Pricing Financial Instruments: The Finite Difference Method

Book Description

Numerical methods for the solution of financial instrument pricing equations are fast becoming essential for practitioners of modern quantitative finance. Among the most promising of these new computational finance techniques is the finite difference method-yet, to date, no single resource has presented a quality, comprehensive overview of this revolutionary quantitative approach to risk management.

Pricing Financial Instruments, researched and written by Domingo Tavella and Curt Randall, two of the chief proponents of the finite difference method, presents a logical framework for applying the method of finite difference to the pricing of financial derivatives. Detailing the algorithmic and numerical procedures that are the foundation of both modern mathematical finance and the creation of financial products-while purposely keeping mathematical complexity to a minimum-this long-awaited book demonstrates how the techniques described can be used to accurately price simple and complex derivative structures.

From a summary of stochastic pricing processes and arbitrage pricing arguments, through the analysis of numerical schemes and the implications of discretization-and ending with case studies that are simple yet detailed enough to demonstrate the capabilities of the methodology- Pricing Financial Instruments explores areas that include:
* Pricing equations and the relationship be-tween European and American derivatives
* Detailed analyses of different stability analysis approaches
* Continuous and discrete sampling models for path dependent options
* One-dimensional and multi-dimensional coordinate transformations
* Numerical examples of barrier options, Asian options, forward swaps, and more

With an emphasis on how numerical solutions work and how the approximations involved affect the accuracy of the solutions, Pricing Financial Instruments takes us through doors opened wide by Black, Scholes, and Merton-and the arbitrage pricing principles they introduced in the early 1970s-to provide a step-by-step outline for sensibly interpreting the output of standard numerical schemes. It covers the understanding and application of today's finite difference method, and takes the reader to the next level of pricing financial instruments and managing financial risk.

Praise for Pricing Financial Instruments

"Pricing Financial Instruments is the first broad and accessible treatment of finite difference methods for pricing derivative securities. The authors have taken great care to clearly explain both the origins of the pricing problems in a financial setting, as well as many practical aspects of their numerical methods. The book covers a wide variety of applications, such as American options and credit derivatives. Both financial analysts and academic asset-pricing specialists will want to own a copy."-Darrell Duffie, Professor of Finance Stanford University

"In my experience, finite difference methods have proven to be a simple yet powerful tool for numerically solving the evolutionary PDEs that arise in modern mathematical finance. This book should finally dispel the widely held notion that these methods are somehow difficult or abstract. I highly recommend it to anyone interested in the implementation of these methods in the financial arena."-Peter Carr, Principal Bank of America Securities

"A very comprehensive treatment of the application of finite difference techniques to derivatives finance. Practitioners will find the many extensive examples very valuable and students will appreciate the rigorous attention paid to the many subtleties of finite difference techniques."-Francis Longstaff, Professor The Anderson School at UCLA

"The finite difference approach is central to the numerical pricing of financial securities. This book gives a clear and succinct introduction to this important subject. Highly recommended."-Mark Broadie, Associate Professor School of Business, Columbia University

For updates on new and bestselling Wiley Finance books: wiley.com/wbns

Customer Reviews:

A specialised book for special Instruments.......2004-05-09

This book approximates the solution of one-factor and multi-factor PDEs that describe derivatives such as barrier options, convertible bonds, Asian options and credit derivatives.
Standard finite difference schemes are used. In particular, 3-point centred difference schemes approximate the derivatives in the S directions while Crank-Nicolson (averaging) is used to approximate the t derivative. Stability and convergence of the schemes are proved using the Lax Equivalence theoerem. Special attention is paid to resolving the, by now well known problems associated with the Crank Nicolson method. The workarounds are choosing smaller meshes near discontinuous boundaries, coordinate transformations and choosing the right sampling points.
The book is a good attempt (in my opinion) to show how to apply FDM in financial engineering applications. It is probably most useful for those who have already experience of FDM. It is NOT an introductory book.
Some of the criticisms are (this is why I give it a 3 star):

1. The von Neumann stability analyis technique is only applicable to constant coefficient, linear PDE. It is outdated, better methods being the maximum principle and viscosity solutions.

2. The discrete set of equations need to be solved by rather esoteric matrix solvers bacause the authors discretise a PDE in all directions. Using ADI or operator splitting instead lets us solve one-dimensional problem with Tridiagonal LU Decomposition.

3. A lot of detail on meshes has unfortunately been left out.

4. Using Crank Nicolson only aggrevates the problems in FDM schemes. There ARE better methods out there.

5. TYPOS!! for example, equation (4.13) on page 122. The S term is missing.

On the other hand, this book is aimed at real-life problems. However, extra detail needs to be added in my opinion in order to make it more accessible to a wider audience.

Excellent Content - Sloppy Editing.......2002-11-26

Reading this book produced three instances where previously encountered material was explained from a new and different point of view, the clouds parted, and I was bathed in the bright sunshine of understanding. Creation and valuation of hedging portfolios, reduced to their fundamentals, is now far less taxing to the memory. Explanations for the discretization of time and space now render previously mysterious numerical algorithms obvious in their intent. American options discused in a free boundry framework are far more intuitive than in the optimal stoping time approach. As much as I enjoyed the content, the occurence of numerous editing oversights was a considerable annoyance. This was even more surprising when I read the other customer review which indicated that one of the authors was an editor. Editors should be held to a higher standard and so I deducted an extra star!

A clear treatment, with well-chosen subjects.......2001-01-16

Tavella and Randall have produced a compact, yet complete treatment of finite difference techniques in finance. I met Curt Randall in 1996 when his SciFinance software was in its infancy (though there is currently no connection between us). This software automatically generates C code to solve PDE's. That is an order of magnitude -- maybe two orders -- harder than just writing the code by hand. I inferred that Dr. Randall has a unique understanding of finite-difference methods for solving PDE's. For these reasons, I was very interested to see his book. For a more general treatment finite difference schemes, see Gordon Smith's 1986 book.

The mathematical motivations for all the techniques presented are given, with no wasted exposition. I liked the lucid analyses of stability, which many books in finance gloss over. I also liked the mention and partial analysis of a large set of solvers of sparse linear systems. having not followed the literature on jump processes in recent years, I was quite happy to see their treatment as well.

This book is all of what it claims to be, and no more. I do not recommend it as a textbook, or as a reference for those not already somewhat familiar with the subject, either from the mathematics side or the finance side. You will not get an explanation of what an eigenvalue or fourier transform is. The Lax Equivalence Theorem is cited, but not motivated or proven. No mention is given of when it might make more sense to use, say, a Monte Carlo scheme to find an option price. You won't find much economics in the book. But you will find a clear, correct, and useful analysis of more or less all aspects of finite difference schemes as they relate to solving contingent claims pricing problems.

A focussed book on an important subject.......2000-05-10

The pricing theory due to Black Scholes and Merton is widely recognized as one of the most significant contributions of economics to practice. There are now many good introductory books surveying the vast literature on the subject. So what is needed is a book showing how to implement various models in practice. The book by Tavella and Randall is the first in what I hope is a series of such books. The authors are well known in computational circles: Tavella is the editor of the highly regarded Journal of Computational Finance and Randall is a Principal at SciComp, a leading developer of software synthesis technology for the finance industry. The authors focus on finite differences, which is an important generalization of the common tree approach, and thus is one of the most widely used numerical techniques in finance.

The book's first two chapters introduce the mathematics of financial derivatives in an intuitively appealing manner. For example, measure changes are introduced as a powerful tool without strong demands on the reader in terms of background. Also, linear complementarity is used in the context of valuing American options, again in an intuitive fashion. The third chapter introduces finite differences in the context of the familiar parabolic PDE governing derivative security values. It is in this and the remaining chapters that much useful material can be found. For example, the cell averaging technique in chapter 4 is a very useful device for dampening the error introduced by slope discontinuities which commonly occur in financial problems. The authors also give the first textbook treatment of the important class of pure jump models such as the variance gamma model, which are growing in popularity. The chapter on coordinate transformations gives the finite difference version of what some finance people term the adaptive mesh method.

In summary, this book is a must-read for anyone seriously interested in implementing derivative security pricing models. I hope the authors plan to follow up with a more advanced version which can cover such interesting topics as multi-grid, hopskotch, operator splitting, and the like.

Book Description

Until now, the relationship between a company and its customers or suppliers has consisted of arms-length haggling over the price of a part or a service. Today, reveals alliance expert Jordan D. Lewis, customers and suppliers are actually embracing each other—sharing data, design work, and even research and development. The result, Lewis finds, has been a dramatic improvement in each firm's costs, quality, cycle times, and customer satisfaction—without added expense. Building on his groundbreaking work, Partnerships for Profit, Lewis shows managers how to maximize the potential of these new customer-supplier alliances—described by the Wall Street Journal as a "revolution"—by drawing upon his hands-on experience and research with best-practice firms worldwide such as Motorola, Chrysler, and Marks & Spencer.

Although more and more firms now recognize the importance of customer-supplier alliances, few actually know how to make them work. Using interviews with employees ranging from top executives to purchasing and sales people, Lewis takes the reader inside these leading-edge companies and their top suppliers to show precisely how the "connected" corporation can double its competitive resources by forging customer-supplier relationships for greater financial strength, higher market share, more value, and increased operating flexibility.

Lewis provides the tools managers need to structure and manage effective and successful alliances. He discusses all of the initial questions on how to get started—when to use alliances, how to choose the best partners, and how to set clear objectives targeted on high performance. Specific techniques are presented to foster joint creativity—from building interfirm teams to systems-based thinking—as well as methods for monitoring alliance performance and progress. Lewis also shows ways to develop the foundation of cooperation, negotiation, and trust between partners which is so crucial in achieving optimum competitive advantage.

By capitalizing on the new customer-supplier alliances, any firm can increase its competitiveness regardless of industry, company size, or whether its focus is on goods or services. Lewis provides managers of all types with the framework they need to avoid the pitfalls and enjoy the full benefits of the connected corporation.

Customer Reviews:

Highly Recommended!.......2001-03-07

Author Jordan D. Lewis uses the experiences of four major companies - Motorola, Philips Consumer Electronics Company, Marks & Spencer and Chrysler - to show the benefits of creating an alliance with your suppliers. The book, which is thorough and complete, if a bit long-winded, explains the benefits of such customer-supplier alliances, shows how to get started if you want to form a partnership and spells out how to maintain the relationship. The obligatory tables and figures are conveniently listed right after the table of contents. If you are in a huge rush, you can skip the book and just read the tables, because you will probably get a condensed version of the same information. But we at getAbstract think you'll enjoy reading how these four companies fumbled through the awkward initial stages of customer-supplier alliances and then emerged into trend-setting, money-making success.

Book Description

The book presents recent estimates of the rates in changes of major land classes such as forest, cropland and pasture. Among the causative mechanisms behind land change, synergetic factor combinations are found to be more common than single key factor explanations. Aggregated globally, multiple impacts of local land changes are shown to significantly affect central aspects of Earth System functioning. Innovative developments and applications in the fields of modeling and scenario construction are presented. Finally, conclusions are drawn about the most pressing implications for the design of appropriate intervention policies, and on new directions and frontiers of research.
The edited book synthesizes research achievements by dozens of scientists related to the Land-Use/Cover Change (LUCC) project of the International Geosphere-Biosphere Programme (IGBP) and the International Human Dimensions Programme on Global Environmental Change (IHDP). It summarizes relevant findings on global land-use change which arose from value-adding activities of the LUCC project, starting in 1995 and extending until its termination in October 2005. The main intention is to describe how human modification of land cover became a major driving force of Earth System changes over the past 300 years, a period of most rapid transformations, with fundamental implications for current landscape configurations. In writing this book, current knowledge and understanding is reported on the rates, causes/pathways, impacts, future scenarios/models, policy implications and new research directions in the field of land-use/cover change.

A Biomass Future for the North American Great Plains: Toward Sustainable Land Use and Mitigation of Greenhouse Warming (Advances in Global Change Research)

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A Biomass Future for the North American Great Plains: Toward Sustainable Land Use and Mitigation of Greenhouse Warming (Advances in Global Change Research)
Norman J. Rosenberg
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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ASIN: 1402056001

Book Description

The Great Plains of North America is a major global breadbasket but its agriculture is stressed by drought, heat spells, damaging winds, soil erosion and declining ground water resources. The great inter-annual variability in crop production and declining rural populations weaken an economy already highly dependent upon government support. The region’s ecological fragility and economic weakness is attributed by many to removal of its original grass cover. Abandonment of agricultural cropping and restoration of the grass cover is one proposed solution to the region’s problems.

Simulation models suggest that the agriculture and water resources of the Plains may be stressed even further as its climate changes because of global warming, which is due primarily to the emissions of greenhouse gases from fossil fuel combustion. This book explores the possibility that the ecology and economy of the Plains region (and similar regions) would benefit from the introduction of perennial biomass crops. Biomass production and processing on the Plains (possibly aided by genetic engineering) would partially restore a perennial vegetative cover and create new employment opportunities. Biomass also offers a means of reducing fossil fuel use, providing fuel to local power plants and a feedstock for production of cellulosic ethanol, a gasoline substitute. Interest in biofuels is growing rapidly in public, political and business circles with rising fossil fuel prices and because of a growing recognition of the need for energy independence in petroleum importing countries.

African Savannas: Global Narratives & Local Knowledge of Environmental Change

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African Savannas: Global Narratives & Local Knowledge of Environmental Change
Thomas Bassett , and Donald Crummey
Manufacturer: Heinemann
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Binding: Paperback

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Book Description

Images of degradation and chaos predominate many scholarly and popular conceptions of the African environment. This interdisciplinary collection uses collaborative research from the major savanna regions that stretch across Africa to challenge these notions. It argues that the interpretation of landscapes requires a consideration of the unique political and ecological practices in Africa. The image of environment and society in African savannas cultivated by this book is one of innovation, resilience, and spatial and temporal variability. It is an image that stresses the vitality and importance of local African knowledge for understanding environmental change. Accessibly written, this collection will appeal to general readers concerned about ecological issues in Africa. However, environmental policy makers, international aid donors, NGOs and grassroots activists will also find the book timely, pertinent and useful.

African Greenhouse Gas Emission Inventories and Mitigation Options: Forestry, Land-Use Change, and Agriculture

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African Greenhouse Gas Emission Inventories and Mitigation Options: Forestry, Land-Use Change, and Agriculture

Manufacturer: Springer
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Binding: Hardcover

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ASIN: 0792339428

Book Description

As atmospheric concentrations of greenhouse gases continue to increase, so does the potential for atmospheric warming and associated climate change. In an effort to address the threat of global climate change, 155 countries signed the UN Framework Convention on Climate Change at the Earth Summit in Rio de Janeiro in June 1992. As of the first session of the Conference of the Parties, 128 nations had ratified the Convention. Among their other commitments, Parties to the Convention must develop and periodically update national inventories of net anthropogenic greenhouse gas emissions using comparable methodologies, and must develop and implement national programs to mitigate greenhouse gas emissions.
To further the development of emission inventories and mitigation options within the African context, 64 governmental and non-governmental scientists and policy analysts from 23 nations gathered at a workshop near Johannesburg, South Africa from 29 May to 2 June 1995. The workshop focused on forestry, land-use change, and agriculture, because these sectors not only are responsible for the majority of emissions from the continent and provide promising opportunities for emissions mitigation, but also are a vital component of African economic growth and development.
This book presents the workshop's major conclusions and findings, as well as individual papers that were prepared for the workshop, each of which was peer-reviewed and accepted for publication as part of the workshop process. The papers cover four areas: (1) issues are associated with data collection and emission factor determination; (2) problems associated with applying the IPCC inventory methodologies in Africa; (3) results of national inventory assessments in Africa; and (4) possible emissions mitigation options and methods for evaluating their potential viability.
As the first book dedicated solely to greenhouse gas emissions and mitigation options in Africa, this will be an invaluable resource to scientists, policymakers, and development specialists interested in global climate change and Africa.

Changes in Land Use and Land Cover: A Global Perspective

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Changes in Land Use and Land Cover: A Global Perspective

Manufacturer: Cambridge University Press
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Binding: Hardcover

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ASIN: 0521470854

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This book deals with the relationship between land use and land cover: between human activities and the transformation of the Earth’s surface. It describes the recent changes in the world’s farmland, forests, grasslands and settlements, and the impacts of these changes on soil, water resources and the atmosphere. It explores what is known about the importance of various underlying human sources of land transformation: population growth, technological change, political-economic institutions, political structure, and attitudes and beliefs. Three working group reports outline important avenues for future research: the construction of a global land model, the division of the world into regional situations of land transformation, and a wiring diagram to structure the division of research among fields of study.

Economic Analysis of Land Use in Global Climate Change Policy

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Economic Analysis of Land Use in Global Climate Change Policy
Thomas W. Herte
Manufacturer: Routledge
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Environmental Policies and N.G.O. Influence: Land Degradation and Sustainable Resource Management in Sub-Saharan Africa (Routledge Research Global Environmental Change Series, 4)

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Environmental Policies and N.G.O. Influence: Land Degradation and Sustainable Resource Management in Sub-Saharan Africa (Routledge Research Global Environmental Change Series, 4)
Alan Thomas
Manufacturer: Routledge
ProductGroup: Book
Binding: Hardcover

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ASIN: 0415189632

Book Description

This volume examines important case studies such as NGO campaigns for sustainable water management in Zimbabwe, Botswana and Nigeria and opposition to the fencing of rangelands in Botswana.

Global Change and Arctic Terrestrial Ecosystems (Ecological Studies)

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Global Change and Arctic Terrestrial Ecosystems (Ecological Studies)

Manufacturer: Springer-Verlag Telos
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ASIN: 0387943560

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Global warming is likely to have the greatest impact at high latitudes, making the Arctic an important region both for detecting global climate change and for studying its effects on terrestrial ecosystems. The chapters in this volume address current and anticipated impacts of global climate change on Arctic organisms, populations, ecosystem structure and function, biological diversity, and the atmosphere.

Global Environmental Change and Land Use

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Global Environmental Change and Land Use

Manufacturer: Springer
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Binding: Hardcover

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ASIN: 1402013469

Book Description

This book highlights one of the most important aspects of global change - the interaction of land use and the climate system. In separate chapters the book treats modelling of land-use patterns, the effects on climate, the effect of land use on the global carbon cycle, hydrological aspects of land use, aspects of climate change on food availability in West Africa, and the spatial requirements of bioenergy plantations. The current collection of chapters provides a unique, integrated treatment of land use in the context of global change.

Audience: This book should provide a stimulus for researchers and policy-makers alike to treat land use and land-use change in a multi-disciplinary manner.

Land and Limits: Interpreting Sustainability in the Planning Process (Routledge Research Global Environmental Change Series, 7.)

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Land and Limits: Interpreting Sustainability in the Planning Process (Routledge Research Global Environmental Change Series, 7.)
Richard Cowell
Manufacturer: Routledge
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Binding: Library Binding

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ASIN: 0415162769

Book Description

In a new and critical analysis, this book explores the impact of an influential idea - sustainable development - on the institutions and practices governing use of land. It examines the paradox that in spite of increasing attention to sustainability, land use conflict is as ubiquitous and intense as ever.

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