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Hope you're doing great! I'm struggling to develop the code for the Third Order Greeks.

In all places I have searched, the development is missing.

For example:

enter image description here

But I don't know how to develop it, in order to code it in VBA.

Could you help me or know where I can search?

Thanks beforehand!

Kind regards,

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    $\begingroup$ I suppose you work with the Black Scholes model? Does this help: en.m.wikipedia.org/wiki/Greeks_(finance) Have a look at the section “formulas for European options”. (It’s however a nice exercise to try to compute them by yourself) $\endgroup$
    – Kevin
    Apr 25, 2020 at 8:07
  • $\begingroup$ Thank you! Yes, I'm working de BS Model and I have seen the Wikipedia page. However, also in the section of Formulas, the third order greeks are not developed. It just said it is the derivative of the second order greek :/ $\endgroup$
    – Arimarhol
    Apr 26, 2020 at 9:21
  • $\begingroup$ That's funy because I do see the formulae for ultima, speed, zomma, color there. So the wikipedia page does list the third-order greeks :) They're not just given in the list I linked previously (just scroll to the bottom of that list to find third-order Greeks!), they also have their own section: en.wikipedia.org/wiki/Greeks_(finance)#Third-order_Greeks $\endgroup$
    – Kevin
    Apr 26, 2020 at 9:26
  • $\begingroup$ Yes, as I mentioned before I did see the formula e.g Ultima=derivative of Vomma/derivative of sigma but what I need is the math development for the two derivatives. E.g Sped= -(gamma(1+d1/sigma*Sqr(T))/S $\endgroup$
    – Arimarhol
    Apr 26, 2020 at 9:36
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    $\begingroup$ And as I said, if you go to the section which tabulates all formulae, on the bottom of the Wikipedia page, you’ll find an explicit formula for ultima $\endgroup$
    – Kevin
    Apr 26, 2020 at 9:42

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Here's an implementation (in Matlab, not VBA).

https://github.com/crodriguezvega/black-scholes-european-option/blob/master/blsEuropeanOption.m

EDIT: a second implementation (again in Matlab) including the third order Greeks:

https://kr.mathworks.com/matlabcentral/fileexchange/69544-calcgreeks-calculate-option-greeks-european-black-scholes?focused=0e261091-4b38-4724-97c0-574b9b92004b&tab=function

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  • $\begingroup$ Thank you! However, I think you can compute them because I could do it for Zomma but with Ultima and Speed I couldn't. $\endgroup$
    – Arimarhol
    Apr 26, 2020 at 9:26

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