Gamma of Asian Option

helix · March 3rd, 2008, 10:48 pm

Hi,I came across a curious result today which I can't get my head around. If I price an Asian option at inception (fixed strike, arithmetic avg of discrete fixings), the gamma is larger than a vanilla with same maturity & strike. Given that the vol of the average is quite a bit lower than the stock (by approx 1/sqrt(3) lets say) I expected the gamma to be substantiallyl lower. What's going on? Thanks for any insight!

DavidJN · March 4th, 2008, 12:13 pm

You are watching the average height of people in a room. The game starts with one person in the room who is six feet tall. Then a second person comes in. What happens to the average if they're not six feet tall? Later there are 100 people in the room and their average height is six feet. One more person walks into the room and that person is not six feet tall. What happens to the average height then? Get it?

helix · March 4th, 2008, 1:53 pm

you're talking about the dynamics of the average - as more people come in the incremental change in the avg height becomes smaller and smaller, i.e. the vol of the average falls. But how does this observation explain why the option gamma is larger than the equivalent vanilla?

kramelo · March 4th, 2008, 5:35 pm

I would consider the fact that the upper boundary for an asian price is the average price of plain vanilla maturing at the asian option fixing dates. This way of looking to an asian option could tell you some thing about a good approx of its greeks. The gammas of the shortest of these options are higher so their average is higher if compared with the gamma of the plain vanilla option expiring like the asian.

Alan · March 4th, 2008, 6:27 pm

QuoteOriginally posted by: helixHi,I came across a curious result today which I can't get my head around. If I price an Asian option at inception (fixed strike, arithmetic avg of discrete fixings), the gamma is larger than a vanilla with same maturity & strike. Given that the vol of the average is quite a bit lower than the stock (by approx 1/sqrt(3) lets say) I expected the gamma to be substantiallyl lower. What's going on? Thanks for any insight!Have you tried taking that vanilla, lowering the sigma, and seeing what happens to gamma?regards,

kramelo · March 4th, 2008, 9:06 pm

so gamma increase when vola decrease.. interesting as result.. you could publish something related to this

quanter9 · February 1st, 2012, 1:02 pm

Can I use curran's closed form solution ( as given in Hugg) for computaion of greeks?Should I use central difference in Greeks computaion, is this method is accurate?Is curran's formala is differeciable with respect to undelying price, volatility and interest rate for Greeks computaion(closed form solutions for Greeks). If so Please provide me the required links or if any body differenciated it kindly share with meThis will be greate help for meRegards

quanter9 · February 3rd, 2012, 5:38 am

Hi Helix,How you calculated Gamma of asian options, I mean which model is used in computaion of GammaAre you using any closed form solution or implemented numerical methods ?Please help me in coputaion of Asian option GammaRegards,