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Collateral Margining in Arbitrage-Free Counterparty Valuation Adjustment including Re-Hypotecation and Netting

Brigo, Damiano; Capponi, Agostino; Pallavicini, Andrea; Papatheodorou, Vasileios
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 20/01/2011 Português
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26.99%
This paper generalizes the framework for arbitrage-free valuation of bilateral counterparty risk to the case where collateral is included, with possible re-hypotecation. We analyze how the payout of claims is modified when collateral margining is included in agreement with current ISDA documentation. We then specialize our analysis to interest-rate swaps as underlying portfolio, and allow for mutual dependences between the default times of the investor and the counterparty and the underlying portfolio risk factors. We use arbitrage-free stochastic dynamical models, including also the effect of interest rate and credit spread volatilities. The impact of re-hypotecation, of collateral margining frequency and of dependencies on the bilateral counterparty risk adjustment is illustrated with a numerical example.

Correlation breakdown, copula credit default models and arbitrage

Tzani, Rodanthy; Polychronakos, Alexios P.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 31/08/2009 Português
Relevância na Pesquisa
26.99%
The recent "correlation breakdown" in the modeling of credit default swaps, in which model correlations had to exceed 100% in order to reproduce market prices of supersenior tranches, is analyzed and argued to be a fundamental market inconsistency rather than an inadequacy of the specific model. As a consequence, markets under such conditions are exposed to the possibility of arbitrage. The general construction of arbitrage portfolios under specific conditions is presented.; Comment: 15 pages

Viscosity Characterization of the Arbitrage Function under Model Uncertainty

Wang, Yinghui
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 30/01/2015 Português
Relevância na Pesquisa
26.99%
We show that in an equity market model with Knightian uncertainty regarding the relative risk and covariance structure of its assets, the arbitrage function -- defined as the reciprocal of the highest return on investment that can be achieved relative to the market using nonanticipative strategies, and under any admissible market model configuration -- is a viscosity solution of an associated Hamilton-Jacobi-Bellman (HJB) equation under appropriate boundedness, continuity and Markovian assumptions on the uncertainty structure. This result generalizes that of Fernholz and Karatzas (2011), who characterized this arbitrage function as a classical solution of a Cauchy problem for this HJB equation under much stronger conditions than those needed here.; Comment: arXiv admin note: text overlap with arXiv:1202.2999 by other authors

Diversity and relative arbitrage in equity markets

Fernholz, Robert; Karatzas, Ioannis; Kardaras, Constantinos
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 20/03/2008 Português
Relevância na Pesquisa
26.99%
A financial market is called "diverse" if no single stock is ever allowed to dominate the entire market in terms of relative capitalization. In the context of the standard Ito-process model initiated by Samuelson (1965) we formulate this property (and the allied, successively weaker notions of "weak diversity" and "asymptotic weak diversity") in precise terms. We show that diversity is possible to achieve, but delicate. Several illustrative examples are provided, which demonstrate that weakly-diverse financial markets contain relative arbitrage opportunities: it is possible to outperform (or underperform) such markets over sufficiently long time-horizons, and to underperform them significantly over arbitrary time-horizons. The existence of such relative arbitrage does not interfere with the development of option pricing, and has interesting consequences for the pricing of long-term warrants and for put-call parity. Several open questions are suggested for further study.; Comment: 28 pages

No-Arbitrage Prices of Cash Flows and Forward Contracts as Choquet Representations

Fischer, Tom
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
26.99%
In a market of deterministic cash flows, given as an additive, symmetric relation of exchangeability on the finite signed Borel measures on the non-negative real time axis, it is shown that the only arbitrage-free price functional that fulfills some additional mild requirements is the integral of the unit zero-coupon bond prices with respect to the payment measures. For probability measures, this is a Choquet representation, where the Dirac measures, as unit zero-coupon bonds, are the extreme points. Dropping one of the requirements, the Lebesgue decomposition is used to construct counterexamples, where the Choquet price formula does not hold despite of an arbitrage-free market model. The concept is then extended to deterministic streams of assets and currencies in general, yielding a valuation principle for forward markets. Under mild assumptions, it is shown that a foreign cash flow's worth in local currency is identical to the value of the cash flow in local currency for which the Radon-Nikodym derivative with respect to the foreign cash flow is the forward FX rate.; Comment: JEL Classification: G12, G13

A note on asymptotic exponential arbitrage with exponentially decaying failure probability

Du, Kai; Neufeld, Ariel David
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 26/07/2012 Português
Relevância na Pesquisa
26.99%
The goal of this paper is to prove a result conjectured in F\"ollmer and Schachermayer [FS07], even in slightly more general form. Suppose that S is a continuous semimartingale and satisfies a large deviations estimate; this is a particular growth condition on the mean-variance tradeoff process of S. We show that S then allows asymptotic exponential arbitrage with exponentially decaying failure probability, which is a strong and quantitative form of long-term arbitrage. In contrast to F\"ollmer and Schachermayer [FS07], our result does not assume that S is a diffusion, nor does it need any ergodicity assumption.