Bounds on total economic capital: the DNB case study

Abstract

Most banks use the top-down approach to aggregate their risk types when computing total economic capital. Following this approach, marginal distributions for each risk type are first independently estimated and then merged into a joint model using a copula function. Due to lack of reliable data, banks tend to manually select the copula as well as its parameters. In this paper we assess the model risk related to the choice of a specific copula function. The aim is to compute upper and lower bounds on the total economic capital for the aggregate loss distribution of DNB, the largest Norwegian bank, and the key tool for computing these bounds is the Rearrangement Algorithm introduced in Embrechts et al. (J. Bank. Financ. 37(8):2750-2764. The application of this algorithm to a real situation poses a series of numerical challenges and raises a number of warnings which we illustrate and discuss.

A Review on Ambiguity in Stochastic Portfolio Optimization

“…In the remainder of this paper we restrict our considerations to ambiguity sets defined by Wasserstein neighborhoods. In particular, we set the distance d(x, y) = ||x − y|| 1 …”

“…Still the dependence structure is crucial when it comes to aggregating the individual risks. We refer to Aas and Puccetti [1] for an illustrative example. Since risk measurement is the corner stone of any portfolio selection strategy, the methods and results concerning dependence uncertainty are particularly relevant in our context.…”

Reducing model risk via positive and negative dependence assumptions

“…Even if DUspreads of VaR and ES are numerically available for practically any joint portfolio of risks, their relevance in actuarial practice has been recently questioned since they can be considerably large; see Aas and Puccetti (2014) for a real case study.…”

“…This is studied later in Section 4 when deriving risk bounds for convex risk measures. When one uses Value-at-Risk, the assumption of comonotonicity within the subgroups cannot be regarded as conservative from a mathematical viewpoint (VaR is well known not to be a coherent risk measure) but serves to rule out the worst-case VaR distributions attained by negative dependence as described in Wang and Wang (2011), Embrechts et al (2013) and Aas and Puccetti (2014). However, it turns out that the upper bound on the VaR of the aggregate position will not be essentially reduced by positive dependence assumptions especially when the portfolio consists of a relatively large number of random variables.…”

Rearrangement algorithm and maximum entropy

“…The RA has applications in various disciplines. Embrechts et al (2013) use the RA in quantitative risk management to obtain sharp approximations for the maximum possible Value-at-Risk (VaR) of a portfolio sum of d dependent risks when all marginal distributions are known but no information on dependence is available; see Aas and Puccetti (2014) for a case study. The RA can also be used in situations under which partial information on dependence is available (see Bernard et al 2017a, b;Bernard and Vanduffel 2015).…”