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Sequential arbitrage measurements and interest rate envelopes

Balbás, Alejandro; López, Susana
Fonte: Springer Publicador: Springer
Tipo: info:eu-repo/semantics/acceptedVersion; info:eu-repo/semantics/article Formato: application/pdf
Publicado em /09/2008 Português
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This paper proposes new measures that provide us with the level of sequential arbitrage in bond markets. All the measures vanish in an arbitrage-free market and all of them are positive otherwise. Each measure is generated by a dual pair of optimization problems. Primal problems permit us to compute optimal sequential arbitrage strategies, if available. Each dual problem generates a concrete proxy for the term structure of interest rates. The set of proxies allows us to obtain the exact market price of any bond and may measure several effects. For instance, the credit risk spread of nondefault free bonds, or the embedded option price of callable or extendible bonds. The developed theory has been tested empirically.; Research partially supported by Welzia Management SGIIC, RD_Sistemas, Comunidad Autónoma de Madrid (Spain), Grant s-0505/tic/000230, and MEyC (Spain), Grant SEJ2006-15401-C04-03

Martingales and Arbitrage: a new look

Balbás, Alejandro; Jimenez Guerra, Pedro
Fonte: Springer Publicador: Springer
Tipo: info:eu-repo/semantics/acceptedVersion; info:eu-repo/semantics/article
Publicado em /06/2009 Português
Relevância na Pesquisa
This paper addresses the equivalence between the absence of arbitrage and the existence of equivalent martingale measures. The equivalence will be established under quite weak assumptions since there are no conditions on the set of trading dates (it may be finite or countable, with bounded or unbounded horizon, etc.) or on the trajectories of the price process (for instance, they do not have to be right-continuous). Besides we will deal with arbitrage portfolios rather than free-lunches. The concept of arbitrage is much more intuitive than the concept of free lunch and has more clear economic interpretation. Furthermore it is more easily tested in theoretical models or practical applications. In order to overcome the usual mathematical difficulties arising when dealing with arbitrage strategies, the set of states of nature will be widened by drawing on projective systems of Radon probability measures, whose projective limit will be the martingale measure. The existence of densities between the "real" probabilities and the "risk-neutral" probabilities will be guaranteed by introducing the concept of "projective equivalence". Hence some classical counter-examples will be solved and a complete characterization of the absence of arbitrage will be provided in a very general framework.; Research partially supported by “Comunidad Autónoma de Madrid” (Spain)...