Delta-Gamma Approximation

[hughk]

Hello Everyone!

First post! (Yay!) Sorry if this is fairly basic, but for some reason its not panning out as expected when calculating future approximate pricing for SPX options. For example:

Assuming a increase of 50 points on the index, and using the SPX US 05/18/13 P1525 option with the following parameters:

Last Price Historic Vol Implied Vol Vol Spread Delta Gamma Theta Vega
$25.60 11.73 13.05 1.32 -0.396 0.069 -0.276 2.528

Plugging into the Delta-Gamma approximation formula of:

C(St+h) = C(St) + є∆(St) + (1/2)є2Γ(St)

results in: $25.60 + (50)*(-0.396) + 0.5*0.069*(50^2) = $92.52

Does this method not work for index options?!

Thanks in advance

 

[AndrewChang]

Hello Everyone!

First post! (Yay!) Sorry if this is fairly basic, but for some reason its not panning out as expected when calculating future approximate pricing for SPX options. For example:

Assuming a decrease of 50 points on the index, and using the SPX US 05/18/13 P1525 option with the following parameters:

Last Price Historic Vol Implied Vol Vol Spread Delta Gamma Theta Vega
$25.60 11.73 13.05 1.32 -0.396 0.069 -0.276 2.528

Plugging into the Delta-Gamma approximation formula of:

C(St+h) = C(St) + є∆(St) + (1/2)є2Γ(St)

results in: $25.60 + (50)*(-0.396) + 0.5*0.069*(50^2) = $92.52

Does this method not work for index options?!

Thanks in advance

$25.60 + (-50)*(-0.396) + 0.5*0.069*(50^2) = $131.65

 

[hughk]

**sorry meant increase by 50 points... Thanks for the quick reply though

 

[AndrewChang]

**sorry meant increase by 50 points... Thanks for the quick reply though

Delta gamma approximation is kind of risky for something like this. 50 points is a 3% + move so the approximation will indeed be off. Another reason is also probably of third derivative with respect to spot. Third derivative causes a lot of errors for something that is around 40 delta and for something around 60 delta, which this exactly is. Approximating what your delta should be at this point,
(\Delta = \Delta_0 + \gamma * dS = 50*(0.069) - 0.396 = 3.054)
which is impossible.