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American Options, the Method of Images and Closed Form Solutions

American Options, the Method of Images and Closed Form Solutions
Author: Gabriela Baumgartner
Publisher:
Total Pages: 29
Release: 2018
Genre:
ISBN:
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This paper considers solutions for a class of optimal stopping problems, maximising the expected product of a Wiener process and a positive decreasing scale function. The general approach to such problems involves a partial differential equation with movable boundary. The method of images is a useful tool for solving fixed-boundary PDE problems. We adapt this method to a sub-class of movable boundary problems. When the scale function in the original problem is a survival function of Generalised Pareto (GPD) type, we use a self-similarity property to reduce the PDE to an ODE. This ODE was widely studied in the 19th century, and the solution involves confluent hypergeometric functions. In cases of integer parameters, we give simpler closed form solutions involving the normal distribution function. The same approach also works when the Wiener process is reflected at zero.

Derivative Securities and Difference Methods

Derivative Securities and Difference Methods
Author: You-lan Zhu
Publisher: Springer Science & Business Media
Total Pages: 536
Release: 2004-08-27
Genre: Business & Economics
ISBN: 9780387208428
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This book studies pricing financial derivatives with a partial differential equation approach. The treatment is mathematically rigorous and covers a variety of topics in finance including forward and futures contracts, the Black-Scholes model, European and American type options, free boundary problems, lookback options, interest rate models, interest rate derivatives, swaps, caps, floors, and collars. Each chapter concludes with exercises.

Mathematical Modeling and Methods of Option Pricing

Mathematical Modeling and Methods of Option Pricing
Author: Lishang Jiang
Publisher: World Scientific
Total Pages: 344
Release: 2005
Genre: Science
ISBN: 9812563695
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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.

The Advanced Fixed Income and Derivatives Management Guide

The Advanced Fixed Income and Derivatives Management Guide
Author: Saied Simozar
Publisher: John Wiley & Sons
Total Pages: 368
Release: 2015-06-15
Genre: Business & Economics
ISBN: 111901414X
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A highly-detailed, practical analysis of fixed income management The Advanced Fixed Income and Derivatives Management Guide provides a completely novel framework for analysis of fixed income securities and portfolio management, with over 700 useful equations. The most detailed analysis of inflation linked and corporate securities and bond options analysis available;, this book features numerous practical examples that can be used for creating alpha transfer to any fixed income portfolio. With a framework that unifies back office operations, such as risk management and portfolio management in a consistent way, readers will be able to better manage all sectors of fixed income, including bonds, mortgages, credits, and currencies, and their respective derivatives, including bond and interest rate futures and options, callable bonds, credit default swaps, interest rate swaps, swaptions and inflation swaps. Coverage includes never-before-seen detail on topics including recovery value, partial yields, arbitrage, and more, and the companion website features downloadable worksheets that can be used for measuring the risks of securities based on the term structure models. Many theoretical models of the Term Structure of Interest Rates (TSIR) lack the accuracy to be used by market practitioners, and the most popular models are not mathematically stable. This book helps readers develop stable and accurate TSIR for all fundamental rates, enabling analysis of even the most complex securities or cash flow structure. The components of the TSIR are almost identical to the modes of fluctuations of interest rates and represent the language with which the markets speak. Examine unique arbitrage, risk measurement, performance attribution, and replication of bond futures Learn to estimate recovery value from market data, and the impact of recovery value on risks Gain deeper insight into partial yields, product design, and portfolio construction Discover the proof that corporate bonds cannot follow efficient market hypothesis This useful guide provides a framework for systematic and consistent management of all global fixed income assets based on the term structure of rates. Practitioners seeking a more thorough management system will find solutions in The Advanced Fixed Income and Derivatives Management Guide.

A Closed-Form Solution to American Options under General Diffusions

A Closed-Form Solution to American Options under General Diffusions
Author: Jing Zhao
Publisher:
Total Pages: 29
Release: 2012
Genre:
ISBN:
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This paper investigates American option pricing under general diffusion processes with nonconstant dividend yield. Specifically, the underlying asset price is assumed to have both the dividend yield and the volatility to be functions of time and the underlying asset price. Using homotopy analysis in Topology, the determination of the optimal early exercise boundary and that of the American option price are separated in the valuation procedure. Then, an exact and explicit solution for American options on a dividend-paying stock is derived as a Maclaurin series. Meanwhile, the corresponding optimal early exercise boundary is also obtained in a closed-form solution. As the solutions are in series expansion, an auxiliary parameter is introduced to control the convergence region and convergence rate. For practical use, the Pade technique is employed to further accelerate the convergence speed. Examples are given to demonstrate the validity, effectiveness and flexibility of the proposed approach.

Model Rules of Professional Conduct

Model Rules of Professional Conduct
Author: American Bar Association. House of Delegates
Publisher: American Bar Association
Total Pages: 216
Release: 2007
Genre: Law
ISBN: 9781590318737
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The Model Rules of Professional Conduct provides an up-to-date resource for information on legal ethics. Federal, state and local courts in all jurisdictions look to the Rules for guidance in solving lawyer malpractice cases, disciplinary actions, disqualification issues, sanctions questions and much more. In this volume, black-letter Rules of Professional Conduct are followed by numbered Comments that explain each Rule's purpose and provide suggestions for its practical application. The Rules will help you identify proper conduct in a variety of given situations, review those instances where discretionary action is possible, and define the nature of the relationship between you and your clients, colleagues and the courts.

Image Analysis

Image Analysis
Author: Rikke Gade
Publisher: Springer Nature
Total Pages: 625
Release: 2023-04-26
Genre: Technology & Engineering
ISBN: 3031314387
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This two-volume set (LNCS 13885-13886) constitutes the refereed proceedings of the 23rd Scandinavian Conference on Image Analysis, SCIA 2023, held in Lapland, Finland, in April 2023. The 67 revised papers presented were carefully reviewed and selected from 108 submissions. The contributions are structured in topical sections on datasets and evaluation; action and behaviour recognition; image and video processing, analysis, and understanding; detection, recognition, classification, and localization in 2D and/or 3D; machine learning and deep learning; segmentation, grouping, and shape; vision for robotics and autonomous vehicles; biometrics, faces, body gestures and pose; 3D vision from multiview and other sensors; vision applications and systems.

Mathematical Models of Financial Derivatives

Mathematical Models of Financial Derivatives
Author: Yue-Kuen Kwok
Publisher: Springer Science & Business Media
Total Pages: 541
Release: 2008-07-10
Genre: Mathematics
ISBN: 3540686886
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This second edition, now featuring new material, focuses on the valuation principles that are common to most derivative securities. A wide range of financial derivatives commonly traded in the equity and fixed income markets are analysed, emphasising aspects of pricing, hedging and practical usage. This second edition features additional emphasis on the discussion of Ito calculus and Girsanovs Theorem, and the risk-neutral measure and equivalent martingale pricing approach. A new chapter on credit risk models and pricing of credit derivatives has been added. Up-to-date research results are provided by many useful exercises.