IRC and CRM: Modelling Framework for the ‘Basel 2.5’ Risk Measures

• Published date: 01 September 2013
• Date: 01 September 2013
• DOI: http://doi.org/10.1111/j.1468-036X.2013.12015.x
• Author: Vladimir Chorniy,Sascha Wilkens,Jean‐Baptiste Brunac

IRC and CRM: Modelling Framework

for the ‘Basel 2.5’Risk Measures

Sascha Wilkens, Jean‐Baptiste Brunac and

Vladimir Chorniy

BNP Paribas, Risk Methodology and Analytics, London, UK

E-mails: Sascha.Wilkens@bnpparibas.com; Jean-Baptiste.Brunac@bnpparibas.com;

Vladimir.Chorniy@bnpparibas.com

Abstract

This paper presents a modelling framework for the Incremental Risk Charge (IRC)

and Comprehensive Risk Measure (CRM) as the new capital requirements for

market risks in a bank’s trading book (‘Basel 2.5’). Both are Value‐at‐Risk‐type

measures projecting losses over a one‐year capital horizon at a 99.9% confidence

level and are applicable to credit flow and credit correlation instruments,

respectively. With no consensus on industry standards for suitable internal models

as yet, the article discusses selected risk factor models to derive simulation‐based

loss distributions and the associated risk figures. Example calculations and

implementation aspects complement the discussion.

Keywords: incremental risk, IRC, comprehensive risk, CRM, basel 2.5

JEL classification: G13, G18

1. Introduction and Regulatory Background

In the aftermath of the world‐wide credit crisis of the years 2007 and 2008 and recognising

the fact that banks hold substantial positions in structured and potentially illiquid credit

instruments in their trading books, the Basel Committee proposed new capital charges to

complement the existing market risk capital requirements (Basel Committee on Banking

Supervision, 2009, 2011). Shortcomings targeted by the new charges are, amongst others,

differences in the underlying liquidity of trading book positions where market losses can

be driven by the potential for large cumulative price moves over several weeks or months,

as well as the limitations of a 99% one‐day or ten‐day Value‐at‐Risk (VaR); the latter

We appreciate helpful input and suggestions from Fakher Ben Atig, Maria Teresa Cardoso,

Laurent Carlier, Peter Dobranszky, Andrei Greenberg, Tom Hanney, Vera Minina,

Sébastien Rérolle, Anton Simanenka and an anonymous referee. The views expressed in

this paper are those of the authors and do not necessarily reflect the views and policies of

BNP Paribas. Correspondence: Sascha Wilkens.

European Financial Management, Vol. 19, No. 4, 2013, 801–829

doi: 10.1111/j.1468-036X.2013.12015.x

© 2013 John Wiley & Sons Ltd

usually does not adequately reflect large default losses that occur less frequently and thus

cannot be scaled to longer time horizons.

The new charges became effective January 2012 and are based on internal models,

which require validation by the institutions’home regulators. Recent guidelines have

clarified certain modelling details (European Banking Authority, 2012). The Incremental

Risk Charge (IRC) is intended to cover market risks from credit rating migrations and

defaults for flow instruments such as bonds and credit default swaps (CDS). Importantly,

sovereign bonds and CDS are to be included, even if they were not to attract risk charges

under the standardised approach. Long and short positions in an institution’s own debt

arising from trading or market‐making activity in its own bonds and credit protection on

itself (for example, via credit index trades) are to be reflected only with regard to migration

risk. IRC also applies to covered bonds and non‐tranched asset‐backed securities (e.g.,

pass‐through MBS).

1

More complex instruments such as collateralised debt obligations

(CDO) and their hedges (including CDS), excluding re‐securitisation positions (e.g.,

CDO^2) and Leveraged Super Senior (LSS) tranches, are subject to a separate, extended

market risk model –the Comprehensive Risk Measure (CRM). CRM has to cover all price

risks (e.g., credit spread volatility, volatility of implied correlations), in addition to credit

migrations and defaults as in IRC. CDS that are recognised in CRM as hedges are not to be

included in IRC. Without a designated CRM model, the credit correlation trading activity

is subject to capital requirements based on the standardised measurement method, which

is essentially a banking book‐type calculation that only imperfectly recognises risk

reduction via hedging.

2

The standardised method is to be applied in any case to all

securitisation positions not covered by CRM.

Both IRC and CRM are measures based on the 99.9% loss quantile at a one‐year capital

horizon and have to be computed at least on a weekly basis. Rebalancing of positions may

be taken into account via shorter liquidity horizons (not shorter than three months),

coupled with a ‘constant level of risk’concept. This contrasts with VaR, which is a 99%

quantile measure and has a short‐term focus.

Despite the importance of the topic, with the exception of a few papers focussing on

particular details (Glasserman, 2009; Finger, 2011), no literature is available on a

comprehensive modelling framework for IRC and CRM. The only notable exceptions are

the works by Martin et al. (2011) and Skoglund and Chen (2011), where the basic

algorithmic steps of an IRC‐compatible multifactor model are formulated explicitly. This

paper closes this research gap by discussing modelling approaches for both IRC and

CRM. The development of risk factor models and their correlation structures is

complemented by example calculations and the discussion of implementation aspects. It

becomes transparent that high confidence levels and long projection horizons, in

conjunction with limited backtesting feasibility, leave a substantial model risk.

1

See European Banking Authority (2012, pp. 9–11). A bank may choose to also include

equity positions in IRC in case equity and credit instruments are jointly managed (e.g.,

convertible bond arbitrage).

2

The method can be very punitive for the complex credit correlation trading business,

featuring large offsetting positions, which are typically well‐hedged against credit spread and

correlation risks, and would thus render the business non‐sustainable from a capital

requirement perspective. The CRM figure is floored to a fraction of the standardised

measurement method for the credit correlation book (see also the example in Section 4.4).

© 2013 John Wiley & Sons Ltd

802 Sascha Wilkens et al.