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

[d0rian]

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.

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.

Wait, I think I'm getting turned around on something. Isn't the volatility input for BS calculation purposes the volatility of the underlying? (aka HV or something close to it?) My understanding of the "implied" part of I.V. is that it's calculated from an option's observed price (i.e. solving for IV using the option's price as a starting point...hence there are different IV's derived from each of the bid/ask/midpoint prices for the option contract as observed in the market, right?)

I was confused by stepandfetchit's post above suggesting to "use the volatility value that results in the correct output", because in the pre-market environment, of course, there aren't any live quotes (aka outputs) from which to work backwards and derive the IV. In the example I used of an underlying gapping down 15% pre-market, I assumed that the volatility value I needed to use to calculate option values would be derived by starting with the HV of the underlying (I'd have an HV value that takes into account the underlying's price movements up until the prior day's close), and adjusting by some factor to reflect the unanticipated sharp gap down (in my hypothetical scenario of unexpected bad news for a normally-stable stock.) Am I mis-understanding something fundamental here, or perhaps asking the wrong question?

 

[Option_Attack]

Yes, volatility is an input to the pricing model. IV generally follows HV, as you can see from HV/IV graphs, but it can be quite different at times. IV is calculated iteratively. Basically rerunning the model until a certain volatility matches the quoted option price. That is then the Implied volatility.

I think step might have meant that you start with current IV found from the option's Last Trade. Then you can tweak it a bit based on your expectation for the new IV. You would not want to start with the stock's current HV. That would probably be way off.

 

[Kevin Schmit]

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?

As a first order approximation, use last close IV from the 250 strike. So if the 295 strike was .53 IV and the 250 strike was .60 IV, assume ATM IV will be around .60 IV. This is the "sticky strike" rule.

For a more accurate approximation add a stock specific multiplier:

new_ATM_IV = 250_strike_IV + betaDown * (250_strike_IV - 295_strike_IV)

derive betaDown(Up) from past down(up) moves with shrinkage towards market single-name average betaDown(Up)

 

[d0rian]

Yes, volatility is an input to the pricing model. IV generally follows HV, as you can see from HV/IV graphs, but it can be quite different at times. IV is calculated iteratively. Basically rerunning the model until a certain volatility matches the quoted option price. That is then the Implied volatility.

I think step might have meant that you start with current IV found from the option's Last Trade. Then you can tweak it a bit based on your expectation for the new IV. You would not want to start with the stock's current HV. That would probably be way off.

OK, yes that was my understanding of the 'implied' in implied volatility > i.e. essentially reversing the BS formula by starting with an option price (be it the Bid, Ask, or Last Trade), and solving for the volatility, which would be the volatility implied by that price.

But that's getting at the source of my confusion here: in the context of a hypothetical -15% gap down, why would you ever start with an IV that was based on a price from the prior day, which would have contemplated an underlying far less volatile than the one that just reported an unexpected spate of bad news? Moreover, many of the contracts I'm looking at are somewhat thinly traded and/or have wide spreads -- so if a particular contract hasn't traded for a few days, or only has super-wide MM quotes of, say $1.00 / $2.80 or something, the idea of starting with an IV that was derived from either a several-day-old price or a spread that wide seems problematic.

 

[ironchef]

As a first order approximation, use last close IV from the 250 strike. So if the 295 strike was .53 IV and the 250 strike was .60 IV, assume ATM IV will be around .60 IV. This is the "sticky strike" rule.

For a more accurate approximation add a stock specific multiplier:

new_ATM_IV = 250_strike_IV + betaDown * (250_strike_IV - 295_strike_IV)

derive betaDown(Up) from past down(up) moves with shrinkage towards market single-name average betaDown(Up)

Not sticky delta?

 

[sle]

As a first order approximation, use last close IV from the 250 strike. So if the 295 strike was .53 IV and the 250 strike was .60 IV, assume ATM IV will be around .60 IV. This is the "sticky strike" rule.

Yeah, there are three usual suspects for vol dynamics. First one is sticky delta where implied volatility for a fixed delta level is assumed to stay constant. It's not really applicable to equities for various reasons. Then there is sticky strike where you assume that implied volatility for a given option should remain the same. Predictably, this one usually underestimates the moves in volatility due to movement in spot. Finally (but not least), there is sticky local vol which assumes that volatility follows a path. A useful approximation is that for a given OTM strike K, when the spot get's there, the implied volatility will increase 2x the IV difference between ATM and OTM (i.e. ATM + [K - ATM]*2).

 

[stepandfetchit]

Wait, I think I'm getting turned around on something. Isn't the volatility input for BS calculation purposes the volatility of the underlying? (aka HV or something close to it?) My understanding of the "implied" part of I.V. is that it's calculated from an option's observed price (i.e. solving for IV using the option's price as a starting point...hence there are different IV's derived from each of the bid/ask/midpoint prices for the option contract as observed in the market, right?)

I was confused by stepandfetchit's post above suggesting to "use the volatility value that results in the correct output", because in the pre-market environment, of course, there aren't any live quotes (aka outputs) from which to work backwards and derive the IV. In the example I used of an underlying gapping down 15% pre-market, I assumed that the volatility value I needed to use to calculate option values would be derived by starting with the HV of the underlying (I'd have an HV value that takes into account the underlying's price movements up until the prior day's close), and adjusting by some factor to reflect the unanticipated sharp gap down (in my hypothetical scenario of unexpected bad news for a normally-stable stock.) Am I mis-understanding something fundamental here, or perhaps asking the wrong question?

If you examine the inputs to the BSM, you should realize that all except one can be known to whatever precision you desire. The "volatility" input is the only mystery. By using Newton-Rapson or other converging method, use BSM to solve for the IIV! -- Please beware this is still garbage in garbage out, so if you use invalid inputs, such as incorrect interest, dividend, lack of time precision, etc, you get what you deserve.

I just realized you desire to predict the future, not quantify what is. Reliable predictions for Volatility or IIV are the holy grail. Since your time frame is very confined (say hours), sle's advice seems best suited for predicting volatility movement. This is not yet in my toolkit.

 

[Option_Attack]

You might try some of the tricks from the other posters to estimate the new vol input. Or maybe use the percent change in HV and apply that to the Last trade IV. I would recommend not trading in ANY thinly traded options. You can usually get in somewhere between the b/a, but you are likely to get skinned alive trying to get out at a reasonable price.

OK, yes that was my understanding of the 'implied' in implied volatility > i.e. essentially reversing the BS formula by starting with an option price (be it the Bid, Ask, or Last Trade), and solving for the volatility, which would be the volatility implied by that price.

But that's getting at the source of my confusion here: in the context of a hypothetical -15% gap down, why would you ever start with an IV that was based on a price from the prior day, which would have contemplated an underlying far less volatile than the one that just reported an unexpected spate of bad news? Moreover, many of the contracts I'm looking at are somewhat thinly traded and/or have wide spreads -- so if a particular contract hasn't traded for a few days, or only has super-wide MM quotes of, say $1.00 / $2.80 or something, the idea of starting with an IV that was derived from either a several-day-old price or a spread that wide seems problematic.

 

[ironchef]

Yeah, there are three usual suspects for vol dynamics. First one is sticky delta where implied volatility for a fixed delta level is assumed to stay constant. It's not really applicable to equities for various reasons. Then there is sticky strike where you assume that implied volatility for a given option should remain the same. Predictably, this one usually underestimates the moves in volatility due to movement in spot. Finally (but not least), there is sticky local vol which assumes that volatility follows a path. A useful approximation is that for a given OTM strike K, when the spot get's there, the implied volatility will increase 2x the IV difference between ATM and OTM (i.e. ATM + [K - ATM]*2).

Why is sticky delta not applicable to equities?

 

[Kevin Schmit]

Why is sticky delta not applicable to equities?

Ocasionally, it is. When the SPX, for example is quietly drifting up day after day under very low implied vol, it can seem like the entire vol surface floats with the atm strike, as if it has become unmoored -- i.e. sticky delta/moneyness. But that doesn't happen often. Usually single-name equity and equity index vol are somewhere between sticky-strike and sticky local vol/implied-tree.

The stickiness rules are regime dependent and I really couldn't tell you why one holds more than another in any given market regime. If I had to guess, I would say that flows and trader psychology determine which stickyness rule holds at any given time and for any given single name. Emanual Derman wrote the seminal paper on stickyness, you can probably find it by googling. Unfortunately he wrote it a few years before vol became a massively traded asset class (vol futures, options, etfs, structured notes/products, etc.) -- I think the game has changed quite a bit since he wrote the paper, but it should give you the basics.

In the equation I posted above, a beta coeffidient of 0 corresponds to sticky-strike and a beta coefficient of 1 corresponds to sticky-local-vol (local vol has twice the skew slope of BS IV). In a crash or market dislocation, the downside beta coefficient can be greater than 1, but at the same time the skew tends to flatten, which complicates the stickiness assumption in the tails.