Hi,In BS's world, we all know there is a reasonable ratio between theoretical gamma and decay, which is 0.5*vol^2*S^2. Some trader may call it "alpha". However,in real world, most traders use market (shradow) gamma which is discrete computed insted of theoretic gamma. Also, they may be interested in modify decay but not the theoretic decay. The modify decay is the price of an option today using currect market factor less the same option but one day shoter in current market , which means it may refer to different volatility level / swap point levelMy confusion is that is there any relation between market gamma and modify decay? it seems they did not follow BS's assumptions, so I initially guss they don't have the firm ratio compared to theoreirc one. However, sometimes I found very strange ratio of them,say it may short maket gamma and loss modify decay,especially in a exotic option portfolio. It's not reasonable for a trader that losing mony in gamma and also losing money in decay. So did I have any wrong understanding in market gamma and modify decay?Thank a lot for your help.

> It's not reasonable for a trader that losing mony in gamma and also losing money in decayHave you accounted for carrying costs? A deep vanilla put on stock might show positive theta because of put-call parity: put = call - stock + PV(strike) ... so theta on the deep put is mostly 1-day's interest on the strike.

Hi Athletico,Thanks for ur reply, I understand the case u mentioned which leads to long gamma and win decay, but my confusion is on market gamma and modify decay but not theoretical ones.Our traders told me how they look at their spot risk : they run the spot ladder report which show P&L change while spot change. And the P&L change may also come from volatility change due to spot movement. Thus they are different from theoretical greeks.For decay, they may face not only theortical decay but also forward decay and volatility decay.So if we long/short market gamma, should we expect lose/win decay on our portfolio??

Hi DinnerEven under basic BS assumptions the ".5*vol^2*S^2 factor" (coming straight form the BS PDE) only holds if you are reasonably delta- and rho-hedged - which would probably be the case.Now by looking at "modified decay" and "market gamma" (assuming that you're still using BS, but with term-structures and smile) you are introducing a lot more variables in the equation, basically for a given vanilla option, decay depends also on the slope of the term-structures (rates, atm vol, smile) and the assumptions you're making about fwd parameters, on the day of the week (wednesday effect), on the carry cost etc. Gamma depends on the shape of the smile curve, on the functional form that you chose for it (interpolation), and also on the smile dynamics assumptions (what happens to the surface when spot moves : sticky strike, sticky delta, sticky delta + spot/rr correl etc.).So although the opposite gamma/theta rule holds in most cases for one given option, at book level this is not necessarily true. In fact, introducing the term-structure alone (without smile) can cause gamma & theta to have the same sign on a vanilla book. Then to analyse this I guess you'd need to go down at trade level (or to roughly replicate your book with a smaller set of options) and break gamma/theta down by individual impact of each factor : start with BS, then add carry, then term structure, smile etc. to find out which positions are hurting most.