Estimating the size of the move based on implied vol of the near month at-the money s

Discussion in 'Options' started by mktmkr, Dec 15, 2008.

  1. mktmkr


    Day before earnings, $100.00 stock, at-the money straddle priced at 40 implied vol, what’s the expected move in the underlying, what’s the quick and dirty method
    Thanx in advance
  2. dmo


    The IV of 40% implies a one-standard-deviation move of 40 in a year's time if the underlying stock is at 100. In other words, there is a 68.3% chance that a year from now the stock will be trading no more than 40 higher or lower (actually the fact that option pricing is based on a lognormal distribution rather than a normal distribution changes that somewhat - extends the upside and decreases the downside).

    How to change that to a daily volatility? It goes by the square root of time, and there are 365 days in a year. Not all of those are trading days, but I prefer to use 365 rather than 255 (number of trading days in a year) because the convention in options is to use calendar days to expiration, not trading days.

    The square root of 365 is about 19, and 40/19=2.1. So you could say that the market is implying a one-standard-deviation move for the next day of 2.1.
  3. Pretty good. I typically use a ratio for aquick calculation. When the IV is at 80, then the expected move could be 5% in either direction. So, 80:5=40:X. X is look for a 2.5% move in either direction.
  4. mktmkr


    dmo, thank you very much for the a good book you want to recommend as a refresher...looked thru Natenberg and didn't see it...maybe just didn't look hard enough

    jwcapital...thank you also for the response...sorry but I did not follow the formula
    If you don't mind...would you explain?

    To put some meat on the bone

    GS...earnings due tomorrow...
    Stock 65
    Implied vol / at the money 160

    8.42(65) =about a $5.5 1 daily stand. d
    About a 95% chance the move will be within $11
    Sound about right, what do you think

    jwcapital...sorry for the ignorance, but if you could expand it would be great, also any reference material you may want to suggest would be appreciated

    Thanks guys
  5. mktmkr,

    Another useful item in this kind of scenario is a Probability calculator. has one for free. Just go to their home page and click on Probability Calculator. You then might want to save it as a favorite.

    You enter the relavent data and it comes up with the % likelyhood of the stock touching and finishing above or below the given targets.

    I have attached a picture with the info you gave filled out for GS. It shows a 93.3% likelyhood of the stock finishing between 55 and 75.

    I hope you can see the picture OK, etc.

  6. mktmkr


    guys, truly thank you for the responce and taking the time...been of this site for a while...good to be back
  7. dmo


    Your calculations look about right - again, they'd be somewhat more precise if you incorporated the lognormal distribution, although I can't tell you offhand how to do that. As for a reference book - I'm quite sure Natenberg covers this in one of his volatility chapters.

    Of course, the practical utility of all this depends upon stock price and probability distributions actually following a lognormal distribution. Unfortunately, they seem not to. Outlier events seem to happen quite a bit more often than theory would predict. That's why you read a lot about "fat tails" in academic literature on options.

    Self-promoters like Nassim Taleb have used this fact to blast Black, Scholes and Merton. He actually wrote an article that appeared in FT two weeks ago, blaming Black, Scholes and Merton for the whole financial mess we find ourselves in, and demanding that their Nobel prize be recalled!

    FWIW, I think that's ridiculous. For me, BS is a sturdy theoretical framework against which you can compare reality to help you understand what's going on and where you are. If you use it that way, it works unbelievably well. Nobody ever suggested that BS or ANY formula models reality with precision, and can be relied on blindly.
  8. mktmkr


    dmo, completely's a pricing tool and not a crystal ball...I will look thru Natenberg thoroughly tonight...but what you gave me is what I was looking for...converting to daily vol and st.d
    thanx again
  9. Move Implied by Implied Vol = Spot / Sqrt(254) x ImplVol

    So Given
    Spot 100
    Implied Vol 20%

    Move Implied by Implied Vol = 100 / 15.93 x 20%
    Move Implied by Implied Vol = 1.25 pts

    If you bought an option and made it delta neutral immediately with the underlying and the market moves 1.25 pts a day (either up or down) and then you delta hedge at the end of each day. Your Mtm P/L on the whole startegy will stay approximatley zero.
    This of course assumes that implied vols remain unchanged. Actually what really will happen is you will make a small bit each day and then when weekend comes and goes, you will give up that small accumalated gain beacuse of 3 days negative theta. If the option is long dated you will run small'ish negative theta values, but will have small positive gamma so the number of shares required to delta hedge will be fewer than a nearer dated option.

    What i have just said is all ver theoretical but can be used as a yard stick.
  10. mktmkr


    also, because pricing models use lognormal dist. you have the skew in the price, otm puts...ect. at least i think that is one of the important reasons
    #10     Dec 15, 2008