bibliographies and index.

"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"--

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

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