VaR delta are described. Section 7.5 concludes the chapter by analyzing autonomy and
pricing limits for credit risk.
7.1 Defi ning VaR-Based Limits for Market Risk: Identifying
Risk-Taking Centers
When de ning a risk policy for business units in the trading business, which would be
exposed mainly to either market risks (e.g., in the case of equity trading) or the credit
risk of traded nancial instruments (e.g., corporate bonds, credit derivatives), the fi rst
topic to be considered is identifying which units should be given a limit. This in turn
requires (1) defi ning the highest level in the hierarchy of business units and desks to which
VaR limits should be set and (2) checking whether the boundaries between the tasks of
different units allow one to defi ne VaR limits ef ciently by reducing risk overlaps as much
as possible.
The fi rst problem is related, for instance, to whether VaR limits should be set only
up to the equity trading business unit or also to the level of the main desks composing
the unit (e.g., cash, futures, plain-vanilla options, exotic option trading) or even to
the level of the individual trader. A more detailed disaggregation of VaR limits might
help if VaR is considered an ef cient way to set operational risk limits for the single entity
(i.e., business unit, desk, or individual trader) and if the bank is willing to measure
the performances based not only on expost utilized VaR, but also on the amount of
capital assigned to the unit, which depends precisely on its VaR limit. As we see later on,
this may also be used to create incentives to use more intensively the allocated capital for
each entity, i.e., to reduce the percentage of idle, unutilized capital. In theory, then, a more
pervasive attribution of VaR limits would be desirable.
At the same time, there may be reasons to keep VaR limits at a higher hierarchical
level. One case is when VaR limits may control only partially the real risk of the exposures
of a desk. A bank adapting a variancecovariance approach could hardly use it to control
the day-to-day risk of its equity option desk. Of course, a more sophisticated VaR model
could be more helpful, but a bank with a small option desk may still consider that invest-
ing in a better VaR model is not worth the extra cost and effort. In this case, VaR limits
should be set at a higher level and the desk should simply be given limits based only on
option greeks such as delta and vega (i.e., sensitivities to changes in the underlying asset
price and implied volatility). These simpler limits are also widely used in more sophisti-
cated banks, since they help in capturing the risk profi le of the option portfolio, even on
an intraday basis, when VaR measurement with a more sophisticated model could be too
diffi cult.
More generally, it is useful to recall that VaR is usually calculated based on the traders
portfolio after the mapping process has been performed. A poorly mapped portfolio in
which some of the real risks “disappear” during the mapping phase (e.g., an option posi-
tion that is transformed into a linear equivalent through a delta-only approximation, an
undiversifi ed stock portfolio whose VaR is approximated as beta times the stock index
VaR) can hardly be controlled through VaR limits. Failing to model existing risks properly
could be considered one of the sources of operational risk in the trading business, but a
careful check of existing limitations is important when defi ning a VaR limit system (see
also Box 7-1).
DEFINING VaR-BASED LIMITS FOR MARKET RISK 171

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