# How to compute IVx (Implied volatility for a specific expiration) and the expected move with options?

By searching online, I have found three methods to compute the expected move of a stock based on option prices and implied volatilities:

Method 1: Extract the price of a Straddle ATM of the front month
--> Exp_Move = (call ATM + put ATM)

Method 2: Take the price of a Straddle ATM of the front month and multiply it by 0.85
--> Exp_Move = (call ATM + put ATM)*0.85

Method 3: Compute the expected move by scaling the implied volatility of the nearest expiration
--> Exp_Move = Stock_Price * IV/100 * SQRT(n/365)

DOUBT NO. 1: Which one is the most accurate one between method 1 and method 2? Where does the "0.85" come from?

DOUBT NO. 2: To compute the Exp_Move with Method 3 I need the IV... I still do not understand how I can compute the IVx of the front month expiration based on the implied volatility of the options with that expiration. Is that a sort of weighted average of the implied volatilities? I noticed on tastyworks's website this description:

Implied Volatility (IVx): The implied volatility (IVx) metric displayed in the option chain is calculated using the VIX-style calculation described at the following link.

However, this seems something almost impossible to reproduce based on historical option data provided by OptionMetrics. Is there a way to reach very accurate estimation of the IVx based on the implied volatilities or the prices of the options of that precise expiration?

I attach a couple of pictures of the same option chain where I explain what I am trying to compute... (By the way... I have no idea why two different brokers platforms provide slightly different IVx values...).

Image 1 - Option chain on tastyworks IVx: Image 2 - Option chain on thinkorswim IVx: • Note that all of these give you a range of expected moves either up or down. i.e. if the "excepted move" based on IV is \$3, that means that there's a 68% (1 sd) chance that the stock will move between +/- \$3. Feb 18 '20 at 20:36

Each option has its own implied volatility. There are a number of option pricing models so I would assume that it's possible that there may be mild variance in the calculation via each one. I've used Black Scholes for about 30 years so I don't know to what degree it varies from model to model.

There are also a number of ways to calculate the average implied volatility for each expiration as well as the average implied volatility for all of the options of a stock. One well known option author/service weights each individual option's implied volatility by its trading volume and its distance in or out-of-the-money. Another popular service calculates it by weighting delta and vega of each option. Therefore, the Composite Volatility number may vary somewhat from one method of calculation to another. That's not critical because the variance should be small and decisions should be made from the comparison of all numbers calculated via the same model.

I can't tell you which method of expected move calculation is most accurate. Even if I could, I think that it's a subjective as well as unreliable number because implied volatility varies day to day, sometimes significantly. If it increases, your expected move increases and vice versa. In addition, I wouldn't put much credence in such a number because options are derivatives that for the most part follow the price of the underlying (secondary changes due to time decay, change in implied volatility, pending dividends, etc.). The underlying isn't going to move "X" percent because the option market is suggesting that it will.

• I am performing a backtest on how reliable are the different expected moves formulas around earnings announcements. In particular, if you look at the weekly options that are near to expiration just before the earnings announcements, you can retrieve some interesting information about the magnitude of the stock price movement after the news. You mentioned "One well known option author/service weights each individual option's implied volatility by its trading volume and its distance in or out-of-the-money"... Do you have a practical/empirical example or reference in R, Python, Excel,...?
– jack
Feb 17 '20 at 17:58
• I have no references. Here's some add'l generic info Feb 17 '20 at 18:10

Implied volatility tends to trade over realized volatility. That is almost assuredly why you've read to make such an adjustment (the ~85% figure is a very ballpark number and would vary on a case-by-case basis). Look at a data vendor that such as ivolatility.com graphs to get a sense of how much and how often implieds are over realizeds. Do note ivolatility uses its own proprietary one-month implied vol index for each stock.

That being said I've never heard anyone offer 85% of the straddle price as the expected move in the stock. The price of the straddle is the expected move. If you think it would move more you would buy it, and if you think it will move less you would sell it. There are market factors at play that don't make this perfect. (i.e. customers know that realizeds are lower and like to sell front month options. This causes market makers to be consistently long them, paying theta, and deflating the price to equilibrium).

Doubt #2: How to calculate IV for a given time-to-expiration?

To calculate the implied volatility for a single option you need an options pricing model (such as Black Scholes for European options or a Binomial tree for American options). Then you need a numerical method to solve for volatility given all other inputs (such as Newton's method).

When speaking of coming up with some sort of volatility index using all strikes for one or more expirations there are literally infinite ways to do it. The most heavily watched and well known volatility index is CBOE's VIX Index. Traders of the VIX index and its related products know quite well the many idiosyncrasies deriving from its calculation.

Overall: Options are an extremely complex instrument. They have been studied heavily for 50 years now. The wealth of information and literature about them is immense. By nature they are statistical, dynamic and estimated. Do not expect to quickly arrive at any quick or easy truths.

• I agree with you about the fact that 0.85 is a completely random number. In fact, I am convinced that the most reliable way of estimating the implied move embedded in option prices is to look at the price of the ATM straddle. For the second part of your answer I know how to compute the implied volatility of a single option but I don't understand how brokers computer the implied volatility for a the bundle of options composing a specific expiration. I don't know if you have ever used Thinkorswimm or Tastyworks... these two platform provides an IVx value for each exipration.
– jack
Feb 17 '20 at 17:50
• Have a look at the attached screenshot to easily understand what I am referring to. Moreover, thinkorsimm provides a MMM (Market Maker Move) estimation, which is based on a proprietary fromula that makes use of time to expiration, stock price and differential of implied volatility in the front and back month. I was working to understand how they compute the MMM but it doesn't seem to be that easy... I think that it might be something related to the formula Exp_move = Stock_price * IV/100 * sqrt(n/365).
– jack
Feb 17 '20 at 17:54
• From my answer: "When speaking of coming up with some sort of volatility index using all strikes for one or more expirations there are literally infinite ways to do it." If you want Thinkorswim or Tastyworks per-expiration vol-index formula you will have to ask them. They probably won't tell you. It's likely very similar to the VIX calculation but for one expiration. Vol indices are of limited utility. The VIX has an r-squared with realized near 75-80%. A major criticism of it is the added complexity gains nothing or very little. Feb 17 '20 at 19:27

Not fully answering your whole question, but a quick and dirty way to get the expected daily move by using the Implied Vol is to divide the implied vol by 16. (Taken from the Sheldon Natenberg book)

So an implied vol of 80% would imply that a 1 standard deviation move per day of 5%