Can the Black-Scholes Model Survive under Transaction Costs? An Affirmative Answer PDF Download
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Author: Michal Czerwonko
Publisher:
ISBN:
Category :
Languages : en
Pages : 37
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Book Description
We examine the stochastic dominance bounds for call options in the presence of proportional transaction costs, developed in a discrete time and for a discrete or continuous state model of the returns of the underlying asset by Constantinides and Perrakis (CP, 2002, 2007). We consider a lognormal diffusion model of these returns and we formulate a discrete time trading version that converges to diffusion as the time partition becomes progressively more dense. Given the existence of a partition-independent and tight upper bound already derived in CP (2002), we focus on the lower bound, for which the results of that study were not available in a useful formulation. We then show that the CP lower bound for European call options converges to a non-trivial and tight limit that is a function of the transaction cost parameter. This limit defines a reservation purchase price under realistic trading conditions for the call options. The limit is a Black-Scholes type expression that becomes equal to the exact Black-Scholes value if the transaction cost parameter is set equal to zero, thus providing the only known generalization of the Black-Scholes model that produces useful results under transaction costs. We also develop a novel numerical algorithm that computes the CP lower bound for any discrete time partition and converges to the theoretical continuous time limit in a relatively small number of iterations. Last, we extend the lower bound results to American index options.
Author: Michal Czerwonko
Publisher:
ISBN:
Category :
Languages : en
Pages : 37
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Book Description
We examine the stochastic dominance bounds for call options in the presence of proportional transaction costs, developed in a discrete time and for a discrete or continuous state model of the returns of the underlying asset by Constantinides and Perrakis (CP, 2002, 2007). We consider a lognormal diffusion model of these returns and we formulate a discrete time trading version that converges to diffusion as the time partition becomes progressively more dense. Given the existence of a partition-independent and tight upper bound already derived in CP (2002), we focus on the lower bound, for which the results of that study were not available in a useful formulation. We then show that the CP lower bound for European call options converges to a non-trivial and tight limit that is a function of the transaction cost parameter. This limit defines a reservation purchase price under realistic trading conditions for the call options. The limit is a Black-Scholes type expression that becomes equal to the exact Black-Scholes value if the transaction cost parameter is set equal to zero, thus providing the only known generalization of the Black-Scholes model that produces useful results under transaction costs. We also develop a novel numerical algorithm that computes the CP lower bound for any discrete time partition and converges to the theoretical continuous time limit in a relatively small number of iterations. Last, we extend the lower bound results to American index options.
Author: Stylianos Perrakis
Publisher:
ISBN:
Category :
Languages : en
Pages : 48
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Book Description
We derive a reservation purchase price for a call option price under proportional transaction costs. The price is derived in discrete time for a general distribution of the returns of the underlying asset, as in Constantinides and Perrakis (CP, 2002, 2007). We then consider a lognormal diffusion model of these returns, and we formulate a discrete time trading version that converges to diffusion as the time partition becomes progressively more dense. Given the existence of a partition-independent and tight upper bound already derived in CP (2002), we focus on the lower bound. We show that the CP approach results in a lower bound for European call options that converges to a non-trivial and tight limit that is a function of the transaction cost parameter. This limit defines a reservation purchase price under realistic trading conditions for the call options and becomes equal to the exact Black-Scholes-Merton value if the transaction cost parameter is set equal to zero. We also develop a novel numerical algorithm that computes the CP lower bound for any discrete time partition and converges to the theoretical continuous time limit in a relatively small number of iterations. Last, we extend the lower bound results to American index and index futures options.
Author: Stylianos Perrakis
Publisher: Springer
ISBN: 3030115909
Category : Business & Economics
Languages : en
Pages : 277
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Book Description
This book illustrates the application of the economic concept of stochastic dominance to option markets and presents an alternative option pricing paradigm to the prevailing no arbitrage simultaneous equilibrium in the frictionless underlying and option markets. This new methodology was developed primarily by the author, working independently or jointly with other co-authors, over the course of more than thirty years. Among others, it yields the fundamental Black-Scholes-Merton option value when markets are complete, presents a new approach to the pricing of rare event risk, and uncovers option mispricing that leads to tradeable strategies in the presence of transaction costs. In the latter case it shows how a utility-maximizing investor trading in the market and a riskless bond, subject to proportional transaction costs, can increase his/her expected utility by overlaying a zero-net-cost portfolio of options bought at their ask price and written at their bid price, irrespective of the specific form of the utility function. The book contains a unified presentation of these methods and results, making it a highly readable supplement for educators and sophisticated professionals working in the popular field of option pricing. It also features a foreword by George Constantinides, the Leo Melamed Professor of Finance at the Booth School of Business, University of Chicago, USA, who was a co-author in several parts of the book.
Author: Marek Capiński
Publisher: Cambridge University Press
ISBN: 1107001692
Category : Business & Economics
Languages : en
Pages : 179
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Book Description
Master the essential mathematical tools required for option pricing within the context of a specific, yet fundamental, pricing model.
Author: Söhnke M. Bartram
Publisher: CFA Institute Research Foundation
ISBN: 195292703X
Category : Business & Economics
Languages : en
Pages : 95
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Book Description
Artificial intelligence (AI) has grown in presence in asset management and has revolutionized the sector in many ways. It has improved portfolio management, trading, and risk management practices by increasing efficiency, accuracy, and compliance. In particular, AI techniques help construct portfolios based on more accurate risk and return forecasts and more complex constraints. Trading algorithms use AI to devise novel trading signals and execute trades with lower transaction costs. AI also improves risk modeling and forecasting by generating insights from new data sources. Finally, robo-advisors owe a large part of their success to AI techniques. Yet the use of AI can also create new risks and challenges, such as those resulting from model opacity, complexity, and reliance on data integrity.
Author: Andrew Ang
Publisher: Now Publishers Inc
ISBN: 1601984685
Category : Business & Economics
Languages : en
Pages : 99
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Book Description
The Efficient Market Hypothesis (EMH) asserts that, at all times, the price of a security reflects all available information about its fundamental value. The implication of the EMH for investors is that, to the extent that speculative trading is costly, speculation must be a loser's game. Hence, under the EMH, a passive strategy is bound eventually to beat a strategy that uses active management, where active management is characterized as trading that seeks to exploit mispriced assets relative to a risk-adjusted benchmark. The EMH has been refined over the past several decades to reflect the realism of the marketplace, including costly information, transactions costs, financing, agency costs, and other real-world frictions. The most recent expressions of the EMH thus allow a role for arbitrageurs in the market who may profit from their comparative advantages. These advantages may include specialized knowledge, lower trading costs, low management fees or agency costs, and a financing structure that allows the arbitrageur to undertake trades with long verification periods. The actions of these arbitrageurs cause liquid securities markets to be generally fairly efficient with respect to information, despite some notable anomalies.
Author: John C. Cox
Publisher: Prentice Hall
ISBN:
Category : Business & Economics
Languages : en
Pages : 518
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Book Description
Includes the first published detailed description of option exchange operations, the first published treatment using only elementary mathematics and the first step-by-step procedure for implementing the Black-Scholes formula in actual trading.
Author: Deniz Ozenbas
Publisher: Springer Nature
ISBN: 3030748170
Category : Business enterprises
Languages : en
Pages : 111
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Book Description
This open access book addresses four standard business school subjects: microeconomics, macroeconomics, finance and information systems as they relate to trading, liquidity, and market structure. It provides a detailed examination of the impact of trading costs and other impediments of trading that the authors call rictions It also presents an interactive simulation model of equity market trading, TraderEx, that enables students to implement trading decisions in different market scenarios and structures. Addressing these topics shines a bright light on how a real-world financial market operates, and the simulation provides students with an experiential learning opportunity that is informative and fun. Each of the chapters is designed so that it can be used as a stand-alone module in an existing economics, finance, or information science course. Instructor resources such as discussion questions, Powerpoint slides and TraderEx exercises are available online.
Author: Jaksa Cvitanic
Publisher: MIT Press
ISBN: 9780262033206
Category : Business & Economics
Languages : en
Pages : 528
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Book Description
An innovative textbook for use in advanced undergraduate and graduate courses; accessible to students in financial mathematics, financial engineering and economics. Introduction to the Economics and Mathematics of Financial Markets fills the longstanding need for an accessible yet serious textbook treatment of financial economics. The book provides a rigorous overview of the subject, while its flexible presentation makes it suitable for use with different levels of undergraduate and graduate students. Each chapter presents mathematical models of financial problems at three different degrees of sophistication: single-period, multi-period, and continuous-time. The single-period and multi-period models require only basic calculus and an introductory probability/statistics course, while an advanced undergraduate course in probability is helpful in understanding the continuous-time models. In this way, the material is given complete coverage at different levels; the less advanced student can stop before the more sophisticated mathematics and still be able to grasp the general principles of financial economics. The book is divided into three parts. The first part provides an introduction to basic securities and financial market organization, the concept of interest rates, the main mathematical models, and quantitative ways to measure risks and rewards. The second part treats option pricing and hedging; here and throughout the book, the authors emphasize the Martingale or probabilistic approach. Finally, the third part examines equilibrium models—a subject often neglected by other texts in financial mathematics, but included here because of the qualitative insight it offers into the behavior of market participants and pricing.
Author: François-Serge Lhabitant
Publisher: John Wiley & Sons
ISBN: 0470687770
Category : Business & Economics
Languages : en
Pages : 573
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Book Description
"An excellent and comprehensive source of information on hedge funds! From a quantitative view Lhabitant has done it once again by meticulously looking at the important topics in the hedge fund industry. This book has a tremendous wealth of information and is a valuable addition to the hedge fund literature. In addition, it will benefit institutional investors, high net worth individuals, academics and anyone interested in learning more about this fascinating and often mysterious world of privately managed money. Written by one of the most respected practitioners and academics in the area of hedge funds." —Greg N. Gregoriou, Professor of finance and research coordinator in the School of Business and Economics at Plattsburgh State University of New York "This is a landmark book on quantitative approaches to hedge funds. All those with a stake in building hedge fund portfolios will highly profit from this exhaustive guide. A must read for all those involved in hedge fund investing." —Pascal Botteron, Ph.D., Head of Hedge Fund Product Development, Pictet Asset Management "François-Serge Lhabitant's second book will prove to be a bestseller too - just like Hedge Funds: Myths and Limits. He actually manages to make quantitative analysis 'approachable'- even for those less gifted with numbers. This book, like its predecessor, includes an unprecedented mix of common sense and sophisticated technique. A fantastic guide to the 'nuts and bolts' of hedge fund analysis and a 'must' for every serious investor." —Barbara Rupf Bee, Head of Alternative Fund Investment Group, HSBC Private Bank, Switzerland "An excellent book, providing deep insights into the complex quantitative analysis of hedge funds in the most lucid and intuitive manner. A must-have supplement to Lhabitant's first book dealing with the mystical and fascinating world of hedge funds. Highly recommended!" —Vikas Agarwal, Assistant Professor of Finance, J. Mack Robinson College of Business, Georgia State University "Lhabitant has done it again! Whereas most books on hedge funds are nothing more than glorified marketing brochures, Lhabitant's new book tells it how it is in reality. Accessible and understandable but at the same time thorough and critical." —Harry M. Kat, Ph.D., Professor of Risk Management and Director Alternative Investment Research Centre, Cass Business School, City University "Lhabitant's latest work on hedge funds yet again delivers on some ambitious promises. Successfully bridging theory and practice in a highly accessible manner, those searching for a thorough yet unintimidating introduction to the quantitative methods of hedge fund analysis will not be disappointed." —Christopher L. Culp, Ph.D., Adjunct Professor of Finance, Graduate School of Business, The University of Chicago and Principal, Chicago Partners LLC
