The concept of comonotonicity in actuarial science and finance: applications

Dhaene, Jan; Denuit, Michel; Goovaerts, Marc; Kaas, Rob; Vyncke, David

doi:10.1016/s0167-6687(02)00135-x

Cited by 305 publications

(169 citation statements)

References 16 publications

(10 reference statements)

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“…The reason is that the Jamshidian decomposition cannot be applied. An alternative could be the comonotonicity approach of Dhaene et al (2002a) and Dhaene et al (2002b), which results in a lower and upper bound for the bond put option. As an alternative for a two-factor model, a model with a jump component can be considered.…”

Section: Discussionmentioning

confidence: 99%

Risk management of a bond portfolio using options

Annaert

Deelstra

Heyman

et al. 2007

Insurance: Mathematics and Economics

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In this paper, we elaborate a formula for determining the optimal strike price for a bond put option, used to hedge a position in a bond. This strike price is optimal in the sense that it minimizes, for a given budget, either Value-at-Risk or Tail Value-at-Risk. Formulas are derived for both zero-coupon and coupon bonds, which can also be understood as a portfolio of bonds. These formulas are valid for any short rate model that implies an affine term structure model and in particular that implies a lognormal distribution of future zero-coupon bond prices. As an application, we focus on the Hull-White one-factor model, which is calibrated to a set of cap prices. We illustrate our procedure by hedging a Belgian government bond, and take into account the possibility of divergence between theoretical option prices and real option prices. This paper can be seen as an extension of the work of Ahn et al. (1999), who consider the same problem for an investment in a share.JEL classification: G11, C61 IME-codes: IE43, IE50, IE51

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Section: Discussionmentioning

confidence: 99%

Risk management of a bond portfolio using options

Annaert

Deelstra

Heyman

et al. 2007

Insurance: Mathematics and Economics

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“…Next we study the dependence in a discounted discrete annuity as discussed in Dhaene et al (2002b). Example 4.2 Consider a series of deterministic payments α 1 , α 2 , .…”

Section: Estimationmentioning

confidence: 99%

A multivariate dependence measure for aggregating risks

Dhaene

Linders

Schoutens

et al. 2014

Journal of Computational and Applied Mathematics

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To evaluate the aggregate risk in a financial or insurance portfolio, a risk analyst has to calculate the distribution function of a sum of random variables. As the individual risk factors are often positively dependent, the classical convolution technique will not be sufficient. On the other hand, assuming a comonotonic dependence structure will likely overrate the real aggregate risk. In order to choose between both approximations, or perhaps use a weighted average, we should have an indication on the accuracy. Clearly this accuracy will depend on the copula between the individual risk factors, but it is also influenced by the marginal distributions. In this paper we introduce a multivariate dependence measure that takes both aspects into account. This new measure differs from other multivariate dependence measures, as it focuses on the aggregate risk rather than on the copula or the joint distribution function itself. We prove several interesting properties of this new measure and discuss its relation to other dependence measures. We also give some comments on the estimation and conclude with examples and numerical results.

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“…However, it is impossible to determine the distribution function of S analytically in closed form, because S is a sum of non-independent lognormal variables. We will use the convex upper and lower bounds for S satisfying S ≤ cx S ≤ cx S c as introduced in Dhaene et al (2002b):…”

Section: Problem Descriptionmentioning

confidence: 99%

Convex order approximations in the case of cash flows of mixed signs

Dhaene

Goovaerts

Vanmaele

et al. 2012

Insurance: Mathematics and Economics

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In Van Weert et al. (2010), results are obtained showing that, when allowing some of the cash flows to be negative, convex order lower bound approximations can still be used to solve general investment problems in a context of provisioning or terminal wealth. In this paper, a correction and further clarification of the reasoning of Van Weert et al. (2010) are given, thereby significantly expanding the scope of problems and cash flow patterns for which the terminal wealth or initial provision can be accurately approximated. Also an interval for the probability level is derived in which the quantiles of the lower bound approximation can be computed. Finally, it is shown how one can move from a context of provisioning of future obligations to a saving and terminal wealth problem by inverting the time axis.

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The concept of comonotonicity in actuarial science and finance: applications

Cited by 305 publications

References 16 publications

Risk management of a bond portfolio using options

Risk management of a bond portfolio using options

A multivariate dependence measure for aggregating risks

Convex order approximations in the case of cash flows of mixed signs

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