Stochastic Dominance And Option Pricing In Discrete And Continuous Time

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Stochastic Dominance and Option Pricing in Discrete and Continuous Time

Author : Ioan Mihai Oancea
Publisher :
ISBN 13 :
Total Pages : 48 pages
Book Rating : 4.:/5 (129 download)

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Book Synopsis Stochastic Dominance and Option Pricing in Discrete and Continuous Time by : Ioan Mihai Oancea

Download or read book Stochastic Dominance and Option Pricing in Discrete and Continuous Time written by Ioan Mihai Oancea and published by . This book was released on 2007 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper examines option pricing in a universe in which it is assumed that markets are incomplete. It derives multiperiod discrete time option bounds based on stochastic dominance considerations for a risk-averse investor holding only the underlying asset, the riskless asset and (possibly) the option for any type of underlying asset distribution, discrete or continuous. It then considers the limit behavior of these bounds for special categories of such distributions as trading becomes progressively more dense, tending to continuous time. It is shown that these bounds nest as special cases most, if not all, existing arbitrage- and equilibrium-based option pricing models. Thus, when the underlying asset follows a generalized diffusion both bounds converge to a single value. For jump-diffusion processes, stochastic volatility models, and GARCH processes the bounds remain distinct and define several new option pricing results containing as special cases the arbitrage-based results.

On Stochastic Dominance Optionbounds in Discrete and Continuous Space and Time with Stochastic and Deterministic Volatility and Pricing with Constant Relative Risk Aversion

Download On Stochastic Dominance Optionbounds in Discrete and Continuous Space and Time with Stochastic and Deterministic Volatility and Pricing with Constant Relative Risk Aversion PDF Online Free

Author : Eli Rose
Publisher :
ISBN 13 :
Total Pages : 103 pages
Book Rating : 4.:/5 (128 download)

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Book Synopsis On Stochastic Dominance Optionbounds in Discrete and Continuous Space and Time with Stochastic and Deterministic Volatility and Pricing with Constant Relative Risk Aversion by : Eli Rose

Download or read book On Stochastic Dominance Optionbounds in Discrete and Continuous Space and Time with Stochastic and Deterministic Volatility and Pricing with Constant Relative Risk Aversion written by Eli Rose and published by . This book was released on 2020 with total page 103 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis makes original contributions to the field of asset pricing, which is a field dedicated to describing the prices of financial instruments and their characteristics. The prices of these financial instruments are determined by the behavior of investors who buy and sell them, and so asset pricing is ultimately done by modeling the behavior of investors. One method for achieving this is through the framework of stochastic dominance. This thesis specifically deals with a specific class of financial instruments called European options and reviews the literature on stochastic dominance option pricing and discusses new methods for finding stochastic dominance bounds on options in both discrete and continuous time under both deterministic and stochastic volatility. The results presented here extends the works of Ritchken and Kuo (1988) and Perrakis and Ryan (1984). Furthermore, stochastic dominance bounds for Heston's (1993) stochastic volatility model are obtained under certain assumptions. Finally, this thesis extends the work of Carr and Madan (1999) and solves for the characteristic function of the call price given the physical characteristic function under the CRRA utility model.

Stochastic Dominance Option Pricing

Author : Ioan Mihai Oancea
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (11 download)

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Book Synopsis Stochastic Dominance Option Pricing by : Ioan Mihai Oancea

Download or read book Stochastic Dominance Option Pricing written by Ioan Mihai Oancea and published by . This book was released on 2006 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis examines the pricing of options under several models with market incompleteness. The theoretical approach relies on the absence of stochastically dominating portfolios containing the underlying asset, the option and the riskless bond. The stochastic dominance approach provides two bounds on the equilibrium pricing of options by risk-averse investors. The two bounds are discounted conditional expectations of the option payoff under two probability measures. This research generalizes the previous stochastic dominance pricing results in discrete time to non-i.i.d. underlying asset return processes and to contingent claims with non-convex payoffs. The new results are then used to examine the stochastic dominance pricing bounds for several discrete and continuous time processes of the underlying asset. The continuous time bounds are obtained by constructing a sequence of discrete approximations that converge weakly to a given continuous time process. The weak convergence property provides the convergence of the two option bounds, which are discounted expectations of the option payoff. In the case of a univariate diffusion process, the two option bounds converge to a common limit. The two bounds converge to distinct limits when the underlying asset follows a jump-diffusion mixture. The non-iid stochastic dominance pricing results are then applied to the pricing of options for a LARCH specification of the underlying asset returns. The two stochastic dominance bounds are obtained both for conditional normal and non-normal returns. The impact of the model estimation error is examined by generating a return sample from a known model and computing the stochastic dominance bounds implied by several estimated models.

Stochastic Dominance Option Pricing

Author : Stylianos Perrakis
Publisher : Springer
ISBN 13 : 3030115909
Total Pages : 277 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Stochastic Dominance Option Pricing by : Stylianos Perrakis

Download or read book Stochastic Dominance Option Pricing written by Stylianos Perrakis and published by Springer. This book was released on 2019-05-03 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Introduction to Option Pricing Theory

Author : Gopinath Kallianpur
Publisher : Birkhäuser
ISBN 13 : 9781461267966
Total Pages : 0 pages
Book Rating : 4.2/5 (679 download)

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Book Synopsis Introduction to Option Pricing Theory by : Gopinath Kallianpur

Download or read book Introduction to Option Pricing Theory written by Gopinath Kallianpur and published by Birkhäuser. This book was released on 2012-10-06 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the appearance of seminal works by R. Merton, and F. Black and M. Scholes, stochastic processes have assumed an increasingly important role in the development of the mathematical theory of finance. This work examines, in some detail, that part of stochastic finance pertaining to option pricing theory. Thus the exposition is confined to areas of stochastic finance that are relevant to the theory, omitting such topics as futures and term-structure. This self-contained work begins with five introductory chapters on stochastic analysis, making it accessible to readers with little or no prior knowledge of stochastic processes or stochastic analysis. These chapters cover the essentials of Ito's theory of stochastic integration, integration with respect to semimartingales, Girsanov's Theorem, and a brief introduction to stochastic differential equations. Subsequent chapters treat more specialized topics, including option pricing in discrete time, continuous time trading, arbitrage, complete markets, European options (Black and Scholes Theory), American options, Russian options, discrete approximations, and asset pricing with stochastic volatility. In several chapters, new results are presented. A unique feature of the book is its emphasis on arbitrage, in particular, the relationship between arbitrage and equivalent martingale measures (EMM), and the derivation of necessary and sufficient conditions for no arbitrage (NA). {\it Introduction to Option Pricing Theory} is intended for students and researchers in statistics, applied mathematics, business, or economics, who have a background in measure theory and have completed probability theory at the intermediate level. The work lends itself to self-study, as well as to a one-semester course at the graduate level.

Discrete Time vs Continuous Time Stock-Price Dynamics and Implications for Option Pricing

Author : Damiano Brigo
Publisher :
ISBN 13 :
Total Pages : 19 pages
Book Rating : 4.:/5 (129 download)

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Book Synopsis Discrete Time vs Continuous Time Stock-Price Dynamics and Implications for Option Pricing by : Damiano Brigo

Download or read book Discrete Time vs Continuous Time Stock-Price Dynamics and Implications for Option Pricing written by Damiano Brigo and published by . This book was released on 2002 with total page 19 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the present paper we construct stock price processes with the same marginal log-normal law as that of a geometric Brownian motion and also with the same transition density (and returns' distributions) between any two instants in a given discrete-time grid. We then illustrate how option prices based on such processes differ from Black and Scholes', in that option prices can be either arbitrarily close to the option intrinsic value or arbitrarily close to the underlying stock price. We also explain that this is due to the particular way one models the stock-price process in-between the grid time instants which are relevant for trading. The theoretical result concerning scalar stochastic differential equations with prescribed diffusion coefficient whose densities evolve in a prescribed exponential family, on which part of the paper is based, is presented in detail.

The Stochastic Dominance Valuation of Options Under Transaction Costs

Author : Michal Czerwonko
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (11 download)

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Book Synopsis The Stochastic Dominance Valuation of Options Under Transaction Costs by : Michal Czerwonko

Download or read book The Stochastic Dominance Valuation of Options Under Transaction Costs written by Michal Czerwonko and published by . This book was released on 2008 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the first essay American call and put options on the S & P 500 index futures that violate the stochastic dominance bounds of Constantinides and Perrakis (CP, 2007) over 1983-2006 are identified as potentially profitable investment opportunities. Call bid prices more frequently violate their upper bound than put bid prices do, while evidence of underpriced calls and puts over this period is scant. In out-of-sample tests, the inclusion of short positions in such overpriced calls, puts, and, particularly, straddles in the market portfolio is shown to increase the expected utility of any risk averse investor and also increase the Sharpe ratio, net of transaction costs and bid-ask spreads. The results are strongly supportive of mispricing and also strongly supportive of the CP bounds as screening mechanisms for mispriced options. The second essay introduces a result for call lower bound more powerful that the one applied in the first part of this thesis. The Proposition 5 call lower bound in Constantinides and Perrakis (2002) is shown to have a non-trivial limit as the time interval tends to zero. This establishes the bound as the first call lower bound known in the literature on derivative pricing in the presence of transaction costs with a non-trivial limit. The bound is shown to be tight even for a low number of time subdivisions. Novel numerical methods to derive recursive expectations under a Markovian but non-identically distributed stochastic process are presented. The third essay relaxes an assumption in the first part of this thesis on the optimal trading policy in the presence of transaction costs. We derive the boundaries of the region of no transaction when the risky asset follows a mixed jump-diffusion instead of a simple diffusion process. These boundaries are shown to differ from their diffusion counterparts in relation to the jump intensity for lognormally distributed jump size. A general numerical approach is presented for iid risky asset returns in discrete time. An error in an earlier published work on the region of no transaction for discretized diffusions is demonstrated and corrected results are presented. Comparative results with a recent study on the same topic are presented and it is shown that the numerical algorithm has equally attractive approximation properties to the unknown continuous time limit.

Handbook Of Financial Econometrics, Mathematics, Statistics, And Machine Learning (In 4 Volumes)

Author : Cheng Few Lee
Publisher : World Scientific
ISBN 13 : 9811202400
Total Pages : 5053 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Handbook Of Financial Econometrics, Mathematics, Statistics, And Machine Learning (In 4 Volumes) by : Cheng Few Lee

Download or read book Handbook Of Financial Econometrics, Mathematics, Statistics, And Machine Learning (In 4 Volumes) written by Cheng Few Lee and published by World Scientific. This book was released on 2020-07-30 with total page 5053 pages. Available in PDF, EPUB and Kindle. Book excerpt: This four-volume handbook covers important concepts and tools used in the fields of financial econometrics, mathematics, statistics, and machine learning. Econometric methods have been applied in asset pricing, corporate finance, international finance, options and futures, risk management, and in stress testing for financial institutions. This handbook discusses a variety of econometric methods, including single equation multiple regression, simultaneous equation regression, and panel data analysis, among others. It also covers statistical distributions, such as the binomial and log normal distributions, in light of their applications to portfolio theory and asset management in addition to their use in research regarding options and futures contracts.In both theory and methodology, we need to rely upon mathematics, which includes linear algebra, geometry, differential equations, Stochastic differential equation (Ito calculus), optimization, constrained optimization, and others. These forms of mathematics have been used to derive capital market line, security market line (capital asset pricing model), option pricing model, portfolio analysis, and others.In recent times, an increased importance has been given to computer technology in financial research. Different computer languages and programming techniques are important tools for empirical research in finance. Hence, simulation, machine learning, big data, and financial payments are explored in this handbook.Led by Distinguished Professor Cheng Few Lee from Rutgers University, this multi-volume work integrates theoretical, methodological, and practical issues based on his years of academic and industry experience.

Stochastic Dominance Bounds on Option Prices in the Presence of Transaction Costs

Author : Michal Czerwonko
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (13 download)

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Book Synopsis Stochastic Dominance Bounds on Option Prices in the Presence of Transaction Costs by : Michal Czerwonko

Download or read book Stochastic Dominance Bounds on Option Prices in the Presence of Transaction Costs written by Michal Czerwonko and published by . This book was released on 2002 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Handbooks in Operations Research and Management Science: Financial Engineering

Author : John R. Birge
Publisher : Elsevier
ISBN 13 : 9780080553252
Total Pages : 1026 pages
Book Rating : 4.5/5 (532 download)

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Book Synopsis Handbooks in Operations Research and Management Science: Financial Engineering by : John R. Birge

Download or read book Handbooks in Operations Research and Management Science: Financial Engineering written by John R. Birge and published by Elsevier. This book was released on 2007-11-16 with total page 1026 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Stochastic Dominance Option Pricing Bounds with Probability Weighting Functions

Author : 林友嵐
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (124 download)

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Book Synopsis Stochastic Dominance Option Pricing Bounds with Probability Weighting Functions by : 林友嵐

Download or read book Stochastic Dominance Option Pricing Bounds with Probability Weighting Functions written by 林友嵐 and published by . This book was released on 2020 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Option Pricing Under Stochastic Dominance

Author : Stylianos Perrakis
Publisher :
ISBN 13 :
Total Pages : 28 pages
Book Rating : 4.:/5 (159 download)

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Book Synopsis Option Pricing Under Stochastic Dominance by : Stylianos Perrakis

Download or read book Option Pricing Under Stochastic Dominance written by Stylianos Perrakis and published by . This book was released on 1981 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Intermediate Futures And Options: An Active Learning Approach

Author : Cheng Few Lee
Publisher : World Scientific
ISBN 13 : 9811280282
Total Pages : 1001 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Intermediate Futures And Options: An Active Learning Approach by : Cheng Few Lee

Download or read book Intermediate Futures And Options: An Active Learning Approach written by Cheng Few Lee and published by World Scientific. This book was released on 2023-10-16 with total page 1001 pages. Available in PDF, EPUB and Kindle. Book excerpt: Futures and Options are concerned with the valuation of derivatives and their application to hedging and speculating investments. This book contains 22 chapters and is divided into five parts. Part I contains an overview including a general introduction as well as an introduction to futures, options, swaps, and valuation theories. Part II: Forwards and Futures discusses futures valuation, the futures market, hedging strategies, and various types of futures. Part III: Option Theories and Applications includes both the basic and advanced valuation of options and option strategies in addition to index and currency options. Part IV: Advanced Analyses of Options takes a look at higher level strategies used to quantitatively approach the analysis of options. Part V: Special Topics of Options and Futures covers the applications of more obscure and alternative methods in derivatives as well as the derivation of the Black-Scholes Option Pricing Model.This book applies an active interdisciplinary approach to presenting the material; in other words, three projects involving the use of real-world financial data on derivative, in addition to homework assignments, are made available for students in this book.

Almost First Stochastic Dominance

Author : James Huang
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (129 download)

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Book Synopsis Almost First Stochastic Dominance by : James Huang

Download or read book Almost First Stochastic Dominance written by James Huang and published by . This book was released on 2007 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we apply the recently developed concept of almost first stochastic dominance to derive option bounds given the prices of any number of concurrently expiring options. Almost first stochastic dominance is adjusted first stochastic dominance which bars extreme utility functions that cause practical paradoxes. We show that the optimal almost first stochastic dominance option bounds are given by piecewise constant pricing kernels. The number of the segments of the optimal piecewise constant pricing kernel depends on the number of observed options. We then use the above model to test almost first stochastic dominance using data from options markets.

Stochastic Dominance

Author : Haim Levy
Publisher : Springer Science & Business Media
ISBN 13 : 0387293116
Total Pages : 439 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Stochastic Dominance by : Haim Levy

Download or read book Stochastic Dominance written by Haim Levy and published by Springer Science & Business Media. This book was released on 2006-08-25 with total page 439 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to investment decision-making under uncertainty. The book covers three basic approaches to this process: the stochastic dominance approach; the mean-variance approach; and the non-expected utility approach, focusing on prospect theory and its modified version, cumulative prospect theory. Each approach is discussed and compared. In addition, this volume examines cases in which stochastic dominance rules coincide with the mean-variance rule and considers how contradictions between these two approaches may occur.

Can the Black-Scholes Model Survive under Transaction Costs? An Affirmative Answer

Author : Michal Czerwonko
Publisher :
ISBN 13 :
Total Pages : 37 pages
Book Rating : 4.:/5 (129 download)

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Book Synopsis Can the Black-Scholes Model Survive under Transaction Costs? An Affirmative Answer by : Michal Czerwonko

Download or read book Can the Black-Scholes Model Survive under Transaction Costs? An Affirmative Answer written by Michal Czerwonko and published by . This book was released on 2008 with total page 37 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

The Oxford Guide to Financial Modeling

Author : Thomas S. Y. Ho
Publisher : Oxford University Press
ISBN 13 : 0199923981
Total Pages : 762 pages
Book Rating : 4.1/5 (999 download)

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Book Synopsis The Oxford Guide to Financial Modeling by : Thomas S. Y. Ho

Download or read book The Oxford Guide to Financial Modeling written by Thomas S. Y. Ho and published by Oxford University Press. This book was released on 2004-01-15 with total page 762 pages. Available in PDF, EPUB and Kindle. Book excerpt: The essential premise of this book is that theory and practice are equally important in describing financial modeling. In it the authors try to strike a balance in their discussions between theories that provide foundations for financial models and the institutional details that provide the context for applications of the models. The book presents the financial models of stock and bond options, exotic options, investment grade and high-yield bonds, convertible bonds, mortgage-backed securities, liabilities of financial institutions--the business model and the corporate model. It also describes the applications of the models to corporate finance. Furthermore, it relates the models to financial statements, risk management for an enterprise, and asset/liability management with illiquid instruments. The financial models are progressively presented from option pricing in the securities markets to firm valuation in corporate finance, following a format to emphasize the three aspects of a model: the set of assumptions, the model specification, and the model applications. Generally, financial modeling books segment the world of finance as "investments," "financial institutions," "corporate finance," and "securities analysis," and in so doing they rarely emphasize the relationships between the subjects. This unique book successfully ties the thought processes and applications of the financial models together and describes them as one process that provides business solutions. Created as a companion website to the book readers can visit www.thomasho.com to gain deeper understanding of the book's financial models. Interested readers can build and test the models described in the book using Excel, and they can submit their models to the site. Readers can also use the site's forum to discuss the models and can browse server based models to gain insights into the applications of the models. For those using the book in meetings or class settings the site provides Power Point descriptions of the chapters. Students can use available question banks on the chapters for studying.