parallel session 9
Wednesday april 29th
3:40 – 4:55
douala room - Risk Measurement
This paper investigates the strategic use of banks’ internal models for market risk. We study hand-collected data on modelling and disclosure choices and examine how they relate to banks’ reported levels of Value-at-Risk (VaR) and the number of VaR violations. We show that more elaborate internal modelling can correspond to more conservative VaR while being more punitive in terms of higher capital requirements. At the same time, such modelling is also more opaque and fails to capture tail risk precisely when in-house information should be particularly valuable. We conclude that capital requirements for market risk are compromised by strategic modelling, and show how the degree of distortion depends on specific modelling choices.
In the last decades, a topic of increasing interest in portfolio risk analysis is the evaluation of contagion risk (also referred to as systemic risk), which refers to judge how the risk behavior of some components spreads to others or even to the whole portfolio. In this framework, we study the consistency of some recently introduced contagion risk measure, the marginal mean excess (MME), and some well-known measures, including the CoVaR and CoES, with respect to various stochastic orderings under different dependence assumptions. We illustrate the applicability of the results in the context of parametric families of distributions, by showing how changes in the parameters affect the risk of contagion.
In this paper, we propose a methodology to assess basis risk in an index-based insurance (IBI) transaction using s-convex order and s-convex extremal distributions. The payout of an IBI product is a function of some observable and recordable physical parameters of an event and does not depend on the protection buyer’s ultimately incurred loss. The difference in the payouts between a protection buyer’s own losses and the IBI product structured to hedge against those losses defines basis risk. In our framework, basis risk is represented by a random scaling relationship. We first consider convex ordering of unbounded randomly scaled variables. Then we provide the related s-convex extremal distributions and we demonstrate theoretical results on the comparison of s-convex extrema using s-increasing convex functions. In our methodology, s-convex extremal distribution stands for worst case scenario of order s. Further, we introduce the class of generalized penalty functions to measure the consequences of basis risk in each scenario. A key contribution is the introduction of the basis risk measurement in scenario of order s, defined as the s-convex bound of the generalized penalty function. In addition, our methodology allows us to set up basis risk limits as well as to define a basis risk capital requirement. We derive technical results related to our basis risk capital requirement. We end by illustrating theoretical developments by following the whole methodology for different forms of basis risk.
bogota room - Mortality Modelling
Countries have experienced large improvements in mortality all over the world, but the mortality rates within one country often bare substantial differences. We develop new models to project mortality at both the national and subnational levels within a country based on principal components and the random walk process. The baseline two-level model with a national–province structure allows for information pooling across provinces, common national factors, and consistency conditions. The extended three-level model with a national–region–province structure pools information in the region and also allows for common factors within the region. Based on a new comprehensive mortality database for provinces in China over the period 1982–2010, both models provide good estimates and reasonable forecasts for China and its provinces. The baseline two-level model provides good fits and reasonable forecasts with equal width intervals for the provinces. The three-level model has better fits with a lower deviance information criterion (DIC) and provides forecast intervals reflecting regional uncertainty. The sensitivity analyses show that the forecasts are robust when changing the trend assumptions and regional groups.
We investigate joint modeling of longevity trends using the spatial statistical framework of Gaussian Process regression. Our analysis is motivated by the Human Mortality Database (HMD) that provides unified raw mortality tables for nearly 40 countries. Yet few stochastic models exist for handling more than two populations at a time. To bridge this gap, we leverage a spatial covariance framework from machine learning that treats populations as distinct levels of a factor covariate, explicitly capturing the cross-population dependence. The proposed multi-output Gaussian Process models straightforwardly scale up to a dozen populations and moreover intrinsically generate coherent joint longevity scenarios. In our numerous case studies we investigate predictive gains from aggregating mortality experience across nations and genders, including by borrowing the most recently available foreign data. We show that in our approach, information fusion leads to more precise (and statistically more credible) forecasts. We implement our models in R, as well as a Bayesian version in Stan that provides further uncertainty quantification regarding the estimated mortality covariance structure. All examples utilize public HMD datasets.
Hormone Replacement Therapy (HRT) is used as a standard treatment of oestrogen/progesterone deficiency in postmenopausal women. The actual risks and benefits of HRT are still unsettled after sixty years of its use. Existing research on HRT shows contradictory results. The primary aim of this research, funded by the Actuarial Research Centre of the IFoA, is to conduct a retrospective cohort study to investigate the impact of HRT on all-cause mortality in women resident in the United Kingdom (UK). A subset of The Health Improvement Network (THIN) database has been used to extract patients’ information on medical, lifestyle, and socio-demographic status. Records of 112,354 HRT users were matched with 245,320 non-users by age and GP practice. The length of the follow-up was up-to thirty-one years. A parametric Weibull-Cox regression method has been applied to model the survival. Our results from complete case analysis shows that combined HRT (combination of oestrogen and progesterone) reduces the risk of all-cause mortality.
montreal room - Solvency and Risk Measures
The paper provides a stochastic model useful for assessing the five components of insurance profit identified by the well known Homans formula in a framework that is consistent with the accounting principles defined by the Solvency II regulation. In particular, we deal with the random variable demographic profit and loss. The model is also compared with the classical methodology, developed in a local GAAP context. In a market consistent context, the presence of a Best Estimate computed by using real expectations (instead of locked technical basis), shifts the focus on the updated perspective expectations on mortality rates and risk free rates.
To test our proposal, we applied the model to different traditional life-insurance contracts. Main results show that in a local GAAP context, profit cash flows are proportional to the behaviour of the characteristic variables of the various policies. In a market-consistent context, the main portion is released at the inception of the policy, while the other cash flows depend on the eventual revision of initial expectations.
In the market consistent framework, the valuation of demographic profit also includes a portion of the financial gain. Since the risk-free rates are a characterizing element of the Best Estimate, to capture the effect of a change in the yields rate curve on the company profit, the so-called financial gain must also be considered.
Finally, in terms of capital requirement, it is crucial to also look at the variability of the random variable. In this case, we observe that the volatility of demographic profit depends almost exclusively on the variability of financial rates, while the contribution of changes in mortality rates is marginal. That is clearly driven by the volume of mathematical reserves having a large impact on the relevance of financial margin, whereas the volume is not anymore the most key variable (e.g. in term insurance) this major role is by far reduced.
We are currently in a transition period for insurance companies’ regulation, moving from country-specific guidelines to the new IFRS 17 framework. The changes are related to the financial reporting and calculation of reserves. Range Value-at-Risk (RVaR) is a risk measure that averages values between bounds (quantiles). This characteristic allows for the representation of high levels of risks, up to a specified limit, which is convenient for infinite mean distributions, for example. The multivariate cases will be defined. Specific results of RVaR in the extreme value framework will be presented, considering GEV and GPD distributions, as well as asymptotic results for extreme confidence levels. An empirical estimator will be presented with numerical illustrations.
Distortion premium principles have received considerable attention due to their many good properties. In this work we present a family of particular distortion premium principles that coincides with the expected average of the n-i largest claims, with 0 ≤ i ≤ n-1, of a set of n ≥ 2 independent and identically distributed claims. Each premium principle of this family can be represented by mixtures of tail value-at-risks, with beta mixing distributions. From this representation, we obtain a convergence result that connects the tail value-at-risk with the largest claims of a portfolio. A characterization of the excess-wealth order in terms of this family of premiums is provided. As a consequence, we obtain a sufficient condition for ordering the net premiums of two collective risks under the ECOMOR reinsurance treaty.