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Author: Erhan Bayraktar
Publisher:
ISBN:
Category :
Languages : en
Pages : 24
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Book Description
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: Erhan Bayraktar
Publisher:
ISBN:
Category :
Languages : en
Pages : 24
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Book Description
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: Alet Roux
Publisher:
ISBN:
Category :
Languages : en
Pages : 18
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Book Description
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: Erindi Allaj
Publisher:
ISBN:
Category :
Languages : en
Pages : 33
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Book Description
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: Erhan Bayraktar
Publisher:
ISBN:
Category :
Languages : en
Pages : 9
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Book Description
We show that the results of the Fundamental Theorem of Asset Pricing and the super-hedging theorem can be extended to the case in which the options available for static hedging (hedging options) are quoted with bid-ask spreads. In this set-up, we need to work with the notion of robust no-arbitrage which turns out to be equivalent to no-arbitrage under the additional assumption that hedging options with non-zero spread are non-redundant. A key result is the closedness of the set of attainable claims, which requires a new proof in our setting.
Author: Pierre Henry-Labordere
Publisher: CRC Press
ISBN: 1351666223
Category : Mathematics
Languages : en
Pages : 115
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Book Description
Model-free Hedging: A Martingale Optimal Transport Viewpoint focuses on the computation of model-independent bounds for exotic options consistent with market prices of liquid instruments such as Vanilla options. The author gives an overview of Martingale Optimal Transport, highlighting the differences between the optimal transport and its martingale counterpart. This topic is then discussed in the context of mathematical finance.
Author: Frédéric Vrins
Publisher: MDPI
ISBN: 3039287605
Category : Business & Economics
Languages : en
Pages : 190
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Book Description
Credit risk remains one of the major risks faced by most financial and credit institutions. It is deeply connected to the real economy due to the systemic nature of some banks, but also because well-managed lending facilities are key for wealth creation and technological innovation. This book is a collection of innovative papers in the field of credit risk management. Besides the probability of default (PD), the major driver of credit risk is the loss given default (LGD). In spite of its central importance, LGD modeling remains largely unexplored in the academic literature. This book proposes three contributions in the field. Ye & Bellotti exploit a large private dataset featuring non-performing loans to design a beta mixture model. Their model can be used to improve recovery rate forecasts and, therefore, to enhance capital requirement mechanisms. François uses instead the price of defaultable instruments to infer the determinants of market-implied recovery rates and finds that macroeconomic and long-term issuer specific factors are the main determinants of market-implied LGDs. Cheng & Cirillo address the problem of modeling the dependency between PD and LGD using an original, urn-based statistical model. Fadina & Schmidt propose an improvement of intensity-based default models by accounting for ambiguity around both the intensity process and the recovery rate. Another topic deserving more attention is trade credit, which consists of the supplier providing credit facilities to his customers. Whereas this is likely to stimulate exchanges in general, it also magnifies credit risk. This is a difficult problem that remains largely unexplored. Kanapickiene & Spicas propose a simple but yet practical model to assess trade credit risk associated with SMEs and microenterprises operating in Lithuania. Another topical area in credit risk is counterparty risk and all other adjustments (such as liquidity and capital adjustments), known as XVA. Chataignier & Crépey propose a genetic algorithm to compress CVA and to obtain affordable incremental figures. Anagnostou & Kandhai introduce a hidden Markov model to simulate exchange rate scenarios for counterparty risk. Eventually, Boursicot et al. analyzes CoCo bonds, and find that they reduce the total cost of debt, which is positive for shareholders. In a nutshell, all the featured papers contribute to shedding light on various aspects of credit risk management that have, so far, largely remained unexplored.
Author: Sumru Altug
Publisher: Cambridge University Press
ISBN: 1139474367
Category : Business & Economics
Languages : en
Pages : 702
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Book Description
This introduction to general equilibrium modelling takes an integrated approach to the analysis of macroeconomics and finance. It provides students, practitioners, and policymakers with an easily accessible set of tools that can be used to analyze a wide range of economic phenomena. Key features: • Provides a consistent framework for understanding dynamic economic models • Introduces key concepts in finance in a discrete time setting • Develops simple recursive approach for analyzing a variety of problems in a dynamic, stochastic environment • Sequentially builds up the analysis of consumption, production, and investment models to study their implications for allocations and asset prices • Reviews business cycle analysis and the business cycle implications of monetary and international models • Covers latest research on asset pricing in overlapping generations models and on models with borrowing constraints and transaction costs • Includes end-of-chapter exercises allowing readers to monitor their understanding of each topic Online resources are available at www.cambridge.org/altug_labadie
Author: Markus Leippold
Publisher:
ISBN:
Category :
Languages : en
Pages : 22
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Book Description
It is common in the financial mathematics literature to start by fixing a probability space $( Omega, mathcal F, mathbb P)$, on which the underlying price process is defined. We depart from this route in that we do not fix the prior $ mathbb P$. Under very general assumptions, we recover the Fundamental Theorem of Asset Pricing in discrete time under either a multiple-priors or a prior-free setting. We only require that $( Omega, mathcal F)$ is a measurable space, while the multiple priors can be non-equivalent. Furthermore, the initial price of our market model does not need to be constant, but only measurable.
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Author: Lionel Martellini
Publisher:
ISBN:
Category :
Languages : en
Pages : 390
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Book Description
