Option Pricing Models

Discussion in 'Options' started by stoic, Mar 9, 2010.

  1. stoic


    I would like to hear from option traders that utilize option pricing models on just how important they feel dividends are in the calculation. From my own research, using option price models with the dividend and without on the same security produce differences of only a few pennies. The dividend seems to have a relatively minor impact on the option price. Only in the last few weeks before Ex-date does it seem to matter. At that time the dividend ex date and amount are known. This is one of the few known factors and as such would be easy to do in your head and be more a matter of timing depending on the strategy employed. What are your thought?
  2. If the exis before expiration, it effects the options price. If after, not at all. ATM options will be effected more than OTM with most of div is priced into ATM (call drop plus put increase may approach amount of divident)). The furthe rout in time, the less the effect. So oTM and far months least effected.
  3. stoic


    Perhaps I didn't phrase the question correctly. I was not asking what the effect approaching dividends have on the option price, but how important dividends, and more to the point what the consensus is on just how should, if at all, dividends be factored into the option pricing model.
    The original BSM option pricing model did not include dividends.
    Extensions of the model to include dividends seem to fall into two types.

    1) The calculator requires the input of the annual dividend yield. Is the assumption the underlying pays the dividend each quarter? This may be incorrect, some pay only twice per year and others pay once.
    Utilizing the model with real data produced the following results using more than one calculator.

    The underlying stock is ATM @ 65.01 and went ex-div about two weeks ago. I picked a relatively high yield stock at 3.40%. The Historical Volatility is 18.13%

    Apr 65 calls market @ 1.29 for Implied Volatility of 15.77% calculated without the div produced a price of 1.41 a difference of .12 no dividend will be Ex before expiration.

    Jun 65 calls market @ 2.20 for Implied Volatility of 16.38% calculated without the div for a price of 2.52 or .32 diff. and expected ex dividend of .55 before expiration.

    Jan 65 calls market @ 3.70 the IV = 15.72% calculated w/o div = price of 4.78 a difference of 1.08 with an expected dividend payout of 1.65 before expiration.

    2) The calculator asks for a dividend amount and the next ex date.
    Using the same IV from above.
    Apr 65 w div = 1.30 w/o = 1.30 no difference
    Jun 65 w div = 2.16 w/o = 2.21 or .05
    Jan 65 w div = 3.32 w/o = 3.78 or .46

    On the Jan. 65 imputing the total dividend of 2.20 ex in Dec. produced prices of 3.63 and 3.78

    I find the theoretical values produced from the model to be useful but not as the sole basis for making trading decisions. The amount of the dividend and the expected ex-date are one of the few things known. My preference is to not include the dividend as a factor in the option pricing model, but to include it as part of my due diligence in option trading. I was hoping to get a survey of others on this point.
  4. nitro


  5. spindr0


    Apart from needing to seriously proofread, Hornsby had it right as to how dividends affect option prices. If you know the effect then you know how much of the premium that you are receiving is artificial, eg. due to a pending corporate event (ex-div). I think that's an important thing to know because otherwise, one can be seriously wrong in what one thinks the ROI is.

    I don't know what assumptions calculators make but the program should get the dividend frequency right. If one dividend occurs before expiration then it should price one in accordingly, If two then ditto.

    I don't mean to bust chops but I have no clue what you are attempting to demonstrate with all of your calculations. The only thing that I can offer is that if there's one dividend b/t now and June expiration, the puts will be "X" higher and the calls will be "Y" lower. With the options in your example being ATM, X plus Y will be about be about equal to amount of the dividend. If 2 dividends before expiration then X + Y will be approximately double that. Etc.

    Lastly, if dividends are priced into the options, I have no clue why your preference is to not include the dividend as a factor in the option pricing model. :confused:
  6. Roll, Geske and Whaley is one of the earliest models. Since then, there have been many others, including the more esoteric ones, such as Sullivan, as well as Gaporale & Cerrato.
  7. stoic


    1) My reason for providing the calculation was to illustrate the two methods available and the potential problems with both.

    2) Again I am not asking what the effect is, I'm asking for a preference. If one was to get, and use an option pricing model , would one want an input for dividends or not ? I take it from the reply that spindr0 would want that include in the model.

    That's 1 vote for include.

    3) My preference is to not have it included into the option pricing model unless someone shows me a pricing model w/dividends that is better than what I have found so far. That is not saying that I do not make allowances for pending dividends in my trading.
  8. spindr0


    LOL... Here's my last stab at this.

    Reality is, dividends are priced into the options. It makes no sense to use a model that doesn't price the dividends in because then anything that you do with those numbers will be inaccurate. IV will be off as will any pre expiration risk graph. Why have to make allowances for dividends in your trading when the model does that for you? That's like saying you're going to calculate things incorrectly and then extrapolate a fudge factor to get back to accurate numbers.

    Good luck in your search for a model that achieves what you seek.
    botpro likes this.
  9. stoic


    they read, but do they comprehend?
  10. Very interesting! Good point indeed!

    Just another confusion/misconception in options trading! (Some of them fairly vital!)

    Whether upcoming dividends would make calls dearer or puts dearer?

    It should be making both dearer! Even at the same rate! Isn't it?

    The underlying logic is simple! It is just rational!

    Looks like: Too many textbook readers, very few independent thinkers!
    Last edited: Feb 26, 2016
    #10     Feb 26, 2016