Forums > Pricing & Modelling > correcting implied volatility?

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Display using: Strange Total Posts: 1557 Joined: Jun 2004
 Posted: 2018-05-16 14:28 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*(W-F)/vega. Is that right or am I smoking crack? Eher Ende mit Schrecken als Schrecken ohne Ende  ronin Total Posts: 457 Joined: May 2006
 Posted: 2018-05-16 15:04 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: 1557 Joined: Jun 2004
 Posted: 2018-05-16 16:26 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/dFdelta_p = dP/dFvega = dP/d_sigma = dC/d_sigmaMaking all sorts of wacky assumptions, we can saydelta_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 delta-weighted average of the sigma_w, no? Eher Ende mit Schrecken als Schrecken ohne Ende  ronin Total Posts: 457 Joined: May 2006
 Posted: 2018-05-16 16:52 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: 1557 Joined: Jun 2004
 Posted: 2018-05-16 17:06 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 Eher Ende mit Schrecken als Schrecken ohne Ende  ronin Total Posts: 457 Joined: May 2006
 Posted: 2018-05-16 17:17 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: 1557 Joined: Jun 2004
 Posted: 2018-05-16 17:31 That is probably (and almost certainly) true, but calculating implied vols even for a several hundred names is a real project. Eher Ende mit Schrecken als Schrecken ohne Ende  ronin Total Posts: 457 Joined: May 2006
 Posted: 2018-05-17 11:07 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  TakeItAndRun Total Posts: 98 Joined: Apr 2010
 Posted: 2018-05-17 11:35 Strange, I think your first-order approximation is right:   Strange Total Posts: 1557 Joined: Jun 2004
 Posted: 2018-05-18 05:31 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. Eher Ende mit Schrecken als Schrecken ohne Ende  TakeItAndRun Total Posts: 98 Joined: Apr 2010
 Posted: 2018-05-21 09:50 From what I have written, one can can compute the second-order approximation. For the first-order term we have: So we assumed:  Page 1 of 1