CoachVega weighting divides each price error by the Black vega of its quote, so that : a price calibration then minimises implied-volatility errors to first order, without inverting.
Exemples
Example 24.6 (What the weights buy)
On the first day of the synthetic market (four expiries from one month to one year, five strikes each, eighteen after the filter), the Heston fit’s root-mean-square error by expiry, in volatility points, is:
| weights | 1 month | 3 months | 6 months | 1 year | all |
|---|---|---|---|---|---|
| vega | 0.35 | 0.21 | 0.14 | 0.11 | 0.22 |
| equal (price errors) | 0.46 | 0.15 | 0.12 | 0.06 | 0.24 |
Equal weights buy a better one-year fit with a worse one-month one. At the money a one-month option’s vega is the one-year’s divided by , so in price its errors count twelve times less.