A little confused, I consulted the Wilmott forums for guidance on how I can interpret vega/vomma. Another user's post reminded me that the Black-Scholes model assumes that the underlying has constant volatility, so vega is an out-of-model concept. If Black-Scholes assumes that volatility does not change, then would this not render vega/vomma calculations useless since they are based from the Black-Scholes formula? The vega calculation seems odd because one gauges how the option value changes with volatility, but then Black-Scholes assumes volatility does not change. Going a step further, the idea of vomma in a Black-Scholes world seems odd because if volatility does not change, then surely vega would not change?
I understand that Black-Scholes makes some questionable assumptions, but if we price options in a Black-Scholes world, then it seems peculiar that these metrics have come about as a result of the Black-Scholes formula. I would really appreciate any insight.