I just tried to price the implied dividend for a few active, liquid options markets using current prices and I am not convinced my results are accurate.
I am using American options, and using the put-call parity relationship that exists for European options. I've seen that at-the-money (or near-the-money) options will give a pretty accurate description of implied dividends. If I cannot use put-call parity, what methods are use by practitioners to get an implied dividend?
I used an interpolated treasury yield curve for accurate interest rate values, and priced IDIV with $$IDIV = \text{Stock Price } - \text{Strike } \times e^{-rT} - Call(K,T) - Put(K,T)$$
For AAPL:
expiry
2016-11-11 -0.040236
2016-11-18 -0.053026
2016-11-25 -0.061683
2016-12-02 -0.065252
2016-12-09 -0.076144
2016-12-16 -0.029923
2016-12-23 -0.100593
2017-01-20 2.660728
2017-02-17 0.092540
2017-03-17 0.131359
2017-04-21 0.263763
2017-06-16 0.538302
2017-07-21 0.613789
2017-11-17 1.193600
2018-01-19 1.352709
2019-01-18 2.295825
For SPY:
expiry
2016-11-09 0.006997
2016-11-11 0.008535
2016-11-16 -0.000494
2016-11-18 0.006222
2016-11-23 -0.004294
2016-11-25 0.002909
2016-11-30 -0.006724
2016-12-02 -0.008246
2016-12-07 -0.016802
2016-12-09 -0.013155
2016-12-16 0.799113
2016-12-23 0.741128
2016-12-30 0.519134
2017-01-20 0.872681
2017-02-17 0.850424
2017-03-17 1.253229
2017-03-31 1.446670
2017-06-16 2.063210
2017-06-30 2.285904
2017-09-15 2.853458
2017-09-29 2.841766
2017-12-15 3.393382
2018-01-19 3.920152
2018-03-16 4.540356
2018-06-15 5.096783
2018-09-21 5.609085
2018-12-21 6.897434
These seem far enough off that it's not due to computational errors. What else do I need to account for when using American options to price the implied dividend.