How to adjust / calculate Volatility for option valuation when underlying gaps up/down?

I asked this Q as a follow-up in a different thread, but thought it might not get seen so wanted to ask it here: how can I calculate how to adjust the Volatility input value (for use in Black-Scholes valuation) in situations where an underlying has gapped up or down in after-hours / premarket trading so that I can get a preview of what my position values will look like at the open?

In that other thread, I gave this example: TSLA closes on Friday at $295 w/ IV of 53%, but they announce surprise bad news on Sunday and Monday morning premarket trading is in the ~$250 range (so looking like -15% open), how do you adjust the volatility input for your pricing model? Obviously it'll be much higher than 53% but how do you determine what a move in the underlying will do to the volatility for valuation purposes?

Do any of the Greeks, for example, dictate that an x% change in the underlying will result in y% change in volatility?

(And just to be sure I'm asking the right question, it is the historical volatility of the underlying that's the input I'm looking to adjust for use in BS valuation in the context of an after-/pre-market gap up/down, right?)

 

In your example, it may not be higher than 53percent.

Figuring out vol resets is an art.

 

The magic phrase which opened Google results for me was "profit attribution" attached to variants of Black Scholes Merton options blah-blah-blah...

If there is no *set* formula that includes a volatility-change component, realize that *any* non-zero adder you create to account for at least some degree of volatility impact, will get you closer to the eventual market result than none-at-all.

What you wish to account for is a shock -- as newwurldmn notes, (if the underlying has already pushed vol to a high {or low} extreme) there *may*not*be* any remaining vol spike (or drop) left in the market's expectations.

All that said, for the S&P500, I incorporate -1 vol point per percentage change in underlying price, for the narrow-ish range of ±2.0%. So, for a 1.25% drop in price, -1.25*-1 = +1.25pts added to vol. This has been spookily accurate in this ±2.00% range on overnight actions. I suspect that the accuracy tails off beyond that range -- and that would apply especially to non-index underlyings' applications.

this is about as close to a $1,000,000 post as you're going to find.....

 

What's that...something at the bottom...can't quite read it.

 

Curious why you would consider to use Historical Volatility? (that is wrong) If you want precision, use the volatility value that results in the correct output! (ie observed price is identical to the BSM price) -- Solve for correct volatility.

 

The "shock" being emulated is of the market's forward-fearing estimation (on options), not what the underlying's bid-ask machinations eventually produced, right? So: IV, not HV.

 

Thanks, all for the replies so far.

Understood. (If what you're saying is that even without a precise calculation, I'll be better off with a crude manual vol adjustment; e.g. if closing vol was 30% on some relatively stable underlying who announces surprising bad news, manually moving that to 29% for option value re-calculation will obv get me closer to the new value than keeping it at 30%.)

Got it. And yes, if a -15% gap isn't out of line with an underlying's typical movements (or if the market had perhaps been expecting a stock-moving piece of news), I can understand why it may not move from 53%. But in the context of a historically stable underlying and out-of-the-blue bad news, it's safe to say that Vol will increase sharply, yes?

Thanks for this. Just to be clear, are you talking about options ON the SP500 index itself, or are you referring to the rule of thumb you apply for options on any of the component stocks that make up to he index?

Yes, I think I understand this principle, if what I wrote above is more or less accurate.

 

Wait, did you mean "HV, not IV"?

 

%% In TSLA 's case; i would maintain a bear trend.But if they put him in jail MAR 11; i would consider that if price closes up for day/week.And better yet= keep track of profits on stuff that pays dividends; not that i would buy TSLA or TSLA calls even if they paid a dividend., or hits 52 week lows................................................................................

 

If you simply want a ballpark price on ATM options when TSLA opens 15% lower, for example, you can use an options pricing tool and put in all the normal inputs (TSLA price, strike, DTE, int rate) and estimate volatility by starting with current IV and maybe looking at how IV (Not HV) has moved recently on TSLA drops. Then input that volatility into the model to get an estimated before-the-open option price.

TSLA