Can the Black-Scholes-Merton Model Survive under Transaction Costs? An Affirmative Answer PDF Download
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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:
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: 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: 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: 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: Donald MacKenzie
Publisher: MIT Press
ISBN: 0262250047
Category : Technology & Engineering
Languages : en
Pages : 782
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Book Description
In An Engine, Not a Camera, Donald MacKenzie argues that the emergence of modern economic theories of finance affected financial markets in fundamental ways. These new, Nobel Prize-winning theories, based on elegant mathematical models of markets, were not simply external analyses but intrinsic parts of economic processes. Paraphrasing Milton Friedman, MacKenzie says that economic models are an engine of inquiry rather than a camera to reproduce empirical facts. More than that, the emergence of an authoritative theory of financial markets altered those markets fundamentally. For example, in 1970, there was almost no trading in financial derivatives such as "futures." By June of 2004, derivatives contracts totaling $273 trillion were outstanding worldwide. MacKenzie suggests that this growth could never have happened without the development of theories that gave derivatives legitimacy and explained their complexities. MacKenzie examines the role played by finance theory in the two most serious crises to hit the world's financial markets in recent years: the stock market crash of 1987 and the market turmoil that engulfed the hedge fund Long-Term Capital Management in 1998. He also looks at finance theory that is somewhat beyond the mainstream—chaos theorist Benoit Mandelbrot's model of "wild" randomness. MacKenzie's pioneering work in the social studies of finance will interest anyone who wants to understand how America's financial markets have grown into their current form.
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: Andreas Jobst
Publisher: International Monetary Fund
ISBN: 1475505590
Category : Business & Economics
Languages : en
Pages : 70
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Book Description
Little progress has been made so far in addressing—in a comprehensive way—the externalities caused by impact of the interconnectedness within institutions and markets on funding and market liquidity risk within financial systems. The Systemic Risk-adjusted Liquidity (SRL) model combines option pricing with market information and balance sheet data to generate a probabilistic measure of the frequency and severity of multiple entities experiencing a joint liquidity event. It links a firm’s maturity mismatch between assets and liabilities impacting the stability of its funding with those characteristics of other firms, subject to individual changes in risk profiles and common changes in market conditions. This approach can then be used (i) to quantify an individual institution’s time-varying contribution to system-wide liquidity shortfalls and (ii) to price liquidity risk within a macroprudential framework that, if used to motivate a capital charge or insurance premia, provides incentives for liquidity managers to internalize the systemic risk of their decisions. The model can also accommodate a stress testing approach for institution-specific and/or general funding shocks that generate estimates of systemic liquidity risk (and associated charges) under adverse scenarios.
Author: Robert A Jarrow
Publisher: World Scientific
ISBN: 9814470635
Category : Business & Economics
Languages : en
Pages : 609
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Book Description
This book is a collection of original papers by Robert Jarrow that contributed to significant advances in financial economics. Divided into three parts, Part I concerns option pricing theory and its foundations. The papers here deal with the famous Black-Scholes-Merton model, characterizations of the American put option, and the first applications of arbitrage pricing theory to market manipulation and liquidity risk.Part II relates to pricing derivatives under stochastic interest rates. Included is the paper introducing the famous Heath-Jarrow-Morton (HJM) model, together with papers on topics like the characterization of the difference between forward and futures prices, the forward price martingale measure, and applications of the HJM model to foreign currencies and commodities.Part III deals with the pricing of financial derivatives considering both stochastic interest rates and the likelihood of default. Papers cover the reduced form credit risk model, in particular the original Jarrow and Turnbull model, the Markov model for credit rating transitions, counterparty risk, and diversifiable default risk.
Author: Richard R. Lindsey
Publisher: John Wiley & Sons
ISBN: 1118044754
Category : Business & Economics
Languages : en
Pages : 406
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Book Description
Praise for How I Became a Quant "Led by two top-notch quants, Richard R. Lindsey and Barry Schachter, How I Became a Quant details the quirky world of quantitative analysis through stories told by some of today's most successful quants. For anyone who might have thought otherwise, there are engaging personalities behind all that number crunching!" --Ira Kawaller, Kawaller & Co. and the Kawaller Fund "A fun and fascinating read. This book tells the story of how academics, physicists, mathematicians, and other scientists became professional investors managing billions." --David A. Krell, President and CEO, International Securities Exchange "How I Became a Quant should be must reading for all students with a quantitative aptitude. It provides fascinating examples of the dynamic career opportunities potentially open to anyone with the skills and passion for quantitative analysis." --Roy D. Henriksson, Chief Investment Officer, Advanced Portfolio Management "Quants"--those who design and implement mathematical models for the pricing of derivatives, assessment of risk, or prediction of market movements--are the backbone of today's investment industry. As the greater volatility of current financial markets has driven investors to seek shelter from increasing uncertainty, the quant revolution has given people the opportunity to avoid unwanted financial risk by literally trading it away, or more specifically, paying someone else to take on the unwanted risk. How I Became a Quant reveals the faces behind the quant revolution, offering you?the?chance to learn firsthand what it's like to be a?quant today. In this fascinating collection of Wall Street war stories, more than two dozen quants detail their roots, roles, and contributions, explaining what they do and how they do it, as well as outlining the sometimes unexpected paths they have followed from the halls of academia to the front lines of an investment revolution.
