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Approximation of forward curve models in commodity markets with arbitrage-free finite dimensional models

Benth, Fred Espen; Krühner, Paul
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 18/12/2015 Português
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26.74%
In this paper we show how to approximate a Heath-Jarrow-Morton dynamics for the forward prices in commodity markets with arbitrage-free models which have a finite dimensional state space. Moreover, we recover a closed form representation of the forward price dynamics in the approximation models and derive the rate of convergence uniformly over an interval of time to maturity to the true dynamics under certain additional smoothness conditions. In the Markovian case we can strengthen the convergence to be uniform over time as well. Our results are based on the construction of a convenient Riesz basis on the state space of the term structure dynamics.

A microscopic model of triangular arbitrage

Aiba, Y.; Hatano, N.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 24/02/2006 Português
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26.74%
We introduce a microscopic model which describes the dynamics of each dealer in multiple foreign exchange markets, taking account of the triangular arbitrage transaction. The model reproduces the interaction among the markets well. We explore the relation between the parameters of the present microscopic model and the spring constant of a macroscopic model that we proposed previously.; Comment: 17 pages, 14 figures

No-Arbitrage Pricing for Dividend-Paying Securities in Discrete-Time Markets with Transaction Costs

Bielecki, Tomasz R.; Cialenco, Igor; Rodriguez, Rodrigo
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
26.74%
We prove a version of First Fundamental Theorem of Asset Pricing under transaction costs for discrete-time markets with dividend-paying securities. Specifically, we show that the no-arbitrage condition under the efficient friction assumption is equivalent to the existence of a risk-neutral measure. We derive dual representations for the superhedging ask and subhedging bid price processes of a derivative contract. Our results are illustrated with a vanilla credit default swap contract.; Comment: Forthcoming in Mathematical Finance

Default times, non arbitrage conditions and change of probability measures

Coculescu, Delia; Jeanblanc, Monique; Nikeghbali, Ashkan
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 21/12/2008 Português
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26.74%
In this paper we give a financial justification, based on non arbitrage conditions, of the $(H)$ hypothesis in default time modelling. We also show how the $(H)$ hypothesis is affected by an equivalent change of probability measure. The main technique used here is the theory of progressive enlargements of filtrations.

Arbitrage-free Pricing of Credit Index Options: The no-armageddon pricing measure and the role of correlation after the subprime crisis

Morini, Massimo; Brigo, Damiano
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 22/12/2008 Português
Relevância na Pesquisa
26.74%
In this work we consider three problems of the standard market approach to pricing of credit index options: the definition of the index spread is not valid in general, the usually considered payoff leads to a pricing which is not always defined, and the candidate numeraire one would use to define a pricing measure is not strictly positive, which would lead to a non-equivalent pricing measure. We give a general mathematical solution to the three problems, based on a novel way of modeling the flow of information through the definition of a new subfiltration. Using this subfiltration, we take into account consistently the possibility of default of all names in the portfolio, that is neglected in the standard market approach. We show that, while the related mispricing can be negligible for standard options in normal market conditions, it can become highly relevant for different options or in stressed market conditions. In particular, we show on 2007 market data that after the subprime credit crisis the mispricing of the market formula compared to the no arbitrage formula we propose has become financially relevant even for the liquid Crossover Index Options.; Comment: Updated version accepted for publication in Mathematical Finance

On the no-arbitrage market and continuity in the Hurst parameter

Dokuchaev, Nikolai
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
26.74%
We consider a market with fractional Brownian motion with stochastic integrals generated by the Riemann sums. We found that this market is arbitrage free if admissible strategies that are using observations with an arbitrarily small delay. Moreover, we found that this approach eliminates the discontinuity of the stochastic integrals with respect to the Hurst parameter H at H=1/2.; Comment: arXiv admin note: text overlap with arXiv:1509.06112

How Non-Arbitrage, Viability and Num\'eraire Portfolio are Related

Choulli, Tahir; Deng, Jun; Ma, Junfeng
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
26.74%
This paper proposes two approaches that quantify the exact relationship among the viability, the absence of arbitrage, and/or the existence of the num\'eraire portfolio under minimal assumptions and for general continuous-time market models. Precisely, our first and principal contribution proves the equivalence among the No-Unbounded-Profit-with-Bounded-Risk condition (NUPBR hereafter), the existence of the num\'eraire portfolio, and the existence of the optimal portfolio under an equivalent probability measure for any "nice" utility and positive initial capital. Herein, a 'nice" utility is any smooth von Neumann-Morgenstern utility satisfying Inada's conditions and the elasticity assumptions of Kramkov and Schachermayer. Furthermore, the equivalent probability measure ---under which the utility maximization problems have solutions--- can be chosen as close to the real-world probability measure as we want (but might not be equal). Without changing the underlying probability measure and under mild assumptions, our second contribution proves that the NUPBR is equivalent to the "{\it local}" existence of the optimal portfolio. This constitutes an alternative to the first contribution, if one insists on working under the real-world probability. These two contributions lead naturally to new types of viability that we call weak and local viabilities.; Comment: 21 pages

Optimal strategies for operating energy storage in an arbitrage market

Flatley, Lisa; MacKay, Robert S.; Waterson, Michael
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 02/12/2014 Português
Relevância na Pesquisa
26.74%
We characterize profit-maximizing operating strategies, over some time horizon [0,T], for an energy store which is trading in an arbitrage market. Our theory allows for leakage, operating inefficiencies, operating constraints and general cost functions. In the special case where the operating cost of a store depends only on its instantaneous power output (or input), we present an algorithm to determine the optimal strategies. A key feature is that this algorithm is localized in time, in the sense that the action of the store at a time t only requires information about electricity prices over some subinterval of time [t,t_k] contained within [t,T]. To introduce more complex storage models, we discuss methods for an example which includes minimum switching times between modes of operation.; Comment: 19 pages, 1 figure. Submitted to SIAM Journal on Control and Optimization

Statistical Arbitrage and Optimal Trading with Transaction Costs in Futures Markets

Tsagaris, Theodoros
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 22/01/2008 Português
Relevância na Pesquisa
26.74%
We consider the Brownian market model and the problem of expected utility maximization of terminal wealth. We, specifically, examine the problem of maximizing the utility of terminal wealth under the presence of transaction costs of a fund/agent investing in futures markets. We offer some preliminary remarks about statistical arbitrage strategies and we set the framework for futures markets, and introduce concepts such as margin, gearing and slippage. The setting is of discrete time, and the price evolution of the futures prices is modelled as discrete random sequence involving Ito's sums. We assume the drift and the Brownian motion driving the return process are non-observable and the transaction costs are represented by the bid-ask spread. We provide explicit solution to the optimal portfolio process, and we offer an example using logarithmic utility.; Comment: 28 pages, submitted to journal

Arbitrage in markets with bid-ask spreads

Rola, Przemysław
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 12/07/2014 Português
Relevância na Pesquisa
26.74%
In this paper a finite discrete time market with an arbitrary state space and bid-ask spreads is considered. The notion of an equivalent bid-ask martingale measure (EBAMM) is introduced and the fundamental theorem of asset pricing is proved using (EBAMM) as an equivalent condition for no-arbitrage. The Cox-Ross-Rubinstein model with bid-ask spreads is presented as an application of our results.; Comment: 18 pages, 3 figures

How to account for virtual arbitrage in the standard derivative pricing

Ilinski, Kirill
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 03/02/1999 Português
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26.74%
In this short note we show how virtual arbitrage opportunities can be modelled and included in the standard derivative pricing without changing the general framework.; Comment: Latex, 6 pages, Proschal'nii poklon

Arbitrage Pricing of Multi-person Game Contingent Claims

Guo, Ivan; Rutkowski, Marek
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 12/05/2014 Português
Relevância na Pesquisa
26.74%
We introduce a class of financial contracts involving several parties by extending the notion of a two-person game option (see Kifer (2000)) to a contract in which an arbitrary number of parties is involved and each of them is allowed to make a wide array of decisions at any time, not restricted to simply `exercising the option'. The collection of decisions by all parties then determines the contract's settlement date as well as the terminal payoff for each party. We provide sufficient conditions under which a multi-person game option has a unique arbitrage price, which is additive with respect to any partition of the contract.

No-arbitrage in discrete-time markets with proportional transaction costs and general information structure

Bouchard, Bruno
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 04/01/2005 Português
Relevância na Pesquisa
26.74%
We discuss the no-arbitrage conditions in a general framework for discrete-time models of financial markets with proportional transaction costs and general information structure. We extend the results of Kabanov and al. (2002), Kabanov and al. (2003) and Schachermayer (2004) to the case where bid-ask spreads are not known with certainty. In the "no-friction" case, we retrieve the result of Kabanov and Stricker (2003).

Arbitrage risk induced by transaction costs

Piotrowski, E. W.; Sladkowski, J.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
26.74%
We discuss the time evolution of quotation of stocks and commodities and show that they form an Ising chain. We show that transaction costs induce arbitrage risk that usually is neglected. The full analysis of the portfolio theory is computationally complex but the latest development in quantum computation theory suggests that such a task can be performed on quantum computers.; Comment: 9 pages, LaTeX

Generalizations of Functionally Generated Portfolios with Applications to Statistical Arbitrage

Strong, Winslow
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
26.74%
The theory of functionally generated portfolios (FGPs) is an aspect of the continuous-time, continuous-path Stochastic Portfolio Theory of Robert Fernholz. FGPs have been formulated to yield a master equation - a description of their return relative to a passive (buy-and-hold) benchmark portfolio serving as the num\'eraire. This description has proven to be analytically very useful, as it is both pathwise and free of stochastic integrals. Here we generalize the class of FGPs in several ways: (1) the num\'eraire may be any strictly positive wealth process, not necessarily the market portfolio or even a passive portfolio; (2) generating functions may be stochastically dynamic, adjusting to changing market conditions through an auxiliary continuous-path stochastic argument of finite variation. These generalizations do not forfeit the important tractability properties of the associated master equation. We show how these generalizations can be usefully applied to scenario analysis, statistical arbitrage, portfolio risk immunization, and the theory of mirror portfolios.; Comment: 22 pages

Non-Arbitrage under a Class of Honest Times

Choulli, Tahir; Aksamit, Anna; Deng, Jun; Jeanblanc, Monique
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 01/04/2014 Português
Relevância na Pesquisa
26.74%
This paper addresses the question of non-arbitrage (precisely No-Unbounded-Profit-with-Bounded-Risk, NUPBR hereafter) after a specific random time. This study completes the one of Aksamit et al. \cite{aksamit/choulli/deng/jeanblanc}, devoted to the study before the random time, by elaborating results for the part after the random time under consideration. We restrict our attention to honest times, and we characterize the pairs of market and honest time for which the resulting model preserves the NUPBR property. Furthermore, we characterize the honest times that preserve the NUPBR property. These findings are essentially based on new stochastic results that are interesting in themselves. Furthermore, we construct explicitly local martingale deflators for a large class of processes.; Comment: 31 pages. arXiv admin note: text overlap with arXiv:1310.1142

The optimal control of storage for arbitrage and buffering, with energy applications

Cruise, James; Zachary, Stan
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 18/09/2015 Português
Relevância na Pesquisa
26.74%
We study the optimal control of storage which is used for both arbitrage and buffering against unexpected events, with particular applications to the control of energy systems in a stochastic and typically time-heterogeneous environment. Our philosophy is that of viewing the problem as being formally one of stochastic dynamic programming, but of using coupling arguments to provide good estimates of the costs of failing to provide necessary levels of buffering. The problem of control then reduces to that of the solution, dynamically in time, of a deterministic optimisation problem which must be periodically re-solved. We show that the optimal control then proceeds locally in time, in the sense that the optimal decision at each time $t$ depends only on a knowledge of the future costs and stochastic evolution of the system for a time horizon which typically extends only a little way beyond $t$. The approach is thus both computationally tractable and suitable for the management of systems over indefinitely extended periods of time. We develop also the associated strong Lagrangian theory (which may be used to assist in the optimal dimensioning of storage), and we provide characterisations of optimal control policies. We give examples based on Great Britain electricity price data.; Comment: 25 pages...

The fractional volatility model: No-arbitrage, leverage and risk measures

Mendes, R. Vilela; Oliveira, Maria João
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 16/07/2010 Português
Relevância na Pesquisa
26.74%
Based on a criterium of mathematical simplicity and consistency with empirical market data, a stochastic volatility model has been obtained with the volatility process driven by fractional noise. Depending on whether the stochasticity generators of log-price and volatility are independent or are the same, two versions of the model are obtained with different leverage behavior. Here, the no-arbitrage and incompleteness properties of the model are studied. Some risk measures are also discussed in this framework.; Comment: 12 pages latex

Pathwise no-arbitrage in a class of Delta hedging strategies

Schied, Alexander; Voloshchenko, Iryna
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 30/10/2015 Português
Relevância na Pesquisa
26.74%
We consider a strictly pathwise setting for Delta hedging exotic options, based on F\"ollmer's pathwise It\=o calculus. Price trajectories are $d$-dimensional continuous functions whose pathwise quadratic variations and covariations are determined by a given local-volatility matrix. The existence of Delta hedging strategies in this pathwise setting is established via an existence result for a recursive scheme of parabolic Cauchy problems. Our main result establishes the nonexistence of pathwise arbitrage opportunities in a class of strategies containing these Delta hedging strategies and under relatively mild conditions on the local-volatility matrix.

The fairest price of an asset in an environment of temporary arbitrage

Herzberg, Frederik
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
26.74%
In practice there are temporary arbitrage opportunities arising from the fact that prices for a given asset at different stock exchanges are not instantaneously the same. We will show that even in such an environment there exists a ``fairest measure'' (instead of a martingale measure), albeit not necessarily unique. For this end, we define and analyse quantitative notions of unfairness in complete as well as incomplete market settings.; Comment: minor changes to introduction and abstract