Strange


Total Posts: 1434 
Joined: Jun 2004 


Let's say I have an options database that uses incorrect forward for calculating implied vols (and does not force p/c parity). How bad of an approximation would be to take their calculated implied vols for each call/put with the same strike/expiration and take "corrected" IV as weighted average by calculated delta?
My logic is that there is wrong forward (W) and right forward (F), so the error in the implied vol would be roughtly delta*(WF)/vega. Is that right or am I smoking crack? 
I don't interest myself in 'why?'. I think more often in terms of 'when?'...sometimes 'where?'. And always how much?' 



ronin


Total Posts: 328 
Joined: May 2006 


I would say
What you are showing would be the error in option price, but you are still missing on the other side. It's vol delta, not option delta. 
"There is a SIX am?"  Arthur 


Strange


Total Posts: 1434 
Joined: Jun 2004 


Hmm, maybe I have not have coffee yet, here is my logic.
We are implying volatility from two options with a wrong forward, so we get the following: C(f_r, sigma_r) = C(f_w, sigma_w_c) P(f_r, sigma_r) = P(f_w, sigma_w_p) delta_c = dC/dF delta_p = dP/dF vega = dP/d_sigma = dC/d_sigma
Making all sorts of wacky assumptions, we can say
delta_c * (f_r  f_w) = vega * (sigma_w_c  sigma_r) delta_p * (f_r  f_w) = vega * (sigma_w_p  sigma_r)
and solving for sigma_r, we should get the deltaweighted average of the sigma_w, no?

I don't interest myself in 'why?'. I think more often in terms of 'when?'...sometimes 'where?'. And always how much?' 



ronin


Total Posts: 328 
Joined: May 2006 


I've had too many coffees though... Aren't you mixing up BS delta and option delta?
option delta = BS delta + vega * d vol/dF

"There is a SIX am?"  Arthur 


Strange


Total Posts: 1434 
Joined: Jun 2004 


LOL, that would be too advanced for the type of approximation I am trying to make.
I am literally acting as if the only two options in my world are a call and a put, with the same maturity and the same strike. So my delta would be simple BS delta and my vega would be simple BS vega. That's what the database gives me and both calculated with incorrect implied vols and incorrect forward prices (so I have 2 wrong deltas and 2 wrong vegas). Which means that whatever noise comes from the difference between BS delta and some smart delta (i.e. the second term in your equation) should be fairly minor compare to the other "assumptions".
PS. It's pretty annoying that for the money we are paying them, implied vols are total shit 
I don't interest myself in 'why?'. I think more often in terms of 'when?'...sometimes 'where?'. And always how much?' 



ronin


Total Posts: 328 
Joined: May 2006 


TBH, it sounds like one of those where it's actually easier to do the full thing than the shortcut...

"There is a SIX am?"  Arthur 


Strange


Total Posts: 1434 
Joined: Jun 2004 


That is probably (and almost certainly) true, but calculating implied vols even for a several hundred names is a real project. 
I don't interest myself in 'why?'. I think more often in terms of 'when?'...sometimes 'where?'. And always how much?' 



ronin


Total Posts: 328 
Joined: May 2006 


I once looked at something vaguely similar  you had to recalc implied vols for lots of symbols for all strikes and maturities relatively quickly after a trading halt.
The solution was to just recalc some strikes and maturities, and interpolate the rest. E.g., if you just take every other strike and every other maturity, you have eliminated 75% of the calculation. And you really don't even need every other strike. So you can easily end up calculating just 1% or so of the original contracts.
The prob with your approach is that the skew term isn't some high order correction, it's order 1. You'd replace one error with another.
Having said that, some simple algebraic correction followed by arb removal will probably work. Just make sure it's the right algebraic correction...

"There is a SIX am?"  Arthur 



Strange, I think your firstorder approximation is right:





Strange


Total Posts: 1434 
Joined: Jun 2004 


So far I did exactly what I described above and the volatilities look OKish for the first pass. I'd love to quantify the actual error and maybe add some second order corrections. 
I don't interest myself in 'why?'. I think more often in terms of 'when?'...sometimes 'where?'. And always how much?' 



From what I have written, one can can compute the secondorder approximation. For the firstorder term we have:
So we assumed:




