Credit Limits, Stress Testing and Model Risk for Capital Metrics

Abstract

The topics of Economic Capital modelling, reverse stress testing and credit limits are inextricably intertwined as they all focus on exceptional loss events. In this paper, we use the KVA framework in to frame these three topics within a single unified approach. We propose setting credit limits based on an incremental KVA metric interpreted as a measure of capital consumption for each individual client. Compared to Potential Future Exposure (PFE), incremental KVA is more risk sensitive as i) it is portfolio sensitive and detects cross-selling opportunities, ii) captures wrong-way-risk, iii) accounts for idiosyncratic features such as granularity and credit risk concentration, iv) measures also other risks besides the default of the counterparty such as CVA and FVA mark-to-market losses and is suitable to generalisations driven by regulatory changes such as MVA.A reverse stress testing exercise based on KVA metrics reveals stress scenarios of two kinds: the ones where losses are due to an idiosyncratic vulnerability of the portfolio and the ones tied to systemic risk and the credit cycle. The latter are completely missed by the PFE, although crucially important during periods of market distress.Since different pricing models tend to diverge the most for stressed scenarios, model risk has a material impact on capital projections and, consequently, on the KVA metric. We discuss model risk comparing Gaussian interest rate models admitting arbitrarily negative rates with alternative models where rates are bounded from below.