Model-free bounds on Value-at-Risk using extreme value information and statistical distances

Lux, Thibaut; Papapantoleon, Antonis

doi:10.1016/j.insmatheco.2019.01.007

Cited by 8 publications

(5 citation statements)

References 48 publications

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“…Therefore, there has been intensive research in the last decade on improving the Fréchet-Hoeffding bounds by adding partial information on the copula, see e.g. Lux and Papapantoleon [12,13], Nelsen [14], Puccetti, Rüschendorf, and Manko [15] and Tankov [18]. The following results from [12,Sec.…”

Section: Copulas Quasi-copulas and Improved Fréchet-hoeffding Boundsmentioning

confidence: 99%

Detection of arbitrage opportunities in multi-asset derivatives markets

Papapantoleon¹,

Sarmiento²

2020

Preprint

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We are interested in the existence of equivalent martingale measures and the detection of arbitrage opportunities in markets where several multi-asset derivatives are traded simultaneously. More specifically, we consider a financial market with multiple traded assets whose marginal risk-neutral distributions are known, and assume that several derivatives written on these assets are traded simultaneously. In this setting, there is a bijection between the existence of an equivalent martingale measure and the existence of a copula that couples these marginals. Using this bijection and recent results on improved Fréchet-Hoeffding bounds in the presence of additional information, we derive sufficient conditions for the absence of arbitrage and formulate an optimization problem for the detection of a possible arbitrage opportunity. This problem can be solved efficiently using numerical optimization routines. The most interesting practical outcome is the following: we can construct a financial market where each multi-asset derivative is traded within its own no-arbitrage interval, and yet when considered together an arbitrage opportunity may arise.

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Section: Copulas Quasi-copulas and Improved Fréchet-hoeffding Boundsmentioning

confidence: 99%

Detection of arbitrage opportunities in multi-asset derivatives markets

Papapantoleon¹,

Sarmiento²

2020

Preprint

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“…Definition 2. Let X be a random variable with cdf F X (x), the value at risk at the α level is defined by, 4,13,25 V aR[X; α] = inf{x ∈ R, F X (x) ≥ α}, 0 < α < 1.…”

Section: Univariate Distributions and Basic Risk Measuresmentioning

confidence: 99%

Aggregation of Dependent Risks with Heavy-Tail Distributions

Guillén

Sarabia

Prieto

et al. 2019

Int. J. Unc. Fuzz. Knowl. Based Syst.

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Straightforward methods to evaluate risks arising from several sources are specially difficult when risk components are dependent and, even more if that dependence is strong in the tails. We give an explicit analytical expression for the probability distribution of the sum of non-negative losses that are tail-dependent. Our model allows dependence in the extremes of the marginal beta distributions. The proposed model is flexible in the choice of the parameters in the marginal distribution. The estimation using the method of moments is possible and the calculation of risk measures is easily done with a Monte Carlo approach. An illustration on data for insurance losses is presented.

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“…Analogously to the Fr\' echet--Hoeffding bounds in the framework of dependence uncertainty, several authors have developed improved Fr\' echet--Hoeffding bounds that correspond to the framework of partial dependence uncertainty; see, e.g., [24,32,20,21,26]. The improved Fr\' echet--Hoeffding bounds can accommodate different types of additional information, such as the knowledge of the distribution function on a subset of the domain and the knowledge of a measure of association.…”

Section: Introductionmentioning

confidence: 99%

Marginal and Dependence Uncertainty: Bounds, Optimal Transport, and Sharpness

Bartl¹,

Kupper²,

Lux³

et al. 2022

SIAM J. Control Optim.

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Motivated by applications in model-free finance and quantitative risk management, we consider Fr\' echet classes of multivariate distribution functions where additional information on the joint distribution is assumed, while uncertainty in the marginals is also possible. We derive optimal transport duality results for these Fr\' echet classes that extend previous results in the related literature. These proofs are based on representation results for convex increasing functionals and the explicit computation of the conjugates. We show that the dual transport problem admits an explicit solution for the function f = 1 B , where B is a rectangular subset of \BbbR d , and provide an intuitive geometric interpretation of this result. The improved Fr\' echet--Hoeffding bounds provide ad hoc bounds for these Fr\' echet classes. We show that the improved Fr\' echet--Hoeffding bounds are pointwise sharp for these classes in the presence of uncertainty in the marginals, while a counterexample yields that they are not pointwise sharp in the absence of uncertainty in the marginals, even in dimension 2. The latter result sheds new light on the improved Fr\' echet--Hoeffding bounds, since Tankov [J. Appl. Probab., 48 (2011), pp. 389--403] has showed that, under certain conditions, these bounds are sharp in dimension 2.

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Model-free bounds on Value-at-Risk using extreme value information and statistical distances

Cited by 8 publications

References 48 publications

Detection of arbitrage opportunities in multi-asset derivatives markets

Detection of arbitrage opportunities in multi-asset derivatives markets

Aggregation of Dependent Risks with Heavy-Tail Distributions

Marginal and Dependence Uncertainty: Bounds, Optimal Transport, and Sharpness

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