I've heard this several times now: if you're long gamma and delta neutral (I think), how much does the underlying have to move on a daily basis so you don't loose any money (from time decay)? Supposedly the answer is the daily vol but I can't figure out why. Anybody have some insight please? Thanks, NormanPS From the BS PDE, if I'm delta-hedged, I am getting the usual gamma/theta relationship: theta=-1/2vol^2*S^2*gamma. So if the answer were: it has to move by half it's daily variance, then I'd get it but the daily vol seems a little simplistic...

for short position in a vanilla call / put option (the option gamma has always the same sign) you don't loose money if|Spot(t)-Spot(0)|<Spot(0)*sqrt(t)*SigmaImpliedwhere SigmaImplied is the volatility you use to delta-hedge at time 0.Just do Taylor series expansion of your hedging portfolio and use gamma/theta relationship

Thanks for the reply seppar.Frans de Weert 2006 (section 7.4 p86) gives an alternative explanation. Summary: take the gamma/theta relationship theta=-1/2vol^2*S^2*gamma, insert expression for both gamma (N'(d1)/S*vol*sqrt(T)) and theta (S*vol*N'(d1)/2sqrt(T) [2nd term disappears when r=0 for daily moves]) into the PDE, simplify, and you get S*vol*exp(-d1^2/2)/2sqrt(2pi)sqrt(T)=S*vol*exp(-d1^2/2)/2sqrt(2pi)sqrt(T). Basically means gamma profits on delta hedging equals theta (properly explained in book).

hi citynormancould you send me Frans de Weert's paper?thanksQuoteOriginally posted by: citynormanThanks for the reply seppar.Frans de Weert 2006 (section 7.4 p86) gives an alternative explanation. Summary: take the gamma/theta relationship theta=-1/2vol^2*S^2*gamma, insert expression for both gamma (N'(d1)/S*vol*sqrt(T)) and theta (S*vol*N'(d1)/2sqrt(T) [2nd term disappears when r=0 for daily moves]) into the PDE, simplify, and you get S*vol*exp(-d1^2/2)/2sqrt(2pi)sqrt(T)=S*vol*exp(-d1^2/2)/2sqrt(2pi)sqrt(T). Basically means gamma profits on delta hedging equals theta (properly explained in book).

It isn't a paper, it's a book

what is gamma/theta used for?