Closed Form Implied Vol

[NotQuiteRandom]

Hi,

I have been messing around with this paper I found online...

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=567721

The author offers a closed form approximation for implied vol and claims to cover a far larger range than those published to date.

Having implemented it I find that it usually works fine (converges with Newton R) but I am sometimes computing the sqrt of negative numbers and getting erroneous results here:

Sqr(2 * Pi) / (2 * (S + x)) * (2 * c + x - S + Sqr((2 * c + x - S) ^ 2 - 1.85 * (S + x) * (x - S) ^ 2 / (Pi * Sqr(x * S)))) / Sqr(T)

I could substitute the argument under the sqrt for zero but this is hacky to say the least.

Am I missing something or is this a flaw in the paper?

Is anyone familiar with the paper?

Thanks,

NQR

 

[Robertral]

Hi,

I have been messing around with this paper I found online...

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=567721

The author offers a closed form approximation for implied vol and claims to cover a far larger range than those published to date.

Having implemented it I find that it usually works fine (converges with Newton R) but I am sometimes computing the sqrt of negative numbers and getting erroneous results here:

Sqr(2 * Pi) / (2 * (S + x)) * (2 * c + x - S + Sqr((2 * c + x - S) ^ 2 - 1.85 * (S + x) * (x - S) ^ 2 / (Pi * Sqr(x * S)))) / Sqr(T)

I could substitute the argument under the sqrt for zero but this is hacky to say the least.

Am I missing something or is this a flaw in the paper?

Is anyone familiar with the paper?

Thanks,

NQR

What parameters are you putting in? Please give me the case you are using to get negative values.

 

[Glenn]

Have you e-mailed them to ask your question ?
[email protected]
Glenn

 

[NotQuiteRandom]

Robertral - If you are interested please PM me your email I will send you the spreadsheet with an example.

Glenn - thank you for the suggestion, they only warehouse papers. Since posting the above I have emailed the author (a busy academic) who suggested substituting the negative numbers for zeros... too hacky for my liking but it would imply a systemic error rather than an issue with my implementation. I will go through it, perhaps with Robertral's assistance (?) and see if it can be tweaked.

Thanks!

NQR