31.Supervisory delta adjustments reflect the fact that the notional value of a transaction is not by itself a good indication of the associated risk. In particular, exposure to future market movements depends on the direction of the transaction and any non-linearity in the structure.

32.With respect to direction, a derivative may be long exposure to the underlying risk factor (price, rate, volatility, etc.), in which case the value of the derivative will move in the same direction as the underlying – gaining value with increases, losing value with decreases – and the delta is positive to reflect this relationship. The alternative is that a derivative may be short exposure to the underlying risk factor, in which case the value of the derivative moves opposite to the underlying – losing value with increases, and gaining value with decreases – and thus the delta is negative.

33.The non-linearity effects are prominent with transactions that involve contingent payoffs or option-like elements. Options and CDOs are notable examples. For such derivative transactions, the impact of a change in the price of the underlying instrument is not linear or one-for-one. For example, with an option on a foreign currency, when the exchange rate changes by a given amount, the change in the value of the derivative – the option contract – will almost always be less than the change in the exchange rate. Moreover, the amount by which the change is less than one-for-one will vary depending on a number of factors, including the current exchange rate relative to the exercise price of the option, the time remaining to expiration of the option, and the current volatility of the exchange rate. Without an adjustment for that difference, the notional amounts alone would be misleading indications of the potential for counterparty credit risk.

34.The supervisory delta adjustments for all derivatives are presented in the table below, which is repeated from the CCR Standards. These adjustments are defined at the trade level, and are applied to the adjusted notional amounts to reflect the direction of the transaction and its non-linearity.

35.Note that the supervisory delta adjustments for the various option transactions are closely related to the delta from the widely used Black-Scholes model of option prices, although the risk-free interest rate – which would ordinarily appear in this expression – is not included. In general, banks should use a forward price or rate, ideally reflecting any interim cash flows on the underlying instrument, as P in the supervisory delta calculation.

36.The expression for the supervisory delta adjustment for CDOs is based on attachment and detachment points for any tranche of the CDO. The precise specification (including the values of the embedded constants of 14 and 15) is the result of an empirical exercise conducted by the Basel Committee on Banking Supervision to identify a relatively simple functional form that would provide a sufficiently close fit to CDO sensitivities as reported by a set of globally active banks.

Supervisory Delta Adjustments

Definitions

For options:

In this expression, P is the current forward value of the underlying price or rate, K is the exercise or strike price of the option, T is the time to the latest contractual exercise date of the option, σ is the appropriate supervisory volatility from Table 2, and Φ is the standard normal cumulative density function. A supervisory volatility of 50% should be used on swaptions for all currencies.

For CDO tranches:

In this expression, A is the attachment point of the CDO tranche and D is the detachment point of the CDO tranche.