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jayjo
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Joined: March 31st, 2016, 6:46 pm

Pricing Implied Dividends in Practice

November 7th, 2016, 9:17 pm

I tried to price implied dividends from American options (note: knowingly using the wrong formula for European options but restricting to near-the-money) and it appears to be pretty inconsistent for longer dated maturities.

If a company announces a quarterly dividend, but has only announced their dividend for the nearest quarter, what is the best way in practice to imply a dividend from American options? If this is not the common way to do this, what is the way that practitioners price the implied dividend?

My end goal is to use this implied dividend in $$ e^{(r - \delta)T}$$

Is it true that in practice it's just not that big of a deal? How am I supposed to get an implied dividend for T >= 0.5, whereas now it seems to only be available 0.25. 
 
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Alan
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Re: Pricing Implied Dividends in Practice

November 7th, 2016, 10:42 pm

Let's take an example, say IBM. First, I would determine [$]e^{(r_{T_i}-\delta_{T_i})T_i}[$] from the option-implied forward price at each reasonably liquid option expiration [$]T_i[$], using the VIX white paper method. (As you noted, this requires ignoring the American-style nature of the close-to-the-money options). Second, I would compare this with the factor determined by plausible dividend (and ex-date) projections, using the company's history of dividends. Perhaps you can do this for IBM for the maturities that interest you and post some results for further discussion.  
 
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jayjo
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Re: Pricing Implied Dividends in Practice

November 8th, 2016, 4:32 am

I just priced the implied dividend for IBM with these results:

expiry
2016-11-18    0.000273
2016-12-16    0.000961
2017-01-20    0.001716
2017-04-21    0.007185
2017-06-16    0.014436
2018-01-19    0.047493
2019-01-18    0.165742

My only real reference is ycharts which has their dividend yield at 3.46%. Do these seem reasonable? 
 
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Alan
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Re: Pricing Implied Dividends in Practice

November 8th, 2016, 2:40 pm

I have no idea what you're posting, except that the first column are option expirations [$]T_i[$].

Here is what I am suggesting. First, make some dollar dividend projections from the easily-googled div history, project some forward prices from those, and compare to the option-implied forward prices. Post enough detail (with labels) to make sense of what you are doing. I suggest two tables:

Table 1: projected ex-dates and projected dollar dividends at each each ex-date.
Table 2: option expiration dates, projected forward price for each date, option-implied forward price for each date.  

It will also help for Table 2 to include the [$]r_{T_i}[$](%) for each of the [$]T_i[$], and to also post [$]F_{0,T_i}/S_0[$] for both of the forward price columns, where [$]S_0[$] was the stock price at the time of your option chain prices.  So 6 columns for Table 2. I am just trying to get you to post something complete enough so we can see what you are doing. The goal of this exercise is to see if the option-implied forwards (and hence the option-implied dividends) are reasonable in relation to projecting the dividends "by hand". (I expect them to be for IBM, if you are careful).
 
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Paul
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Re: Pricing Implied Dividends in Practice

November 8th, 2016, 3:41 pm

This all seems a little 'sensitive'! However...

Are there bid and offer prices for both types of option? Puts and calls? I was wondering if you could use more data to give ranges for divs and then try to fit a line through them such that the dividend doesn't move much, or rather goes up slightly, maybe with the occasional plummet to zero.

P
 
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jayjo
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Re: Pricing Implied Dividends in Practice

November 9th, 2016, 3:17 pm

Ok here is my process right now... admittedly relatively straightforward.
def calculate_implied_div(df):
    

    for expiration in data.expiry.unique():
        temp = data.copy()
        temp = temp[temp.expiry == expiration]
        temp['spread'] = np.abs(temp['mid_pricePut'] - temp['mid_priceCall'])
        temp = temp[temp['spread'] == temp['spread'].min()]
        implied_div = np.log((temp['strike']*np.exp(-1*temp['rCall']*temp['TCall']) + temp['mid_priceCall'] - temp['mid_pricePut'])
                                 / temp['underlyingPriceCall']) * (-1 * temp['TCall'])
        
        data.loc[data.expiry == expiration, 'implied_div'] = implied_div.values.item()

        
calculate_implied_div(data)


plt.scatter(data.expiry.unique(), data.implied_div.unique())
Image
The functional form of this implied dividend looks OK. 
So I used the put and call that are priced closest to each other instead of closest to ATM.
expiry              T            implied_div      r                               
2016-11-18  0.027397    -0.000044  0.002800
2016-12-16  0.104110    -0.000638  0.002990
2017-01-20  0.200000     0.000632  0.003851
2017-02-17  0.276712     0.000969  0.004439
2017-03-17  0.353425     0.002106  0.004838
2017-06-16  0.602740     0.006221  0.005908
2017-09-15  0.852055     0.013059  0.006656
2017-12-15  1.101370     0.022901  0.007262
2018-01-19  1.197260     0.026608  0.007416
2018-03-16  1.350685     0.034302  0.007661
2018-06-15  1.600000     0.048671  0.008060
2018-09-21  1.868493     0.067275  0.008490
2018-12-21  2.117808     0.088688  0.008900


My question though is if a practitioner is pricing an implied dividend, is this how they do it? Do they not use option prices because of liquidity issues or uncertainty in the dividend, or... some other issue? If I have a model that requires a dividend adjustment, should I just use the current annualized dividend yield? 
 
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fomisha
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Re: Pricing Implied Dividends in Practice

November 11th, 2016, 6:43 pm

No, this is not how practitioners do it. 
You need to keep in mind that:
- these are American options
- there is a material cost of borrowing a stock
- cash dividend models are very different from dividend yield. there are different dividend models, sometimes they also give different results. 
- mid-point is not what practitioners use as a microprice. 
- if there is uncertainty about dividend date you have another level of complications.
- if the volatility accrues at a different rate before and after the dividend (especially during events/announcements) you need to model this explicitly (so, called business vs calendar time).
Feel free to contact me if interested in solutions for these or similar problems.
 
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outrun
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Re: Pricing Implied Dividends in Practice

November 11th, 2016, 6:47 pm