IRC
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Incremental Risk Charge Introduction
Incremental Risk Charge (IRC) attempts to better capture the effects of low probabilities event occurring over long horizons in the trading book. IRC supplements existing Value-at-Risk (VaR) and captures the loss due to default and changes in credit quality at a 99.9% confidence level over a one year capital horizon.
IRC allows liquidity of position to be explicitly modeled, with more liquid positions being replaced more frequently than more illiquid positions. Rebalancing reduces the effect of deteriorating credit quality for liquid instruments, which would otherwise have to be held over the full capital horizon, possibly to default.
However, the rebalancing of more liquid positions is constrained so the portfolio maintains a constant level of risk over the one year horizon. That is, any new positions must maintain the portfolio’s existing risk profile.
| IRC Calculation |
We assume a standard Merton-type structural model. Given a firm with corporate asset value A at time t, it is assumed that stochastic dynamics is governed by
in the usual notation with r_t denoting risk-free rate, σ instantaneous asset volatility and W_t a standard Weiner process. This process is decomposed as a sum of two correlated processes driving common and specific risk components:
representing the sum of corporate exposure to a common and a specific factor, respectively. The obligor / systematic risk correlation is consistent with BCBS 2003 formula for derivation of risk-weighted assets for corporate, sovereign and bank exposures.
We model the joint dynamics among multiple firms by coupling the asset value processes of individual firms with an appropriate correlation structure. The marginal processes are coupled by a joint distribution specified by an appropriate process, e.g. joint normality, Gaussian or other copula.
IRC must include the effects of concentration and correlation. In addition to the market-level correlation between firms, an explicit concentration parameter is included. Concentration refers to the effect of issuer and market concentration on an exposure. In this context correlation refers to the relationship between obligor migrations and systemic risk factors. The correlation between migration and systematic risk factors has been shown to be negligible.
Concentrations are coupled to migrations and defaults by modifying the above decomposition to make the weight of the risk factor across a sector dependent on an additional variable, the concentration parameter. A simple parameterization was chosen so that
That is, higher concentrations will allocate more weight to the systematic risk factor driving default and migration risk across the sector. In this stochastic asset model, an increase in the concentration parameter ρ will increase the volatility of the systematic risk driver. This increases the probability of migration and default within that sector.
The constant level of risk assumption in IRC reflects the view that trading book securities are generally more liquid than the banking book and may be rebalanced more frequently than once a year. IRC should assume a constant level of risk over a one-year capital horizon which may contain shorter liquidity horizons. Positions with shorter liquidity horizons should rebalance, or rollover, any positions which have migrated or defaulted over the previous liquidity horizon.
We assume the same loss distribution is applicable over each liquidity horizon. That is, the Bank holds the portfolio constant over the liquidity horizon, rebalances by selling any migrated or defaulted position, and replaces them so the portfolio is returned to the original level of risk. The process is repeated over additional liquidity horizons until the capital horizon is reached.
The loss distribution, conditional on a constant level of risk, is the convolution of the loss distributions over shorter liquidity horizons. In our Monte Carlo implementation, a constant level of risk constraint is enforced by drawing repeatedly from the single-period loss distribution.
| References |