Dynamic Arbitrage-free Asset Pricing with Proportional Transaction Costs
Author | : Xiaotie Deng |
Publisher | : London : Department of Economics, University of Western Ontario |
Total Pages | : 24 |
Release | : 2000 |
Genre | : Arbitrage |
ISBN | : |
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Author | : Xiaotie Deng |
Publisher | : London : Department of Economics, University of Western Ontario |
Total Pages | : 24 |
Release | : 2000 |
Genre | : Arbitrage |
ISBN | : |
Author | : Alet Roux |
Publisher | : |
Total Pages | : 18 |
Release | : 2007 |
Genre | : |
ISBN | : |
We extend the fundamental theorem of asset pricing to a model where the risky stock is subject to proportional transaction costs in the form of bid-ask spreads and the bank account has different interest rates for borrowing and lending. We show that such a model is free of arbitrage if and only if one can embed in it a friction-free model that is itself free of arbitrage, in the sense that there exists an artificial friction-free price for the stock between its bid and ask prices and an artificial interest rate between the borrowing and lending interest rates such that, if one discounts this stock price by this interest rate, then the resulting process is a martingale under some non-degenerate probability measure. Restricting ourselves to the simple case of a finite number of time steps and a finite number of possible outcomes for the stock price, the proof follows by combining classical arguments based on finite-dimensional separation theorems with duality results from linear optimisation.
Author | : Erhan Bayraktar |
Publisher | : |
Total Pages | : 24 |
Release | : 2015 |
Genre | : |
ISBN | : |
We prove the Fundamental Theorem of Asset Pricing for a discrete time financial market where trading is subject to proportional transaction cost and the asset price dynamic is modeled by a family of probability measures, possibly non-dominated.Using a backward-forward scheme, we show that when the market consists of a money market account and a single stock, no-arbitrage in a quasi-sure sense is equivalent to the existence of a suitable family of consistent price systems. We also show that when the market consists of multiple dynamically traded assets and satisfies efficient friction, strict no-arbitrage in a quasi-sure sense is equivalent to the existence of a suitable family of strictly consistent price systems.
Author | : Ming-Yang Kao |
Publisher | : Springer Science & Business Media |
Total Pages | : 1200 |
Release | : 2008-08-06 |
Genre | : Computers |
ISBN | : 0387307702 |
One of Springer’s renowned Major Reference Works, this awesome achievement provides a comprehensive set of solutions to important algorithmic problems for students and researchers interested in quickly locating useful information. This first edition of the reference focuses on high-impact solutions from the most recent decade, while later editions will widen the scope of the work. All entries have been written by experts, while links to Internet sites that outline their research work are provided. The entries have all been peer-reviewed. This defining reference is published both in print and on line.
Author | : Jochen E.M. Wilhelm |
Publisher | : Springer Science & Business Media |
Total Pages | : 124 |
Release | : 2012-12-06 |
Genre | : Business & Economics |
ISBN | : 3642500943 |
The present 'Introductory Lectures on Arbitrage-based Financial Asset Pricing' are a first attempt to give a comprehensive presentation of Arbitrage Theory in a discrete time framework (by the way: all the re sults given in these lectures apply to a continuous time framework but, probably, in continuous time we could achieve stronger results - of course at the price of stronger assumptions). It has been turned out in the last few years that capital market theory as derived and evolved from the capital asset pricing model (CAPM) in the middle sixties, can, to an astonishing extent, be based on arbitrage arguments only, rather than on mean-variance preferences of investors. On the other hand, ar bitrage arguments provided access to a wider range of results which could not be obtained by standard CAPM-methods, e. g. the valuation of contingent claims (derivative assets) Dr the_ investigation of futures prices. To some extent the presentation will loosely follow historical lines. A selected set of capital asset pricing models will be derived according to their historical progress and their increasing complexity as well. It will be seen that they all share common structural properties. After having made this observation the presentation will become an axiomatical one: it will be stated in precise terms what arbitrage is about and what the consequences are if markets do not allow for risk-free arbitrage opportunities. The presentation will partly be accompanied by an illus trating example: two-state option pricing.
Author | : Erindi Allaj |
Publisher | : |
Total Pages | : 33 |
Release | : 2017 |
Genre | : |
ISBN | : |
This paper studies arbitrage pricing theory in financial markets with implicit transaction costs. We extend the existing theory to include the more realistic possibility that the price at which the investors trade is dependent on the traded volume. The investors in the market always buy at the ask and sell at the bid price. Implicit transaction costs are composed of two terms, one is able to capture the bid-ask spread, and the second the price impact. Moreover, a new definition of a self-financing portfolio is obtained. The self-financing condition suggests that continuous trading is possible, but is restricted to predictable trading strategies having càdlàg (right-continuous with left limits) and càdlàg (left-continuous with right limits) paths of bounded quadratic variation and of finitely many jumps. That is, càdlàg and càdlàg predictable trading strategies of infinite variation, with finitely many jumps and of finite quadratic variation are allowed in our setting. Restricting ourselves to càdlàg predictable trading strategies, we show that the existence of an equivalent probability measure is equivalent to the absence of arbitrage opportunities, so that the first fundamental theorem of asset pricing (FFTAP) holds. It is also shown that the use of continuous and bounded variation trading strategies can improve the efficiency of hedging in a market with implicit transaction costs. To better understand how to apply the theory proposed we provide an example of an implicit transaction cost economy that is linear and non-linear in the order size.
Author | : Albert Tavidze |
Publisher | : Nova Publishers |
Total Pages | : 224 |
Release | : 2003 |
Genre | : Business & Economics |
ISBN | : 9781590338001 |
This series spans the globe presenting leading research in economics. Perhaps it is a sign of the times that economic weapons such as sanctions seem to be as powerful as or more so than tanks. International applications and examples of economic progress are invaluable in a troubled world with economic booms bursting like so many penny balloons. Intra-industry Trade; Extending Brand Equity: The Role of Goal Congruence; Foreign Direct Investment and Dissemination of Job Opening Information in China; Testing Asymmetry in a Cointegrated-VAR-Based Labor Demand Model: Italian Evidence; Negative Externality, Tacit Bargaining and Cigarette Demand: The Case of Environmental Tobacco Smoke in Japan; Does Audit Quality Influence Post-IPO Survival?; Dynamic Arbitrage-free Asset Pricing with Proportional Transaction Costs; Knowledge Structure, Technical Progress, and Underdevelopment Trap; Paternalistic Altruism, Life-Cycle Hypothesis, and the Ricardian Equivalence; Three Approaches to Multi-dimensional Screening; Index.
Author | : Darrell Duffie |
Publisher | : Princeton University Press |
Total Pages | : 488 |
Release | : 2010-01-27 |
Genre | : Business & Economics |
ISBN | : 1400829208 |
This is a thoroughly updated edition of Dynamic Asset Pricing Theory, the standard text for doctoral students and researchers on the theory of asset pricing and portfolio selection in multiperiod settings under uncertainty. The asset pricing results are based on the three increasingly restrictive assumptions: absence of arbitrage, single-agent optimality, and equilibrium. These results are unified with two key concepts, state prices and martingales. Technicalities are given relatively little emphasis, so as to draw connections between these concepts and to make plain the similarities between discrete and continuous-time models. Readers will be particularly intrigued by this latest edition's most significant new feature: a chapter on corporate securities that offers alternative approaches to the valuation of corporate debt. Also, while much of the continuous-time portion of the theory is based on Brownian motion, this third edition introduces jumps--for example, those associated with Poisson arrivals--in order to accommodate surprise events such as bond defaults. Applications include term-structure models, derivative valuation, and hedging methods. Numerical methods covered include Monte Carlo simulation and finite-difference solutions for partial differential equations. Each chapter provides extensive problem exercises and notes to the literature. A system of appendixes reviews the necessary mathematical concepts. And references have been updated throughout. With this new edition, Dynamic Asset Pricing Theory remains at the head of the field.
Author | : Pablo Koch-Medina |
Publisher | : Springer Nature |
Total Pages | : 448 |
Release | : 2020-07-16 |
Genre | : Mathematics |
ISBN | : 3030397246 |
Arbitrage Theory provides the foundation for the pricing of financial derivatives and has become indispensable in both financial theory and financial practice. This textbook offers a rigorous and comprehensive introduction to the mathematics of arbitrage pricing in a discrete-time, finite-state economy in which a finite number of securities are traded. In a first step, various versions of the Fundamental Theorem of Asset Pricing, i.e., characterizations of when a market does not admit arbitrage opportunities, are proved. The book then focuses on incomplete markets where the main concern is to obtain a precise description of the set of “market-consistent” prices for nontraded financial contracts, i.e. the set of prices at which such contracts could be transacted between rational agents. Both European-type and American-type contracts are considered. A distinguishing feature of this book is its emphasis on market-consistent prices and a systematic description of pricing rules, also at intermediate dates. The benefits of this approach are most evident in the treatment of American options, which is novel in terms of both the presentation and the scope, while also presenting new results. The focus on discrete-time, finite-state models makes it possible to cover all relevant topics while requiring only a moderate mathematical background on the part of the reader. The book will appeal to mathematical finance and financial economics students seeking an elementary but rigorous introduction to the subject; mathematics and physics students looking for an opportunity to get acquainted with a modern applied topic; and mathematicians, physicists and quantitatively inclined economists working or planning to work in the financial industry.
Author | : Yuri Kabanov |
Publisher | : Springer Science & Business Media |
Total Pages | : 306 |
Release | : 2009-12-04 |
Genre | : Business & Economics |
ISBN | : 3540681213 |
The book is the first monograph on this highly important subject.