Hello!This is a question I'm interested in today.Are cross-gammas always symmetrical?Also try this. If you can have a cross-gamma can you have corresponding zero diagonal gammas?

Are cross-gammas always symmetrical?"Cross-gammas"? I guess you mean the second derivative wrt two different underlyings S1 and S2? If the derivative instrument in question has a solution of the form F(t,S1,S2), i.e. path independependency, the two possible cross-gammas must of course be the same. (Standard multi-variable analysis) For derivatives which are path dependent in the {S1,S2}-space the gammas WILL be different. Another way to put the same question is when you have two deltas, D1(t,S1,S2) and D2(t,S1,S2) and want to know if these are consistent with some solution F such that D1=dF/dS1 etc. This is true if and only if the integrability condition ROT(D) = 0 is fulfilled where D is the vector {D1,D2} in the {S1,S2} space, which is just another way to say that the cross-gammas are the same. Cf. electrodynamics where there is no potential field for the magnetic field in presence of currents since Rot(B) = j (multiplied by pi and some other constants depending om your choice of units of measurement). If you can have a cross-gamma can you have corresponding zero diagonal gammas?YES. You can for instance counstruct one from a an option on two un-correlated underlyings if the diagonal gammas are of opposite signs, and then construct NEW underlyings as appropriate linear combinations of the old ones (if the diagonals have the same value in the first set, the new variables will be the sum and the difference respectively of the old ones). Cf. the theory of general relativity and a metric with so called light co-ordinates. (And YES, I do have a background in as a physicist in field theory -- although that is now a few years ago)

But is it possible to have only cross-gammas and no diagonal gammas?This is possibly trivial - but will lead to series of importantissues I feel.

Zigster, Yes, that is what I meant. It is possible. I don't know if it is trivial or not, but to someone who has used "light cone gauge" or something like that in field theory it doesn't seem that difficult. Would be nice to hear more about those important issues!

But is it possible to have only cross-gammas and no diagonal gammas?Hmm... I realized that there is a really simple example of this: Let x and y be the underlyings to the derivativeF = exp(a (T-t)) x y(final condition F = x y)which fulfils the 2 dim B&S PDE (constant r and covariance matrix V) if a = Vxy + r(where Vxy is the xy component ov V). Then the gammas are Fxx = Fyy = 0 and Fxy = Fyx = exp(a (T-t)). But what kind of derivative is THIS?

hi Lennart, just to make sure I'm understanding your example,we have F = exp(a(T-t)) xy and we also have a=a(x,y)=Vxy+r ?but then Fxx=Fyy=0 is no more true is it?

Reza, I guess I should have used Latex... Vxy is supposed to mean the constant V_{xy} , i.e. the xy-component of the cov. matrix. I hope my sln is fine then... Did it on an envelope. (OK, perhaps not literally)

I see, it is perfectly fine then, Thanks.

Hello!From a business perspective, and actually this is the main driver for this investigation: Which traded products have zero diagonal gammas, but non-zero cross-gammas?This kind of question is a check on the data one expects.