Risk aggregation in Solvency II: How to converge the approaches of the internal models and those of the standard formula?

Two approaches may be considered in order to determine the Solvency II economic capital: the use of a standard formula or the use of an internal model (global or partial). However, the results produced by these two methods are rarely similar, since the underlying hypothesis of marginal capital aggregation is not verified by the projection models used by companies. We demonstrate that the standard formula can be considered as a first order approximation of the result of the internal model. We therefore propose an alternative method of aggregation that enables to satisfactorily capture the diversity among the various risks that are considered, and to converge the internal models and the standard formula.

Risk aggregation in Solvency II: How to converge the approaches of the internal models and those of the standard formula?

Two approaches may be considered in order to determine the Solvency II economic capital: the use of a standard formula or the use of an internal model (global or partial). However, the results produced by these two methods are rarely similar, since the underlying hypothesis of marginal capital aggregation is not verified by the projection models used by companies. We demonstrate that the standard formula can be considered as a first order approximation of the result of the internal model. We therefore propose an alternative method of aggregation that enables to satisfactorily capture the diversity among the various risks that are considered, and to converge the internal models and the standard formula.

Fast calibration of the Libor Market Model with Stochastic Volatility and Displaced Diffusion

This paper demonstrates the efficiency of using Edgeworth and Gram-Charlier expansions in the calibration of the Libor Market Model with Stochastic Volatility and Displaced Diffusion (DD-SV-LMM). Our approach brings together two research areas; first, the results regarding the SV-LMM since the work of Wu and Zhang (2006), especially on the moment generating function, and second the approximation of density distributions based on Edgeworth or Gram-Charlier expansions. By exploring the analytical tractability of moments up to fourth order, we are able to perform an adjustment of the reference Bachelier model with normal volatilities for skewness and kurtosis, and as a by-product to derive a smile formula relating the volatility to the moneyness with interpretable parameters. As a main conclusion, our numerical results show a 98% reduction in computational time for the DD-SV-LMM calibration process compared to the classical numerical integration method developed by Heston (1993)

Variabilité de la croissance en circonférence des arbres dans les forêts semi-décidues de Lamto (Côte d'Ivoire)

Girth increments of trees were studied using band-dendrometers in some semi-deciduous forests in Lamto (Ivory Coast). Every tree over 20 cm gbh was monitored monthly, during 5 to 9 years, in seven stands. Girth increments' distributions were log-normal in the forest stands studied, a few individuals contributing to the largest part of the forest production. Girth increments vary widely; even between trees of similar size; several types of girth increment were described (regular, intermittent, increasing or decreasing etc.). A yearly periodicity of growth, in conformity with the local climatic cycle, is the pattern most commonly observed, mainly in fast growing trees, but yearly bimodal patterns and dry season increments were also observed. The variability of growth patterns is mainly due to intra-specific variability. At the community level the mortality rate of trees ranges, between stands, from 1 to 4%

One-year reserve risk including a tail factor: closed formula and bootstrap approaches

In this paper, we detail the main simulation methods used in practice to measure one-year reserve risk, and describe the bootstrap method providing an empirical distribution of the Claims Development Result (CDR) whose variance is identical to the closed-form expression of the prediction error proposed by Wüthrich et al. (2008). In particular, we integrate the stochastic modeling of a tail factor in the bootstrap procedure. We demonstrate the equivalence with existing analytical results and develop closed-form expressions for the error of prediction including a tail factor. A numerical example is given at the end of this study.Non‐life insurance, Reserve risk, Claims Development Result, Bootstrap method, Tail factor, Prediction error, Solvency II

Couvert angulaire et architecture forestière: Etudes en Côte d'ivoire

A method for studying the forest cover is described. The possible uses of the method are developed on two examples, one consisting of the analysis of some plots, the other with a set of stands characterized by their architecture

Fast remote but not extreme quantiles with multiple factors. Applications to Solvency II and Enterprise Risk Management

For operational purposes, in Enterprise Risk Management or in insurance for example, it may be important to estimate remote (but not extreme) quantiles of some function ƒ of some random vector. The call to ƒ may be time- and resource-consuming so that one aims at reducing as much as possible the number of calls to ƒ. In this paper, we propose some ways to address this problem of general interest. We then numerically analyze the performance of the method on insurance and Enterprise Risk Management real-world case studies.