Closed Form Solutions For Options In Incomplete Markets
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Closed Form Solutions For Options In Incomplete Markets
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Author : Oana Floroiu
language : en
Publisher:
Release Date : 2013
Closed Form Solutions For Options In Incomplete Markets written by Oana Floroiu and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with categories.
This paper reconsiders the predictions of the standard option pricing models in the context of incomplete markets. We relax the completeness assumption of the Black-Scholes (1973) model and as an immediate consequence we can no longer construct a replicating portfolio to price the option. Instead, we use the good-deal bounds technique to arrive at closed-form solutions for the option price. We determine an upper and a lower bound for this price and find that, contrary to Black-Scholes (1973) options theory, increasing the volatility of the underlying asset does not necessarily increase the option value. In fact, the lower bound prices are always a decreasing function of the volatility of the underlying asset, which cannot be explained by a Black-Scholes (1973) type of argument. In contrast, this is consistent with the presence of unhedgeable risk in the incomplete market. Furthermore, in an incomplete market where the underlying asset of an option is either infrequently traded or non-traded, early exercise of an American call option becomes possible at the lower bound, because the economic agent wants to lock in value before it disappears as a result of increased unhedgeable risk.
Handbooks In Operations Research And Management Science Financial Engineering
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Author : John R. Birge
language : en
Publisher: Elsevier
Release Date : 2007-11-16
Handbooks In Operations Research And Management Science Financial Engineering written by John R. Birge and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-11-16 with Business & Economics categories.
The remarkable growth of financial markets over the past decades has been accompanied by an equally remarkable explosion in financial engineering, the interdisciplinary field focusing on applications of mathematical and statistical modeling and computational technology to problems in the financial services industry. The goals of financial engineering research are to develop empirically realistic stochastic models describing dynamics of financial risk variables, such as asset prices, foreign exchange rates, and interest rates, and to develop analytical, computational and statistical methods and tools to implement the models and employ them to design and evaluate financial products and processes to manage risk and to meet financial goals. This handbook describes the latest developments in this rapidly evolving field in the areas of modeling and pricing financial derivatives, building models of interest rates and credit risk, pricing and hedging in incomplete markets, risk management, and portfolio optimization. Leading researchers in each of these areas provide their perspective on the state of the art in terms of analysis, computation, and practical relevance. The authors describe essential results to date, fundamental methods and tools, as well as new views of the existing literature, opportunities, and challenges for future research.
A Stochastic Control Framework For Real Options In Strategic Evaluation
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Author : Alexander Vollert
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
A Stochastic Control Framework For Real Options In Strategic Evaluation written by Alexander Vollert 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 2012-12-06 with Mathematics categories.
The theoretical foundation for real options goes back to the mid 1980s and the development of a model that forms the basis for many current applications of real option theory. Over the last decade the theory has rapidly expanded and become enriched thanks to increasing research activity. Modern real option theory may be used for the valuation of entire companies as well as for particular investment projects in the presence of uncertainty. As such, the theory of real options can serve as a tool for more practically oriented decision making, providing management with strategies maximizing its capital market value. This book is devoted to examining a new framework for classifying real options from a management and a valuation perspective, giving the advantages and disadvantages of the real option approach. Impulse control theory and the theory of optimal stopping combined with methods of mathematical finance are used to construct arbitrarily complex real option models which can be solved numerically and which yield optimal capital market strategies and values. Various examples are given to demonstrate the potential of this framework. This work will benefit the financial community, companies, as well as academics in mathematical finance by providing an important extension of real option research from both a theoretical and practical point of view.
Numerical Methods In Finance
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Author : René Carmona
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-03-23
Numerical Methods In Finance written by René Carmona 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 2012-03-23 with Mathematics categories.
Numerical methods in finance have emerged as a vital field at the crossroads of probability theory, finance and numerical analysis. Based on presentations given at the workshop Numerical Methods in Finance held at the INRIA Bordeaux (France) on June 1-2, 2010, this book provides an overview of the major new advances in the numerical treatment of instruments with American exercises. Naturally it covers the most recent research on the mathematical theory and the practical applications of optimal stopping problems as they relate to financial applications. By extension, it also provides an original treatment of Monte Carlo methods for the recursive computation of conditional expectations and solutions of BSDEs and generalized multiple optimal stopping problems and their applications to the valuation of energy derivatives and assets. The articles were carefully written in a pedagogical style and a reasonably self-contained manner. The book is geared toward quantitative analysts, probabilists, and applied mathematicians interested in financial applications.
Arbitrage Theory In Continuous Time
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Author : Tomas Bjork
language : en
Publisher: Oxford University Press, USA
Release Date : 2020-01-16
Arbitrage Theory In Continuous Time written by Tomas Bjork and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-16 with Arbitrage categories.
The fourth edition of this widely used textbook on pricing and hedging of financial derivatives now also includes dynamic equilibrium theory and continues to combine sound mathematical principles with economic applications. Concentrating on the probabilistic theory of continuous time arbitrage pricing of financial derivatives, including stochastic optimal control theory and optimal stopping theory, Arbitrage Theory in Continuous Time is designed for graduate students in economics and mathematics, and combines the necessary mathematical background with a solid economic focus. It includes a solved example for every new technique presented, contains numerous exercises, and suggests further reading in each chapter. All concepts and ideas are discussed, not only from a mathematics point of view, but with lots of intuitive economic arguments. In the substantially extended fourth edition Tomas Bjork has added completely new chapters on incomplete markets, treating such topics as the Esscher transform, the minimal martingale measure, f-divergences, optimal investment theory for incomplete markets, and good deal bounds. This edition includes an entirely new section presenting dynamic equilibrium theory, covering unit net supply endowments models and the Cox-Ingersoll-Ross equilibrium factor model. Providing two full treatments of arbitrage theory-the classical delta hedging approach and the modern martingale approach-this book is written so that these approaches can be studied independently of each other, thus providing the less mathematically-oriented reader with a self-contained introduction to arbitrage theory and equilibrium theory, while at the same time allowing the more advanced student to see the full theory in action. This textbook is a natural choice for graduate students and advanced undergraduates studying finance and an invaluable introduction to mathematical finance for mathematicians and professionals in the market.
Financial Modelling With Jump Processes
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Author : Rama Cont
language : en
Publisher: CRC Press
Release Date : 2003-12-30
Financial Modelling With Jump Processes written by Rama Cont and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-12-30 with Business & Economics categories.
WINNER of a Riskbook.com Best of 2004 Book Award! During the last decade, financial models based on jump processes have acquired increasing popularity in risk management and option pricing. Much has been published on the subject, but the technical nature of most papers makes them difficult for nonspecialists to understand, and the mathematic
Numerical Methods In Finance
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Author : L. C. G. Rogers
language : en
Publisher: Cambridge University Press
Release Date : 1997-06-26
Numerical Methods In Finance written by L. C. G. Rogers and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-06-26 with Business & Economics categories.
Numerical Methods in Finance describes a wide variety of numerical methods used in financial analysis.
Asset Pricing And Portfolio Choice Theory
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Author : Kerry Back
language : en
Publisher: Oxford University Press, USA
Release Date : 2010
Asset Pricing And Portfolio Choice Theory written by Kerry Back and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Business & Economics categories.
This book covers the classical results on single-period, discrete-time, and continuous-time models of portfolio choice and asset pricing. It also treats asymmetric information, production models, various proposed explanations for the equity premium puzzle, and topics important for behavioral finance.
Copula Methods In Finance
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Author : Umberto Cherubini
language : en
Publisher: John Wiley & Sons
Release Date : 2004-10-22
Copula Methods In Finance written by Umberto Cherubini 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 2004-10-22 with Business & Economics categories.
Copula Methods in Finance is the first book to address the mathematics of copula functions illustrated with finance applications. It explains copulas by means of applications to major topics in derivative pricing and credit risk analysis. Examples include pricing of the main exotic derivatives (barrier, basket, rainbow options) as well as risk management issues. Particular focus is given to the pricing of asset-backed securities and basket credit derivative products and the evaluation of counterparty risk in derivative transactions.
Risk Neutral Valuation
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Author : Nicholas H. Bingham
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Risk Neutral Valuation written by Nicholas H. Bingham 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 2013-06-29 with Mathematics categories.
Since its introduction in the early 1980s, the risk-neutral valuation principle has proved to be an important tool in the pricing and hedging of financial derivatives. Following the success of the first edition of ‘Risk-Neutral Valuation’, the authors have thoroughly revised the entire book, taking into account recent developments in the field, and changes in their own thinking and teaching. In particular, the chapters on Incomplete Markets and Interest Rate Theory have been updated and extended, there is a new chapter on the important and growing area of Credit Risk and, in recognition of the increasing popularity of Lévy finance, there is considerable new material on: · Infinite divisibility and Lévy processes · Lévy-based models in incomplete markets Further material such as exercises, solutions to exercises and lecture slides are also available via the web to provide additional support for lecturers.