Download or read book Efficient Pricing of an Asian Put Option Using Stiff ODE Methods written by and published by . This book was released on 2007 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: Financial mathematics is a branch of mathematics that assesses the risk and value of various financial instruments. Banks, companies, and other institutions mitigate their risk through financial instruments known as derivatives, that derive their value from some underlying asset. The equations that arise from pricing and modeling can be very complex, leading to the necessity of numerical methods. This project studied the use of certain numerical methods for the pricing of a particular type of option called an Asian option. Asian options can provide favorable risk profiles because the payout is determined based on the average value over a time period, rather than the final value. The price of an Asian option is governed by a partial differential equation in three variables: stock price, average price over the current time interval, and time. The solution method was first to discretize the partial differential equation into a system of ordinary differential equations. Next, the ODE system was integrated using a stiff-ODE solver available in MATLAB. Enhancements to this solution method include specifying the sparsity pattern, implementing an iterative linear solver (GMRES) in place of MATLAB's built-in direct linear solver, and using preconditioning to improve the solution characteristics of that solver.
Download or read book Accounting and Valuation Guide written by AICPA and published by John Wiley & Sons. This book was released on 2019-09-16 with total page 619 pages. Available in PDF, EPUB and Kindle. Book excerpt: Developed for preparers of financial statements, independent auditors, and valuation specialists, this guide provides nonauthoritative guidance and illustrations regarding the accounting for and valuation of portfolio company investments held by investment companies within the scope of FASB ASC 946, Financial Services —Investment Companies, (including private equity funds, venture capital funds, hedge funds, and business development companies). It features16 case studies that can be used to reason through real situations faced by investment fund managers, valuation specialists and auditors, this guide addresses many accounting and valuation issues that have emerged over time to assist investment companies in addressing the challenges in estimating fair value of these investments, such as: Unit of account Transaction costs Calibration The impact of control and marketability Backtesting
Download or read book Accounting and Valuation Guide Valuation of Privately Held Company Equity Securities Issued as Compensation written by AICPA and published by John Wiley & Sons. This book was released on 2016-10-31 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new Guide has been developed by AICPA staff and the Equity Securities Task Force and is the first in a series of 3 NEW AICPA Accounting Valuation Guides to be released. This long anticipated release reflects best practices developed over the previous decade. Since the issuance of FASB ASC 718 and 505-50 in 2004, valuing stock-based compensation ("cheap stock") has been a significant challenge for private companies. This New Guide has been designed to mitigate those challenges. It brings you practical guidance and illustrations related to accounting, disclosures and valuation of privately held company equity securities issued as compensation. This guide includes: Evaluating private and secondary market transactions — What should companies do when transaction activity doesn't match their estimates of value? Adjustments for control and marketability — How should companies think about the value of the enterprise for the purpose of valuing minority securities? When is it appropriate to apply a discount for lack of marketability, and how should the estimated discount be supported? Highly leveraged entities — How should companies incorporate the fair value of debt in the valuation of equity securities? What is the impact of leverage on the expected volatility of various securities? The relevance of ASC 820 (SFAS 157) to cheap stock issues Updated guidance and illustrations regarding the valuation of, and disclosures related to, privately held company equity securities issued as compensation This Guide also provides expanded and more robust valuation material to reflect advances in the theory and practice of valuation since 2004. This edition includes guidance from FASB ASC 718, 505-50, 820-10 and SSVS 1 which were all issued since the last AICPA guidance dedicated to this issue.
Download or read book An Accurate and Efficient Method for Pricing Asian Options written by Chuang-Chang Chang and published by . This book was released on 2003 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we provide an accurate and efficient method for valuing Asian options that works well for the low and medium volatility as well as longer average time window. Numerical results show that our method significantly outperforms the other analytic approximation methods in the literature. The pricing errors in terms of mean square errors for calculating a bundle of Asian options are less than one percent. Our method is fast and efficient compared to the Monte Carlo benchmark method adopted as well.
Download or read book Accurate Efficient Pricing of Arithmetic Average Asian Options Within the Hull White Method written by Pratik Ramprasad and published by . This book was released on 2015 with total page 7 pages. Available in PDF, EPUB and Kindle. Book excerpt: Simulation or other appro ...
Download or read book The Pricing Of Asian Options In High Volatile Markets written by Nabil Kamal Riziq Farra and published by . This book was released on 2015 with total page 78 pages. Available in PDF, EPUB and Kindle. Book excerpt: Financial derivatives are very important tools in risk management since they decrease uncertainty. Moreover, if used effectively, they can grow the income and save the cost. There are many types of financial derivatives, for instance: futures/forwards, options, and swaps. The present thesis deals with the pricing problem for Asian options. The main aim of the thesis is to generalize the Asian option pricing Partial Differential Equation (PDE) in order to handle post-crash markets where the volatility is high. In other words, we seek to extend the work on the Asian option pricing PDE under the well-known Black-Scholes model to a high volatility model. To this end, we first set up a model that accounts for high volatile situations and we solve the Stochastic Differential Equation (SDE) of the underlying asset price. Our illustrations confirm the high volatile behavior of the model. We then derive the Asian option PDE for the suggested model. The resulting PDE is reduced from two-dimensional space to one-dimensional space using a change of variable. Moreover, we derive a relationship between the Asian options prices of the Black-Scholes model and our high volatility model where the increase in volatility is a deterministic function of the interest rate.
Download or read book An Efficient Transform Method for Asian Option Pricing written by Justin Kirkby and published by . This book was released on 2016 with total page 45 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper introduces a novel method to price arithmetic Asian options in Levy-driven models, with discrete and continuous averaging, by expanding on the approach of sequential characteristic function recovery. By utilizing frame duality and a FFT-based implementation of density projection, we obtain rapidly converging value approximations to high precision, consistently resulting in a 10- to 100-fold time reduction compared to state-of-the-art procedures. Theoretical convergence rates are confirmed by an in-depth analysis of error propagation. Formulas for Greeks are provided, in addition to generalized averaging and in-progress option pricing.
Download or read book An Efficient and Stable Method for Short Maturity Asian Options written by Rupak Chatterjee and published by . This book was released on 2017 with total page 21 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we develop a Markov chain-based approximation method to price arithmetic Asian options for short maturities under the case of geometric Brownian motion. It has the advantage of being a closed-form approximation involving only matrices. It is an accurate, efficient, and stable method for the pricing and hedging of short maturity arithmetic Asian options for which previous methods in the literature have shown either slower convergence or instabilities in hedging parameters. We also consider the pricing and hedging of floating-strike Asian options and fixed-strike in-progress Asian options, and demonstrate that our method is as good as and sometimes better than existing approximation methods in the literature.
Download or read book Finite Difference Methods in Financial Engineering written by Daniel J. Duffy and published by John Wiley & Sons. This book was released on 2013-10-28 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: The world of quantitative finance (QF) is one of the fastest growing areas of research and its practical applications to derivatives pricing problem. Since the discovery of the famous Black-Scholes equation in the 1970's we have seen a surge in the number of models for a wide range of products such as plain and exotic options, interest rate derivatives, real options and many others. Gone are the days when it was possible to price these derivatives analytically. For most problems we must resort to some kind of approximate method. In this book we employ partial differential equations (PDE) to describe a range of one-factor and multi-factor derivatives products such as plain European and American options, multi-asset options, Asian options, interest rate options and real options. PDE techniques allow us to create a framework for modeling complex and interesting derivatives products. Having defined the PDE problem we then approximate it using the Finite Difference Method (FDM). This method has been used for many application areas such as fluid dynamics, heat transfer, semiconductor simulation and astrophysics, to name just a few. In this book we apply the same techniques to pricing real-life derivative products. We use both traditional (or well-known) methods as well as a number of advanced schemes that are making their way into the QF literature: Crank-Nicolson, exponentially fitted and higher-order schemes for one-factor and multi-factor options Early exercise features and approximation using front-fixing, penalty and variational methods Modelling stochastic volatility models using Splitting methods Critique of ADI and Crank-Nicolson schemes; when they work and when they don't work Modelling jumps using Partial Integro Differential Equations (PIDE) Free and moving boundary value problems in QF Included with the book is a CD containing information on how to set up FDM algorithms, how to map these algorithms to C++ as well as several working programs for one-factor and two-factor models. We also provide source code so that you can customize the applications to suit your own needs.
Download or read book Advances in Finance and Stochastics written by Klaus Sandmann and published by Springer Science & Business Media. This book was released on 2002-04-23 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: In many areas of finance and stochastics, significant advances have been made since this field of research was opened by Black, Scholes and Merton in 1973. This volume contains a collection of original articles by a number of highly distinguished authors, on research topics that are currently in the focus of interest of both academics and practitioners.
Download or read book How Learning Works written by Susan A. Ambrose and published by John Wiley & Sons. This book was released on 2010-04-16 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Praise for How Learning Works "How Learning Works is the perfect title for this excellent book. Drawing upon new research in psychology, education, and cognitive science, the authors have demystified a complex topic into clear explanations of seven powerful learning principles. Full of great ideas and practical suggestions, all based on solid research evidence, this book is essential reading for instructors at all levels who wish to improve their students' learning." —Barbara Gross Davis, assistant vice chancellor for educational development, University of California, Berkeley, and author, Tools for Teaching "This book is a must-read for every instructor, new or experienced. Although I have been teaching for almost thirty years, as I read this book I found myself resonating with many of its ideas, and I discovered new ways of thinking about teaching." —Eugenia T. Paulus, professor of chemistry, North Hennepin Community College, and 2008 U.S. Community Colleges Professor of the Year from The Carnegie Foundation for the Advancement of Teaching and the Council for Advancement and Support of Education "Thank you Carnegie Mellon for making accessible what has previously been inaccessible to those of us who are not learning scientists. Your focus on the essence of learning combined with concrete examples of the daily challenges of teaching and clear tactical strategies for faculty to consider is a welcome work. I will recommend this book to all my colleagues." —Catherine M. Casserly, senior partner, The Carnegie Foundation for the Advancement of Teaching "As you read about each of the seven basic learning principles in this book, you will find advice that is grounded in learning theory, based on research evidence, relevant to college teaching, and easy to understand. The authors have extensive knowledge and experience in applying the science of learning to college teaching, and they graciously share it with you in this organized and readable book." —From the Foreword by Richard E. Mayer, professor of psychology, University of California, Santa Barbara; coauthor, e-Learning and the Science of Instruction; and author, Multimedia Learning
Download or read book Teaching at Its Best written by Linda B. Nilson and published by John Wiley & Sons. This book was released on 2010-04-20 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: Teaching at Its Best This third edition of the best-selling handbook offers faculty at all levels an essential toolbox of hundreds of practical teaching techniques, formats, classroom activities, and exercises, all of which can be implemented immediately. This thoroughly revised edition includes the newest portrait of the Millennial student; current research from cognitive psychology; a focus on outcomes maps; the latest legal options on copyright issues; and how to best use new technology including wikis, blogs, podcasts, vodcasts, and clickers. Entirely new chapters include subjects such as matching teaching methods with learning outcomes, inquiry-guided learning, and using visuals to teach, and new sections address Felder and Silverman's Index of Learning Styles, SCALE-UP classrooms, multiple true-false test items, and much more. Praise for the Third Edition of Teaching at Its BestEveryone veterans as well as novices will profit from reading Teaching at Its Best, for it provides both theory and practical suggestions for handling all of the problems one encounters in teaching classes varying in size, ability, and motivation." Wilbert McKeachie, Department of Psychology, University of Michigan, and coauthor, McKeachie's Teaching TipsThis new edition of Dr. Nilson's book, with its completely updated material and several new topics, is an even more powerful collection of ideas and tools than the last. What a great resource, especially for beginning teachers but also for us veterans!" L. Dee Fink, author, Creating Significant Learning ExperiencesThis third edition of Teaching at Its Best is successful at weaving the latest research on teaching and learning into what was already a thorough exploration of each topic. New information on how we learn, how students develop, and innovations in instructional strategies complement the solid foundation established in the first two editions." Marilla D. Svinicki, Department of Psychology, The University of Texas, Austin, and coauthor, McKeachie's Teaching Tips
Download or read book Difference Methods and Their Extrapolations written by G.I. Marchuk and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: The stimulus for the present work is the growing need for more accurate numerical methods. The rapid advances in computer technology have not provided the resources for computations which make use of methods with low accuracy. The computational speed of computers is continually increasing, while memory still remains a problem when one handles large arrays. More accurate numerical methods allow us to reduce the overall computation time by of magnitude. several orders The problem of finding the most efficient methods for the numerical solution of equations, under the assumption of fixed array size, is therefore of paramount importance. Advances in the applied sciences, such as aerodynamics, hydrodynamics, particle transport, and scattering, have increased the demands placed on numerical mathematics. New mathematical models, describing various physical phenomena in greater detail than ever before, create new demands on applied mathematics, and have acted as a major impetus to the development of computer science. For example, when investigating the stability of a fluid flowing around an object one needs to solve the low viscosity form of certain hydrodynamic equations describing the fluid flow. The usual numerical methods for doing so require the introduction of a "computational viscosity," which usually exceeds the physical value; the results obtained thus present a distorted picture of the phenomena under study. A similar situation arises in the study of behavior of the oceans, assuming weak turbulence. Many additional examples of this type can be given.
Download or read book Tools for Computational Finance written by Rüdiger U. Seydel and published by Springer Science & Business Media. This book was released on 2012-03-09 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: The disciplines of financial engineering and numerical computation differ greatly, however computational methods are used in a number of ways across the field of finance. It is the aim of this book to explain how such methods work in financial engineering; specifically the use of numerical methods as tools for computational finance. By concentrating on the field of option pricing, a core task of financial engineering and risk analysis, this book explores a wide range of computational tools in a coherent and focused manner and will be of use to the entire field of computational finance. Starting with an introductory chapter that presents the financial and stochastic background, the remainder of the book goes on to detail computational methods using both stochastic and deterministic approaches. Now in its fifth edition, Tools for Computational Finance has been significantly revised and contains: A new chapter on incomplete markets which links to new appendices on Viscosity solutions and the Dupire equation; Several new parts throughout the book such as that on the calculation of sensitivities (Sect. 3.7) and the introduction of penalty methods and their application to a two-factor model (Sect. 6.7) Additional material in the field of analytical methods including Kim’s integral representation and its computation Guidelines for comparing algorithms and judging their efficiency An extended chapter on finite elements that now includes a discussion of two-asset options Additional exercises, figures and references Written from the perspective of an applied mathematician, methods are introduced as tools within the book for immediate and straightforward application. A ‘learning by calculating’ approach is adopted throughout this book enabling readers to explore several areas of the financial world. Interdisciplinary in nature, this book will appeal to advanced undergraduate students in mathematics, engineering and other scientific disciplines as well as professionals in financial engineering.
Download or read book Numerical Methods in Finance written by L. C. G. Rogers and published by Cambridge University Press. This book was released on 1997-06-26 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical Methods in Finance describes a wide variety of numerical methods used in financial analysis.
Download or read book Fox and McDonald s Introduction to Fluid Mechanics written by Robert W. Fox and published by John Wiley & Sons. This book was released on 2020-06-30 with total page 610 pages. Available in PDF, EPUB and Kindle. Book excerpt: Through ten editions, Fox and McDonald's Introduction to Fluid Mechanics has helped students understand the physical concepts, basic principles, and analysis methods of fluid mechanics. This market-leading textbook provides a balanced, systematic approach to mastering critical concepts with the proven Fox-McDonald solution methodology. In-depth yet accessible chapters present governing equations, clearly state assumptions, and relate mathematical results to corresponding physical behavior. Emphasis is placed on the use of control volumes to support a practical, theoretically-inclusive problem-solving approach to the subject. Each comprehensive chapter includes numerous, easy-to-follow examples that illustrate good solution technique and explain challenging points. A broad range of carefully selected topics describe how to apply the governing equations to various problems, and explain physical concepts to enable students to model real-world fluid flow situations. Topics include flow measurement, dimensional analysis and similitude, flow in pipes, ducts, and open channels, fluid machinery, and more. To enhance student learning, the book incorporates numerous pedagogical features including chapter summaries and learning objectives, end-of-chapter problems, useful equations, and design and open-ended problems that encourage students to apply fluid mechanics principles to the design of devices and systems.
Download or read book No Logo written by Naomi Klein and published by Macmillan. This book was released on 2000-01-15 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: "What corporations fear most are consumers who ask questions. Naomi Klein offers us the arguments with which to take on the superbrands." Billy Bragg from the bookjacket.
