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Vega vs Gamma
The analytical expressions for Gamma and Vega of an European call areWhen plotted against S, they look very similar, and yet basically Vega = k * Gamma * S^2.What am I missing?Thanks for help.
Vega vs Gamma
This might not be what you are asking (as your question is fairly open ended) but dont forget that d1 is also a function of S.
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Vega vs Gamma
Sure, but it's the same in both formulae, no?I suspect there's something special about n(d(S))) that somehow neutralises the S^2 both "in the large" and "in the small".Basically my question is, how can the plot of a f(x) look the same as x^2 * f(x)? (Aside from a scaling factor?)
Vega vs Gamma
All the action in gamma is centred on where d_1 is zero (call this S*), outside that its value falls of rapidly, getting exponetially small. So the difference between vega and gamma is to a first approximation just S*^2.P
Vega vs Gamma
QuoteOriginally posted by: PaulAll the action in gamma is centred on where d_1 is zero (call this S*), outside that its value falls of rapidly, getting exponetially small. So the difference between vega and gamma is to a first approximation just S*^2.PIt's as Paul said ... the exponential decay on n(d1) is much more important than the linear change in S.The attached charts shows how the ratio between the similar charts (forward greeks, t=1,K=1: n(d1), vol*gamma, vega) is equal to S or 1/S ... so although they look similar the ratio is as expected.
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Vega vs Gamma
Interesting, thanks everybody.MCarreira, it's strange you would get a linear ratio, I had expected S^2 or 1/S^2...Cheers
Vega vs Gamma
QuoteOriginally posted by: pizzaInteresting, thanks everybody.MCarreira, it's strange you would get a linear ratio, I had expected S^2 or 1/S^2...CheersThe ratio I showed was between n(d1) and both gamma and vega; in this way you can see that the dominant shape is n(d1). The relationships are then S and 1/S.