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I understand that the delta of an option portfolio is just the sum of the deltas of the individual option positions.

What about the other Greeks like gamma and vega? Do the vega and gamma of a portfolio also equal the sum of the individual vegas and gammas of the option positions?

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    $\begingroup$ By rights, you can only add deltas if they're the options have the same underlier... Otherwise you're adding apples and oranges. $\endgroup$ – user3264325 Feb 13 '15 at 4:16
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most models in financial maths are linear so prices and Greeks just add. This is in particular true of Black--Scholes so Yes.

However, once one starts taking into account value adjustments non-linearities appear and it is a lot more complicated.

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  • $\begingroup$ If I have two options P1, P2 (i.e. non-linear) then my portfolio value is P1+P2 and hence all the sensitivities (i.e. greeks) just add, e.g. Gamma(P1+P2) = Gamna(P1) + Gamma(P2). And this is true for any greek, isn't it? Or am I missing the point here? $\endgroup$ – Phil-ZXX Feb 12 '15 at 8:46
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    $\begingroup$ it's the non-linearity of the pricing functional that matters not the non-linearity of the pay-off. Most classical mathematical finance is linear so it works but more recent work on taking into account credit risk destroys this. $\endgroup$ – Mark Joshi Feb 12 '15 at 10:06
  • $\begingroup$ Would you mind making your comment a bit more concrete? What would be a simple example for what you are describing? $\endgroup$ – Phil-ZXX Feb 12 '15 at 11:52
  • $\begingroup$ well suppose i enter into two swaps with the same counterparty going the opposite directions. There is a credit impairment on each that should be accounted for. The credit risk on the two together will be much smaller than the sum of the two and in fact it is smaller than either of the two. $\endgroup$ – Mark Joshi Feb 12 '15 at 22:45
  • $\begingroup$ I appreciate your comment and although I can guess what you are getting at I don't fully understand the subtleties. So would you mind directing to a source where the actual Mathematics is explained? $\endgroup$ – Phil-ZXX Feb 13 '15 at 11:43

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