hidari


Total Posts: 17 
Joined: May 2007 


Could someone please help me understand how these are computed for options
If I take a stock, then the delta = 1 hence the $ delta = number of shares * price of stock.
How does this work for options:
options are for 100 shares:
we know the delta of the position
shouldn't $ delta be : number of options * number of shares per option * delta
thanks for any help  more intersted in how I should think about it rather than the formula
appreciate ur help 




Graeme


Total Posts: 1629 
Joined: Jun 2004 


The key to understanding these things is how to aggregate them. So, you need to think how the greeks translate into p&l. Now, for example, is the p&l on the option when the underlying goes up/down by 1% (the number of options you have and the number of shares per option are both 1, the bookkeeping if they aren't is just that  bookkeeping). So, is the dollar equivalent delta, and can be aggregated across different options, even different underlyings if you are brave or foolhardy.
Similarly is the notional cost of rebalancing the hedge under a 1% move up/down in S. So is used for measuring the notional cost of rebalancing the hedge, and is called the dollar equivalent Gamma.
Dollar vega? That doesn't make sense to me. The thing that is moving (volatility) isn't in currrency units. 
Graeme West 


chiral3

Founding Member

Total Posts: 5100 
Joined: Mar 2004 


For vega you'd shock your vol curve to get the 1% vega, and translate that into your $ vega, i.e., $100 option has a 2% vega  vol moves by $2 the option is $104.... but don't listen to me, I've been drinking..... 
Nonius is Satoshi Nakamoto. 物の哀れ 



granchio


Total Posts: 1541 
Joined: Apr 2004 


$vega is simple... how much $ you make if the volsurface moves up rigidly by 1%.
$delta is trivial
$gamma we can have normalization issues. i like it as the change in $delta for 1% move of the spot 
"Deserve got nothing to do with it"  Clint 



granchio can you explain what you mean by "normalization issues" ?
won't your gamma just be in the same units as your delta  you can think of it as the second order term in a taylor expansion of price , or as the change in delta per "X" move of spot (where "X" is the same move that is used to express the delta) ?





Graeme


Total Posts: 1629 
Joined: Jun 2004 


> $vega is simple... how much $ you make if the volsurface moves up rigidly by 1%.
In what way is that different to (0.01 *) vega?? 
Graeme West 


granchio


Total Posts: 1541 
Joined: Apr 2004 


it's all a matter of conventions... sorry for misusing the grandiloquent "normalization".
graeme::
>> $vega is simple... how much $ you make if the volsurface moves up rigidly by 1%.
>In what way is that different to (0.01 *) vega??>>
not really. depends if in "vega" you include the quantity and the multiplier. we clearly agree, i was just confused by your statement that dollar vega did not make sense
silverside:
just a matter of multipliers and conventions... what do you include in your gamma. i use gamma = d2 value/dS2, where value is the price of 1 unit of a security. then $gamma= quantity*multiplier*gamma*S^2/100 (i.e. the change in $delta for a 1% move in S)

"Deserve got nothing to do with it"  Clint 



Graeme


Total Posts: 1629 
Joined: Jun 2004 


I agree I wasn't clear, I probably should have said that we are already in currency units.
Actually, doing a naive dimensional analysis (remedial physics, I guess, which is about the right level for me) delta is in units of $ per share, wheras vega and rho are in $ already, as volatility and risk free rates are unitless ('pure numbers'). 
Graeme West 


granchio


Total Posts: 1541 
Joined: Apr 2004 


true if you think of "fixed units" options such as standard exchange traded.
for "fixed notional" options such as standard otc's then the price is dimensionless (quoted in % in fact). gain its dimension ($) when multiplied by the notional.
was a physicist myself... dimensional analysis best trick in the trade. last to forget (though not first to learn) 
"Deserve got nothing to do with it"  Clint 




thanks for the reply granchio
i think we are all agreed  although i almost always think of the risk in $ (per trading book or per deal)  just terminology differences ... 


