• TIME TO 2024 UK RANKINGS

  • C++ Programming for Financial Engineering
    Highly recommended by thousands of MFE students. Covers essential C++ topics with applications to financial engineering. Learn more Join!
    Python for Finance with Intro to Data Science
    Gain practical understanding of Python to read, understand, and write professional Python code for your first day on the job. Learn more Join!
    An Intuition-Based Options Primer for FE
    Ideal for entry level positions interviews and graduate studies, specializing in options trading arbitrage and options valuation models. Learn more Join!

Delta-Gamma Approximation

hughk

Joined
3/12/13
Messages
2
Points
11
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
 
hughk said:
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
Click to expand...

$25.60 + (-50)*(-0.396) + 0.5*0.069*(50^2) = $131.65
 
**sorry meant increase by 50 points... Thanks for the quick reply though :)
 
hughk said:
**sorry meant increase by 50 points... Thanks for the quick reply though :)
Click to expand...

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.
 
Back
Top