We know dv01, duration, delta (and probably gamma) … can roll up across positions as weighted average. I think theta too, but how about vega?
Specifically, suppose you have option positions on SPX at different strikes and maturities. Can we compute weighted average of vega? If we simulate a 100bps change in sigma_i (implied vol), from 20% pa to 21% pa, can we estimate net change to portfolio MV?
I doubt it. I feel a 100 bps change in the ATM 1-month option will not happen in tandem with a 100 bps change across the vol surface.
– Along the time-dimension, the long-tenor options will have much __lower__ vol changes.
– Along the strikes, the snapshot vol smile curve already exhibit a significant skew. It’s unrealistic to imagine a uniform 100 bps shift of the entire smile (though many computer system still simulates such a parallel shift.)
Therefore, we can’t simulate a 100 bps bump to sigma_i across a portfolio of options and compute a portfolio MV change. Therefore vega roll-up can’t be computed this way.
What CAN we do then? I guess we might bucket our positions by tenor and aggregate vega. Imperfect but slightly better.