The Numerical Solution Of The American Option Pricing Problem
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Numerical Solution Of The American Option Pricing Problem The Finite Difference And Transform Approaches
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Author : Carl Chiarella
language : en
Publisher: World Scientific
Release Date : 2014-10-14
Numerical Solution Of The American Option Pricing Problem The Finite Difference And Transform Approaches written by Carl Chiarella and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-14 with Business & Economics categories.
The early exercise opportunity of an American option makes it challenging to price and an array of approaches have been proposed in the vast literature on this topic. In The Numerical Solution of the American Option Pricing Problem, Carl Chiarella, Boda Kang and Gunter Meyer focus on two numerical approaches that have proved useful for finding all prices, hedge ratios and early exercise boundaries of an American option. One is a finite difference approach which is based on the numerical solution of the partial differential equations with the free boundary problem arising in American option pricing, including the method of lines, the component wise splitting and the finite difference with PSOR. The other approach is the integral transform approach which includes Fourier or Fourier Cosine transforms. Written in a concise and systematic manner, Chiarella, Kang and Meyer explain and demonstrate the advantages and limitations of each of them based on their and their co-workers' experiences with these approaches over the years.
Fractional Calculus
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Author : Dumitru Baleanu
language : en
Publisher: World Scientific
Release Date : 2012
Fractional Calculus written by Dumitru Baleanu and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.
This title will give readers the possibility of finding very important mathematical tools for working with fractional models and solving fractional differential equations, such as a generalization of Stirling numbers in the framework of fractional calculus and a set of efficient numerical methods.
Time Discrete Method Of Lines For Options And Bonds The A Pde Approach
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Author : Gunter H Meyer
language : en
Publisher: World Scientific
Release Date : 2014-11-27
Time Discrete Method Of Lines For Options And Bonds The A Pde Approach written by Gunter H Meyer and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-27 with Business & Economics categories.
Few financial mathematical books have discussed mathematically acceptable boundary conditions for the degenerate diffusion equations in finance. In The Time-Discrete Method of Lines for Options and Bonds, Gunter H Meyer examines PDE models for financial derivatives and shows where the Fichera theory requires the pricing equation at degenerate boundary points, and what modifications of it lead to acceptable tangential boundary conditions at non-degenerate points on computational boundaries when no financial data are available.Extensive numerical simulations are carried out with the method of lines to examine the influence of the finite computational domain and of the chosen boundary conditions on option and bond prices in one and two dimensions, reflecting multiple assets, stochastic volatility, jump diffusion and uncertain parameters. Special emphasis is given to early exercise boundaries, prices and their derivatives near expiration. Detailed graphs and tables are included which may serve as benchmark data for solutions found with competing numerical methods.
Mathematical Modeling And Methods Of Option Pricing
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Author : Lishang Jiang
language : en
Publisher: World Scientific Publishing Company
Release Date : 2005-07-18
Mathematical Modeling And Methods Of Option Pricing written by Lishang Jiang and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-07-18 with Business & Economics categories.
From the unique perspective of partial differential equations (PDE), this self-contained book presents a systematic, advanced introduction to the Black-Scholes-Merton's option pricing theory.A unified approach is used to model various types of option pricing as PDE problems, to derive pricing formulas as their solutions, and to design efficient algorithms from the numerical calculation of PDEs. In particular, the qualitative and quantitative analysis of American option pricing is treated based on free boundary problems, and the implied volatility as an inverse problem is solved in the optimal control framework of parabolic equations.
Computational Methods For Option Pricing
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Author : Yves Achdou
language : en
Publisher: SIAM
Release Date : 2005-07-18
Computational Methods For Option Pricing written by Yves Achdou and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-07-18 with Technology & Engineering categories.
This book allows you to understand fully the modern tools of numerical analysis in finance.
Option Pricing And Estimation Of Financial Models With R
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Author : Stefano M. Iacus
language : en
Publisher: John Wiley & Sons
Release Date : 2011-02-23
Option Pricing And Estimation Of Financial Models With R written by Stefano M. Iacus and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-02-23 with Business & Economics categories.
Presents inference and simulation of stochastic process in the field of model calibration for financial times series modelled by continuous time processes and numerical option pricing. Introduces the bases of probability theory and goes on to explain how to model financial times series with continuous models, how to calibrate them from discrete data and further covers option pricing with one or more underlying assets based on these models. Analysis and implementation of models goes beyond the standard Black and Scholes framework and includes Markov switching models, Lévy models and other models with jumps (e.g. the telegraph process); Topics other than option pricing include: volatility and covariation estimation, change point analysis, asymptotic expansion and classification of financial time series from a statistical viewpoint. The book features problems with solutions and examples. All the examples and R code are available as an additional R package, therefore all the examples can be reproduced.
Numerical Methods And Optimization In Finance
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Author : Manfred Gilli
language : en
Publisher: Academic Press
Release Date : 2019-08-16
Numerical Methods And Optimization In Finance written by Manfred Gilli and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-08-16 with Business & Economics categories.
Computationally-intensive tools play an increasingly important role in financial decisions. Many financial problems-ranging from asset allocation to risk management and from option pricing to model calibration-can be efficiently handled using modern computational techniques. Numerical Methods and Optimization in Finance presents such computational techniques, with an emphasis on simulation and optimization, particularly so-called heuristics. This book treats quantitative analysis as an essentially computational discipline in which applications are put into software form and tested empirically. This revised edition includes two new chapters, a self-contained tutorial on implementing and using heuristics, and an explanation of software used for testing portfolio-selection models. Postgraduate students, researchers in programs on quantitative and computational finance, and practitioners in banks and other financial companies can benefit from this second edition of Numerical Methods and Optimization in Finance.
The Fitted Finite Volume And Power Penalty Methods For Option Pricing
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Author : Song Wang
language : en
Publisher: Springer Nature
Release Date : 2020-10-27
The Fitted Finite Volume And Power Penalty Methods For Option Pricing written by Song Wang and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-27 with Mathematics categories.
This book contains mostly the author’s up-to-date research results in the area. Option pricing has attracted much attention in the past decade from applied mathematicians, statisticians, practitioners and educators. Many partial differential equation-based theoretical models have been developed for valuing various options. These models do not have any practical use unless their solutions can be found. However, most of these models are far too complex to solve analytically and numerical approximations have to be sought in practice. The contents of the book consist of three parts: (i) basic theory of stochastic control and formulation of various option pricing models, (ii) design of finite volume, finite difference and penalty-based algorithms for solving the models and (iii) stability and convergence analysis of the algorithms. It also contains extensive numerical experiments demonstrating how these algorithms perform for practical problems. The theoretical and numerical results demonstrate these algorithms provide efficient, accurate and easy-to-implement numerical tools for financial engineers to price options. This book is appealing to researchers in financial engineering, optimal control and operations research. Financial engineers and practitioners will also find the book helpful in practice.
Computational Science Iccs 2002
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Author : Peter M.A. Sloot
language : en
Publisher: Springer Science & Business Media
Release Date : 2002-04-12
Computational Science Iccs 2002 written by Peter M.A. Sloot and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-04-12 with Computers categories.
Computational Science is the scienti?c discipline that aims at the development and understanding of new computational methods and techniques to model and simulate complex systems. The area of application includes natural systems – such as biology, envir- mental and geo-sciences, physics, and chemistry – and synthetic systems such as electronics and ?nancial and economic systems. The discipline is a bridge b- ween ‘classical’ computer science – logic, complexity, architecture, algorithms – mathematics, and the use of computers in the aforementioned areas. The relevance for society stems from the numerous challenges that exist in the various science and engineering disciplines, which can be tackled by advances made in this ?eld. For instance new models and methods to study environmental issues like the quality of air, water, and soil, and weather and climate predictions through simulations, as well as the simulation-supported development of cars, airplanes, and medical and transport systems etc. Paraphrasing R. Kenway (R.D. Kenway, Contemporary Physics. 1994): ‘There is an important message to scientists, politicians, and industrialists: in the future science, the best industrial design and manufacture, the greatest medical progress, and the most accurate environmental monitoring and forecasting will be done by countries that most rapidly exploit the full potential ofcomputational science’. Nowadays we have access to high-end computer architectures and a large range of computing environments, mainly as a consequence of the enormous s- mulus from the various international programs on advanced computing, e.g.
Mathematical Modeling And Methods Of Option Pricing
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Author : Lishang Jiang
language : en
Publisher: World Scientific
Release Date : 2005
Mathematical Modeling And Methods Of Option Pricing written by Lishang Jiang and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Science categories.
From the perspective of partial differential equations (PDE), this book introduces the Black-Scholes-Merton's option pricing theory. A unified approach is used to model various types of option pricing as PDE problems, to derive pricing formulas as their solutions, and to design efficient algorithms from the numerical calculation of PDEs.