CoachThe unexplained P&L is the difference between the actual P&L and the sum of the attributed parts. Controllers set thresholds on it, in money and as a share of the P&L, beyond which it must be investigated.
Exemples
Example 27.4 (A risk reversal on a quiet day)
An illustrative book is long USD 320 million of one-year-into-ten-year payer swaptions struck at 4.50% and short the same notional of receivers at 3.50%, a risk reversal around a forward of 4.00%, marked at a normal volatility of 95 basis points (0.75 years to expiry, annuity 8.0). The two legs are worth the same, so the book is worth zero, and by symmetry its gamma, vega and theta are zero too: it is a pure delta position, 139 103 dollars per basis point. Its cross sensitivity is not zero: the vanna is 1 086 dollars per basis point of rate and basis point of volatility, because a higher rate moves the long payer towards the money and the short receiver away from it.
Example 27.5 (The big-move day)
The forward rises 30 basis points and the volatility 12. The book makes USD 4 571 501. The desk’s explain, delta, gamma, vega and theta, gives 4 173 095, all from delta: 398 406 dollars are unexplained, 9% of the day. Adding the vanna term, , explains 391 087 of them; 7 319 remain, higher-order terms (Figure 27.1). The unexplained P&L grows with the product of the rate and volatility moves, which is why it appears on big days (Figure 27.2).