Response to discussion on the EU implementation of MKR and CCR revised standards
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We appreciate that no binding definitions of sensitivities are prescribed here. Indeed, it is interesting to elaborate on the meaning of sensitivities" in this context. The most natural interpretation is to consider market sensitivities, i.e. greeks. In this case, in order to assess the materiality of each risk driver, the bank must identify the primary risk driver each time the exposure is computed, with potential change from day to day and artificial impact on the EAD.
However, other types of sensitivities can be considered, which we deem more suitable for the purpose of assessing the materiality of risk drivers. In particular we propose to use "Global Sensitivity Analysis" (GSA, explained e.g. in I. M. Sobol’, S. Kucherenko, "Global Sensitivity Indices for Nonlinear Mathematical Models. Review", Wilmott Magazine, Vol. 2, 2005, and in S. Kucherenko , S. Tarantola, P. Annoni "Estimation of global sensitivity indices for models with dependent variables", Computer Physics Communications, Vol. 183, April 2012): with this methodology the primary risk driver can be identified once and for all the duration of the transaction. By making use of the ANOVA decomposition of a given function of the risk factors (e.g. trade PV), Sobol’ sensitivity indices to the variation of a subset of risk factors are quantified in terms of contribution to the total variance while all other risk factors are varied as well, thus exploring the whole domain of the function.
GSA is a general approach, which can be applied also to non-linear models and it takes into account possible interactions among risk factors. A heavier computational effort (i.e. the computation of relevant Sobol’ indices) is balanced by the fact that it is needed only for a small subset of trades and it is performed only once per trade.
A similar procedure to the one described at paragraph 72 can be then applied to Sobol’ indices instead of market sensitivities s_{i}.
From our point of view, GSA is a very robust methodology when the assessment of risk factor materiality is necessary and the additional implementation effort needed to compute Sobol' indices is widely compensated by the above mentioned benefits, especially for portfolios with large portions of complex instruments: for small banks, whose trading book is typically small and dominated by simple instruments, it would be sufficient to adopt the qualitative approach or to use market sensitivities. More sophisticated banks, with large trading books containing many complex instruments, could find preferable to adopt a GSA-based quantitative approach in order to obtain a more precise and stable estimation of the risk associated to these transactions."
Question 6. Which would be the most appropriate option for the quantitative approach? Would you recommend another option?
We consider that the most appropriate option for quantitative approach, among the EBA proposals, is the multistep approach described in option 2 (paragraph 72): this option is a multistep approach whereby all the sensitivities of an instrument are first computed, then they are ranked in terms of relative relevance and finally only those that are the most relevant to the total are selected.We appreciate that no binding definitions of sensitivities are prescribed here. Indeed, it is interesting to elaborate on the meaning of sensitivities" in this context. The most natural interpretation is to consider market sensitivities, i.e. greeks. In this case, in order to assess the materiality of each risk driver, the bank must identify the primary risk driver each time the exposure is computed, with potential change from day to day and artificial impact on the EAD.
However, other types of sensitivities can be considered, which we deem more suitable for the purpose of assessing the materiality of risk drivers. In particular we propose to use "Global Sensitivity Analysis" (GSA, explained e.g. in I. M. Sobol’, S. Kucherenko, "Global Sensitivity Indices for Nonlinear Mathematical Models. Review", Wilmott Magazine, Vol. 2, 2005, and in S. Kucherenko , S. Tarantola, P. Annoni "Estimation of global sensitivity indices for models with dependent variables", Computer Physics Communications, Vol. 183, April 2012): with this methodology the primary risk driver can be identified once and for all the duration of the transaction. By making use of the ANOVA decomposition of a given function of the risk factors (e.g. trade PV), Sobol’ sensitivity indices to the variation of a subset of risk factors are quantified in terms of contribution to the total variance while all other risk factors are varied as well, thus exploring the whole domain of the function.
GSA is a general approach, which can be applied also to non-linear models and it takes into account possible interactions among risk factors. A heavier computational effort (i.e. the computation of relevant Sobol’ indices) is balanced by the fact that it is needed only for a small subset of trades and it is performed only once per trade.
A similar procedure to the one described at paragraph 72 can be then applied to Sobol’ indices instead of market sensitivities s_{i}.
From our point of view, GSA is a very robust methodology when the assessment of risk factor materiality is necessary and the additional implementation effort needed to compute Sobol' indices is widely compensated by the above mentioned benefits, especially for portfolios with large portions of complex instruments: for small banks, whose trading book is typically small and dominated by simple instruments, it would be sufficient to adopt the qualitative approach or to use market sensitivities. More sophisticated banks, with large trading books containing many complex instruments, could find preferable to adopt a GSA-based quantitative approach in order to obtain a more precise and stable estimation of the risk associated to these transactions."
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