Estructuras de Dependencia aplicadas a la Gestión de Riesgos en Solvencia II

Abstract

En los últimos años el mapa asegurador del mercado español se ha visto modificado como consecuencia de la crisis financiera. Derivado del entorno de inestabilidad del mercado, el regulador europeo ha aprobado un nuevo marco legislativo que pretende garantizar la estabilidad financiera y la solvencia de las compañías aseguradoras a través del control de los riesgos a los que se exponen. En los distintos capítulos de esta tesis se analiza la forma en que el regulador pretende que las entidades garanticen su estabilidad, esto es, a través del proceso de fijación de los requerimientos de capital, y las herramientas con las cuales el regulador permite su obtención, es decir, el Modelo Estándar o un Modelo Interno. Se aborda la problemática de la estimación de los requerimientos de capital, las implicaciones de la utilización tanto del Modelo Estándar como de un Modelo Interno, así como el proceso de estimación de los parámetros necesarios para su implementación, con especial énfasis en la matriz de correlaciones.

En esta tesis se analiza la problemática en la estimación delos requerimientos de capital que el regulador exige a las entidades. Por una parte se analiza exhaustivamente el Modelo Estándar para el riesgo de primas y reservas no vida. Se derivan las hipótesis estadísticas implícitas en la fórmula estándar con la finalidad de mejorar la comprensión sobre el modelo y poder realizar estimaciones de los parámetros de los que depende, y poder de este modo, adaptar la fórmula estándar al perfil de riesgo de las entidades. Mediante la determinación de la variable aleatoria implícita en la fórmula estándar se está en disposición, en particular, de realizar estimaciones de los coeficientes de correlación necesarios para realizar la agregación de requerimientos de distintas líneas de negocio. Esta cuestión resuelve el vacío que deja la Directiva a este respecto, es decir, la propuesta de un método para la estimación de los coeficientes de correlación y su actualización.

Posteriormente, se propone un Modelo Interno comparable con el Modelo Estándar para el riesgo de primas y reservas no vida. El Modelo Interno está basado en la estimación de los requerimientos de capital mediante una medida de riesgo procedente de una simulación Monte Carlo de un vector de variables aleatorias que representan las distintas líneas de negocio. Para modelizar el comportamiento conjunto de las distintas líneas de negocio, es introducido la modelización a través de cópulas, en particular, la cópula Gaussiana y la cópula t-Student.

Finalmente, se propone la estimación de la matriz de correlaciones, necesaria para realizar las estimaciones de capital tanto en el Modelo Estándar como en el Modelo Interno propuesto, mediante el uso de un Modelo de Credibilidad. Es introducido el uso de un modelo bayesiano como caso particular de Modelo de Credibilidad, que permite fusionar el criterio del regulador en referencia a la matriz de correlaciones que propone, con el criterio de la entidad basado en las estimaciones procedentes de la experiencia histórica.

The publication in the Official Journal of the European Union of the European Parliament and Council of 25 November 2009 Directive on the taking up and pursuit of the business of insurance and reinsurance, also known as Solvency II, 2009/138/EC, marks the official starting point in the implementation of legislative measures of risk management in insurance. While, prior, and there was another regulation, Solvency II has been a legislative change on the approach that insurers must hold in relation to the risks they face as a result of their activity. Solvency II establishes a common legal framework to apply over those insurers based in any of the member states of the European Union to access and exercise the insurance and reinsurance business. The Directive is structured on the three pillars principle. These pillars set the criteria and standards of quantitative and qualitative requirements that entities must undertake to ensure their solvency and financial stability.

Pillar I set rules that determine the criteria for obtaining capital requirements that an entity must maintain over an annual time horizon, commensurate to the risk assumed by the entity, to ensure an acceptable level of solvency through the market consistent economic valuation of the balance sheet of an entity. Pillar I is aimed to determine the minimum financial requirements to ensure that the assets are sufficient in quantity and quality, to meet the liabilities under a certain time horizon.

To do this, the assessment under Pillar I balance must be performed according to market criteria, i.e. both the valuation of assets and liabilities of the entity must be consistent with that which would result from the interaction of free market agents. On the one hand, the balance sheet is determined by the market value of the investments made by the entity. For those assets that by their illiquid nature, or for any other reason, there is no market value, the Directive introduces valuation standards.

The valuation of the liabilities presents difficulties inherent in the insurance business as for example to determine the economic value of the contract obligations insured by entities. These have usually an uncertain amount as well as uncertain in the time of liquidation.

Also, Pillar I determines the composition of the entities’ own funds, i.e., the asset structure that supports that part of the balance, in addition to the financial amounts (capital requirements) of legal character Directive establishes.

Pillar I consider separately different levels of protection. The first level would be constituted by the market valuation of technical provisions, which should reflect an estimate consistent with the level of liabilities and risk margin. The second level would be determined by Pillar I solvency requirements. These requirements should reflect the risk and ensure the solvency of institutions. The Directive sets a minimum threshold of economic requirements under which the entity could not continue their business.

Financial requirements of the first level of protection should reflect the obligations of the entity through insurance contracts undersigned. This capital is reflected in the valuation of technical provisions. The valuation of technical provisions for solvency II, must represent, on the one hand, the present value of the best estimate of future economic flows arising from contractual obligations (best estimate) and secondly, a risk margin (risk margin) to reflect the amount that an entity would have to pay to transfer the obligations arising from insurance contracts, net of the present value of the best estimate of future economic flows arising from obligations.

Moreover, the objective of the economic requirements of the second level of protection is to cover any unexpected losses that an entity may suffer as a result of adverse unexpected fluctuations in claims. This part of the capital requirements directive is known as the Solvency Capital Requirement (SCR). As mentioned, the SCR has a lower bound determined by a threshold called Minimum Capital Solvency Requirement (MSCR), below which an entity could not continue operating.

The Directive states that the SCR should be obtained by a model that reflects the risk profile of the entity, and that is appropriate based on the nature, scale and complexity of the risks assumed by the company. The model proposed by the regulator is called in the Directive as General Formula to calculate the Solvency Capital Requirement.

Under Article 110 of the Directive, the Standard Model can be used by institutions using the parameters set in the Directive as market proxy, or can be adapted to the risk profile of each institution itself by estimating new parameters based on specific historical experience of the entity.

There may be several reasons to make an insurer decides to estimate new parameters. One possible reason may arise from the overestimation of the proxys, which would lead to an SCR greater than that obtained with the use of specific parameters.

Moreover, another reason for the estimation of the parameters could be determined by the fact that the structure of business of an insurance company does not adapt to that proposed by the regulator.

The Directive also provides that under the competent authority’s previous approval, the SCR can be obtained using an internal model. This model cannot account for all or part of the risks facing the entity. In the latter case, the model is referred to in Directive as partial internal model.

The requirements to be met by an internal model are related to implementation and monitoring standards, so those entities that choose to use an internal model, total or partial, for the calculation of the solvency capital requirements must justify their use.

The Standard Model is a set of formulas and methodologies proposed by the regulator with which the insurer can get the amount corresponding to the SCR. An internal model is a procedure offered by the insurer that has the same objective and purposes than the Standard Model, i.e., obtaining capital requirements using a model that reflects the risk profile of the entity. The SCR, obtained with any of the models permitted by the regulator, must be calibrated in such a way that corresponds to the value at risk (VaR) of the entity’s own funds, at a one year horizon, calculated at a 99,5% confidence level.

Pillar II describes the qualitative requirements that entities must comply and which result in those formal procedures and communication to the regulator.

Pillar II of the Directive concerns those aspects relating the procedures of supervision and control by the regulator. Solvency II is defined as a policy of harmonization for entities operating in the states member of the European Union, so it is necessary that the quantitative aspects are accompanied by other qualitative aspects that achieve homogeneity of appropriate methods and monitoring and control tools to be used by local regulators of different States Member. These requirements also include the obligation for any entity to control risk management model, both quantifiable and non-quantifiable. This management model is known as Own Risk Solvency Assessment (ORSA). The ORSA is a communication tool that should serve two purposes.

The first one should be used as an aid in the process of strategic decision making, therefore must be reviewed continuously when the risk profile of the entity changes significantly, incorporating strategic decisions.

The second purpose must serve as a regulator tool of communication. The ORSA must project requirements in future years and justify deviations between projected and present requirements, whatever the model used for this aim. Thus, the model ORSA should be a calibration tool whatever the model chosen to estimate the SCR.

Finally, Pillar III represents those measures intended to ensure the transparency and discipline in the insurance market, through a set of rules for communication of information on the financial position and solvency of financial institutions facing the local regulator, and the rules of communication and transparency of local regulators facing the European regulator.

Pillar III sets the action to be taken by the regulator and the entities in the case of misalignments in fulfilling the requirements of the valuation rules of Pillar I and / or the requirements of Pillar II.

Thus, the European regulator empowers local regulators to take action to ensure the standards imposed under Pillar I and II, and is authorized to take action on states that fail to comply with the requirements of Directive Communication and transparency.