Optimal capital allocation principles

This paper develops a unifying framework for allocating the aggregate capital of a financial firm to its business units. The approach relies on an optimisation argument, requiring that the weighted sum of measures for the deviations of the business unit’s losses from their respective allocated capitals be minimised. This enables the association of alternative allocation rules to specific decision criteria and thus provides the risk manager with flexibility to meet specific target objectives. The underlying general framework reproduces many capital allocation methods that have appeared in the literature and allows for several possible extensions. An application to an insurance market with policyholder protection is additionally provided as an illustration.Capital allocation; risk measure; comonotonicity; Euler allocation; default option; Lloyd’s of London

Optimal capital allocation principles.

This paper develops a unifying framework for allocating the aggregate capital of a financial firm to its business units. The approach relies on an optimisation argument, requiring that the weighted sum of measures for the deviations of the business unit’s losses from their respective allocated capitals be minimised. This enables the association of alternative allocation rules to specific decision criteria and thus provides the risk manager with flexibility to meet specific target objectives. The underlying general framework reproduces many capital allocation methods that have appeared in the literature and allows for several possible extensions. An application to an insurance market with policyholder protection is additionally provided as an illustration.

Optimal Capital Allocation Principles

This article develops a unifying framework for allocating the aggregate capital of a financial firm to its business units. The approach relies on an optimization argument, requiring that the weighted sum of measures for the deviations of the business unit's losses from their respective allocated capitals be minimized. The approach is fair insofar as it requires capital to be close to the risk that necessitates holding it. The approach is additionally very flexible in the sense that different forms of the objective function can reflect alternative definitions of corporate risk tolerance. Owing to this flexibility, the general framework reproduces several capital allocation methods that appear in the literature and allows for alternative interpretations and possible extensions

Optimal capital allocation principles

This paper develops a unifying framework for allocating the aggregate capital of a financial firm to its business units. The approach relies on an optimisation argument, requiring that the weighted sum of measures for the deviations of the business unit’s losses from their respective allocated capitals be minimised. This enables the association of alternative allocation rules to specific decision criteria and thus provides the risk manager with flexibility to meet specific target objectives. The underlying general framework reproduces many capital allocation methods that have appeared in the literature and allows for several possible extensions. An application to an insurance market with policyholder protection is additionally provided as an illustration

Optimal capital allocation principles

This paper develops a unifying framework for allocating the aggregate capital of a financial firm to its business units. The approach relies on an optimisation argument, requiring that the weighted sum of measures for the deviations of the business unit’s losses from their respective allocated capitals be minimised. This enables the association of alternative allocation rules to specific decision criteria and thus provides the risk manager with flexibility to meet specific target objectives. The underlying general framework reproduces many capital allocation methods that have appeared in the literature and allows for several possible extensions. An application to an insurance market with policyholder protection is additionally provided as an illustration

Risk capital allocation and risk quantification in insurance companies

The objective of this thesis is to investigate risk capital allocation methods in detail for both non-life and life insurance business. In non-life insurance business loss models are generally linear with respect to losses of business-lines. However, in life insurance loss models are not generally a linear function of factor risks, i.e. the interest-rate factor, mortality rate factor, etc. In the first part of the thesis, we present the existing allocation methods and discuss their advantages and disadvantages. In a comprehensive simulation study we examine the allocations sensitivity to different allocation methods, different risk measures and different risk models in a non-life insurance business. We also show the possible usage of the Euclidean distance measure and rank correlation coefficients for the comparison of allocation methods. In the second part, we investigate the factor risk contribution theory and examine its application under a life annuity business. We provide two approximations that enable us to apply risk capital allocation methods directly to annuity values in order to measure factor risk contributions. We examine factor risk contributions for annuities with different terms to maturity and the annuities payable at different times in future. We also analyse the factor risk contributions under the extreme scenarios for the factor risks

Innovations in Quantitative Risk Management

Quantitative Finance; Game Theory, Economics, Social and Behav. Sciences; Finance/Investment/Banking; Actuarial Science

Innovations in Quantitative Risk Management

Quantitative Finance; Game Theory, Economics, Social and Behav. Sciences; Finance/Investment/Banking; Actuarial Science

Density forecasting in financial risk modelling

As a result of an increasingly stringent regulation aimed at monitoring financial risk exposures, nowadays the risk measurement systems play a crucial role in all banks. In this thesis we tackle a variety of problems, related to density forecasting, which are fundamental to market risk managers. The computation of risk measures (e.g. Value-at-Risk) for any portfolio of financial assets requires the generation of density forecasts for the driving risk factors. Appropriate testing procedures must then be identified for an accurate appraisal of these forecasts. We start our research by assessing whether option-implied densities, which constitute the most obvious forecasts of the distribution of the underlying asset at expiry, do actually represent unbiased forecasts. We first extract densities from options on currency and equity index futures, by means of both traditional and original specifications. We then appraise them, via rigorous density forecast evaluation tools, and we find evidence of the presence of biases. In the second part of the thesis, we focus on modelling the dynamics of the volatility curve, in order to measure the vega risk exposure for various delta-hedged option portfolios. We propose to use a linear Kalman filter approach, which gives more precise forecasts of the vega risk exposure than alternative, well-established models. In the third part, we derive a continuous time model for the dynamics of equity index returns from a data set of 5-minute returns. A model inferred from high-frequency typical of risk measures calculations. The last part of our work deals with evaluating density forecasts of the joint distribution of the risk factors. We find that, given certain specifications for the multivariate density forecast, a goodness-of-fit procedure based on the Empirical Characteristic Function displays good statistical properties in detecting misspecifications of different nature in the forecasts