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Discrete vs. Continuous Data

Discrete data is counted,
Continuous data is measured


https://www.mathsisfun.com/data/data-discrete-continuous.htm...

One of the difficulties of comparing calls is the fact that important data, strike price and expiration date, are "discrete." As Richard Feynman said of photons, "they come in lumps!" The steps between values are often uneven. I'm using "dollars per day" as a key metric but in its raw form this metric is not comparable because it does not take into account the capital invested in buying the stock. I have smoothed this out somewhat by considering how many contracts one can sell, for example, if one is limiting the investment in any one stock to, say, $10,000. One round lot of $100 shares, two round lots of $50 shares, three round lots of $33 shares. This input is also discrete. One way to smooth this out is to calculate the premium and the maximum capital gains as a percentage of the share price. Then you are left with the problem of how to combine the various trades to get the best results with your available capital. I believe this last problem is solved with linear regression.

I've fixed the bug and partly improved the selection algorithm but the table I show below still has a discrete number anomaly. A week has seven days but the algorithm is using days instead of weeks. Since the option chains were downloaded on Sunday it is using five days to expiration, which is correct but from an investing point of view it should be using one week or seven days no matter on what day of the week I manage to sell calls with a Friday expiration.

Last weekend it was 73 option chains with 16448 calls in total which need to be whittled down to a handful of the best calls to sell. The table below is what an initial selection might look like with default settings, around 100 calls. The table is sorted by dollars per day of premium (col h)

The first row, three ENPH $50 Jun 19 contracts would yield 3.7% in premium alone or 6.4% if called in ONE WEEK! It's not an exception, look at column l, disc, the LVGO call following would yield 4.5% in premium but would yield less, 4.3%, if called -- the loss is from the trade commissions. But remember that this is a very high volatility week, normally yields will be much lower.

Depending on what your goals are you would optimize for premium or for capital gains. The selector has lots of variables one can play with.

https://softwaretimes.com/pics/covered-call-selector.png

  Expiration: 06/19/20
a b c e f g h I j k l m n o
ticker close cont strike b-a ----Premium--- Capital-gains -----Total---- Max
cash p/day cash p/day days disc cash p/day yield

ENPH 48.63 3 50.0 1.83 544.50 108.60 391.50 78.30 5 3.7% 936.00 187.20 6.4%
LVGO 60.00 2 60.0 2.70 535.50 107.10 -19.50 -3.90 5 4.5% 516.00 103.20 4.3%
DT 35.90 4 36.0 1.35 535.50 107.10 20.50 4.10 5 3.7% 556.00 111.20 3.9%
NET 28.82 5 29.0 1.03 510.50 101.60 70.50 14.10 5 3.5% 581.00 116.20 4.0%
PINS 20.87 7 21.0 0.73 506.50 100.60 71.50 14.30 5 3.4% 578.00 115.60 4.0%
KBR 24.78 6 25.0 0.83 493.50 98.10 112.50 22.50 5 3.3% 606.00 121.20 4.1%
WORK 30.86 4 31.0 1.20 475.50 95.10 36.50 7.30 5 3.9% 512.00 102.40 4.1%
DOMO 31.07 4 32.0 1.15 455.50 91.10 352.50 70.50 5 3.7% 808.00 161.60 6.5%
PLAN 44.83 3 45.0 1.53 454.50 90.60 31.50 6.30 5 3.4% 486.00 97.20 3.6%
SFIX 23.44 6 24.0 0.73 433.50 86.10 316.50 63.30 5 3.1% 750.00 150.00 5.3%
CSGS 44.52 3 45.0 1.43 424.50 84.60 124.50 24.90 5 3.2% 549.00 109.80 4.1%
EVBG 128.57 1 130.0 4.08 403.50 80.60 123.51 24.70 5 3.1% 527.01 105.40 4.1%
WORK 30.86 4 31.5 1.00 395.50 79.10 236.50 47.30 5 3.2% 632.00 126.40 5.1%
ROKU 108.08 1 109.0 3.95 390.50 78.10 72.50 14.50 5 3.6% 463.00 92.60 4.3%
PCTY 128.33 1 130.0 3.70 365.50 73.10 147.50 29.50 5 2.8% 513.0 102.60 4.0%
PINS 20.87 7 21.5 0.53 366.50 72.60 421.50 84.30 5 2.5% 788.00 157.60 5.4%
AYX 141.12 1 145.0 3.65 360.50 72.10 368.50 73.70 5 2.6% 729.00 145.80 5.2%
DT 35.90 4 37.0 0.90 355.50 71.10 420.50 84.10 5 2.5% 776.00 155.20 5.4%
CRWD 93.13 1 93.5 3.55 350.50 70.10 18.00 3.60 5 3.8% 368.50 73.70 4.0%
WORK 30.86 4 32.0 0.88 347.50 69.10 436.50 87.30 5 2.8% 784.00 156.80 6.4%
ROKU 108.08 1 110.0 3.50 345.50 69.10 172.50 34.50 5 3.2% 518.00 103.60 4.8%
PLAN 44.83 3 46.0 1.13 334.50 66.60 331.50 66.30 5 2.5% 666.00 133.20 5.0%
NET 28.82 5 30.0 0.68 335.50 66.60 570.50 114.10 5 2.3% 906.00 181.20 6.3%
APPS 9.38 15 10.0 0.23 340.50 66.60 910.50 182.10 5 2.4% 1251.00 250.20 8.9%
CRWD 93.13 1 94.0 3.35 330.50 66.10 68.00 13.60 5 3.5% 398.50 79.70 4.3%
DOMO 31.07 4 33.0 0.80 315.50 63.10 752.50 150.50 5 2.5% 1068.00 213.60 8.6%
ZS 102.41 1 103.0 3.18 313.50 62.60 39.50 7.90 5 3.1% 353.00 70.60 3.4%
ROKU 108.08 1 111.0 3.15 310.50 62.10 272.50 54.50 5 2.9% 583.00 116.60 5.4%
MTCH 87.23 1 88.5 3.05 300.50 60.10 107.50 21.50 5 3.4% 408.00 81.60 4.7%
TER 71.73 2 72.5 1.50 295.50 59.10 134.50 26.90 5 2.1% 430.00 86.00 3.0%
GLOB 141.26 1 145.0 2.98 293.50 58.60 354.50 70.90 5 2.1% 648.00 129.60 4.6%
DOMO 31.07 4 34.0 0.73 287.50 57.10 1152.50 230.50 5 2.3% 1440.00 288.00 11.6%
ROKU 108.08 1 113.0 2.87 282.50 56.40 472.50 94.50 5 2.6% 755.00 151.00 7.0%
KBR 24.78 6 26.0 0.48 283.50 56.10 712.50 142.50 5 1.9% 996.00 199.20 6.7%
WORK 30.86 4 32.5 0.70 275.50 55.10 636.50 127.30 5 2.2% 912.00 182.40 7.4%
ZS 102.41 1 104.0 2.78 273.50 54.60 139.50 27.90 5 2.7% 413.00 82.60 4.0%
ENPH 48.63 3 52.5 0.93 274.50 54.60 1141.50 228.30 5 1.9% 1416.00 283.20 9.7%
CRWD 93.13 1 95.0 2.78 273.50 54.60 168.00 33.60 5 2.9% 441.50 88.30 4.7%
ROKU 108.08 1 112.0 2.77 272.50 54.50 372.50 74.50 5 2.5% 645.00 129.00 6.0%
SFIX 23.44 6 25.0 0.45 265.50 53.10 916.50 183.30 5 1.9% 1182.00 236.40 8.4%
MANH 84.14 1 85.0 2.70 265.50 53.10 66.50 13.30 5 3.2% 332.00 66.40 3.9%
AVLR 105.92 1 110.0 2.68 263.50 52.60 388.50 77.70 5 2.5% 652.00 130.40 6.2%
OSIS 73.35 2 75.0 1.30 255.50 51.10 310.50 62.10 5 1.7% 566.00 113.20 3.9%
SQ 86.71 1 87.0 2.50 245.50 49.10 9.50 1.90 5 2.8% 255.00 51.00 2.9%
DT 35.90 4 38.0 0.63 247.50 49.10 820.50 164.10 5 1.7% 1068.00 213.60 7.4%
PINS 20.87 7 22.0 0.35 240.50 48.10 771.50 154.30 5 1.6% 1012.00 202.40 6.9%
DDOG 77.97 1 80.0 2.45 240.50 48.10 183.50 36.70 5 3.1% 424.00 84.80 5.4%
APPN 52.16 2 55.0 1.23 241.50 48.10 548.50 109.70 5 2.3% 790.00 158.00 7.6%
ROST 92.44 1 96.5 2.43 238.50 47.60 386.50 77.30 5 2.6% 625.00 125.00 6.8%
ROST 92.44 1 93.0 2.43 238.50 47.60 36.50 7.30 5 2.6% 275.00 55.00 3.0%
QLYS 103.20 1 115.0 2.43 238.50 47.60 1160.50 232.10 5 2.3% 1399.00 279.80 13.6%
MTCH 87.23 1 87.5 2.43 238.50 47.60 7.50 1.50 5 2.7% 246.00 49.20 2.8%
WORK 30.86 4 33.0 0.60 235.50 47.10 836.50 167.30 5 1.9% 1072.00 214.40 8.7%
PRGS 38.46 3 40.0 0.80 235.50 47.10 442.50 88.50 5 2.0% 678.00 135.60 5.9%
LVGO 60.00 2 65.0 1.20 235.50 47.10 980.50 196.10 5 2.0% 1216.00 243.20 10.1%
CYBR 98.12 1 104.0 2.40 235.50 47.10 568.50 113.70 5 2.4% 804.00 160.80 8.2%
IRTC 111.04 1 115.0 2.38 233.50 46.60 376.50 75.30 5 2.1% 610.00 122.00 5.5%
CYBR 98.12 1 98.5 2.38 233.50 46.60 18.50 3.70 5 2.4% 252.00 50.40 2.6%
SQ 86.71 1 87.5 2.37 232.50 46.40 59.50 11.90 5 2.7% 292.00 58.40 3.4%
ROST 92.44 1 98.5 2.35 230.50 46.10 586.50 117.30 5 2.5% 817.00 163.40 8.8%
NEWR 68.67 2 70.0 1.18 231.50 46.10 246.50 49.30 5 1.7% 478.00 95.60 3.5%
ZS 102.41 1 105.0 2.33 228.50 45.60 239.50 47.90 5 2.2% 468.00 93.60 4.6%
PLAN 44.83 3 47.0 0.78 229.50 45.60 631.50 126.30 5 1.7% 861.00 172.20 6.4%
EVBG 128.57 1 135.0 2.33 228.50 45.60 623.51 124.70 5 1.8% 852.01 170.40 6.6%
DT 35.90 4 39.0 0.58 227.50 45.10 1220.50 244.10 5 1.6% 1448.00 289.60 10.1%
CRWD 93.13 1 96.5 2.30 225.50 45.10 318.00 63.60 5 2.4% 543.50 108.70 5.8%
CRWD 93.13 1 96.0 2.25 220.50 44.10 268.00 53.60 5 2.4% 488.50 97.70 5.2%
CRWD 93.13 1 97.5 2.18 213.50 42.60 418.00 83.60 5 2.3% 631.50 126.30 6.8%
ROKU 108.08 1 114.0 2.16 211.50 42.30 572.50 114.50 5 2.0% 784.00 156.80 7.3%
CRWD 93.13 1 97.0 2.15 210.50 42.10 368.00 73.60 5 2.3% 578.50 115.70 6.2%
SQ 86.71 1 88.0 2.14 209.50 41.80 109.50 21.90 5 2.4% 319.00 63.80 3.7%
ROST 92.44 1 93.5 2.10 205.50 41.10 86.50 17.30 5 2.2% 292.00 58.40 3.2%
QLYS 103.2 1 105.0 2.10 205.50 41.10 160.50 32.10 5 2.0% 366.00 73.20 3.5%
CYBR 98.12 1 99.0 2.10 205.50 41.10 68.50 13.70 5 2.1% 274.00 54.80 2.8%
ZS 102.41 1 106.0 2.05 200.50 40.10 339.50 67.90 5 2.0% 540.00 108.00 5.3%
MTCH 87.23 1 91.0 1.98 193.50 38.60 357.50 71.50 5 2.2% 551.00 110.20 6.3%
ROKU 108.08 1 115.0 1.95 190.50 38.00 672.50 134.50 5 1.8% 863.00 172.60 8.0%
ESTC 83.49 1 85.0 1.93 188.50 37.60 131.50 26.30 5 2.3% 320.00 64.00 3.8%
WORK 30.86 4 33.5 0.48 187.50 37.10 1036.50 207.30 5 1.5% 1224.00 244.80 9.9%
CYBR 98.12 1 100.0 1.90 185.50 37.10 168.50 33.70 5 1.9% 354.00 70.80 3.6%
QCOM 85.24 1 86.0 1.89 184.50 36.80 56.50 11.30 5 2.2% 241.00 48.20 2.8%
NET 28.82 5 31.0 0.38 185.50 36.60 1070.50 214.10 5 1.3% 1256.00 251.20 8.7%
ZS 102.41 1 107.0 1.85 180.50 36.10 439.50 87.90 5 1.8% 620.00 124.00 6.1%
ROST 92.44 1 99.5 1.85 180.50 36.10 686.50 137.30 5 2.0% 867.00 173.40 9.4%
MTCH 87.23 1 88.0 1.85 180.50 36.10 57.50 11.50 5 2.1% 238.00 47.60 2.7%
ROST 92.44 1 94.0 1.83 178.50 35.60 136.50 27.30 5 1.9% 315.00 63.00 3.4%
CRWD 93.13 1 98.0 1.80 175.50 35.10 468.00 93.60 5 1.9% 643.50 128.70 6.9%
AYX 141.12 1 150.0 1.80 175.50 35.10 868.50 173.70 5 1.2% 1044.00 208.80 7.4%
AVLR 105.92 1 115.0 1.80 175.50 35.10 888.50 177.70 5 1.7% 1064.00 212.80 10.0%
SQ 86.71 1 89.0 1.78 173.50 34.60 209.50 41.90 5 2.0% 383.00 76.60 4.4%
UPLD 32.01 4 35.0 0.43 167.50 33.10 1176.50 235.30 5 1.3% 1344.00 268.80 10.5%
ROST 92.44 1 98.0 1.70 165.50 33.10 536.50 107.30 5 1.8% 702.00 140.40 7.6%
ROKU 108.08 1 116.0 1.69 164.50 32.90 772.50 154.50 5 1.5% 937.00 187.40 8.7%
VRNT 43.74 3 45.0 0.55 160.50 32.10 358.50 71.70 5 1.2% 519.00 103.80 4.0%
MTCH 87.23 1 92.0 1.65 160.50 32.10 457.50 91.50 5 1.8% 618.00 123.60 7.1%
CYBR 98.12 1 99.5 1.65 160.50 32.10 118.50 23.70 5 1.6% 279.00 55.80 2.8%
ROST 92.44 1 94.5 1.63 158.50 31.60 186.50 37.30 5 1.7% 345.00 69.00 3.7%
WORK 30.86 4 34.0 0.40 155.50 31.10 1236.50 247.30 5 1.3% 1392.00 78.40 11.3%
MTCH 87.23 1 89.5 1.60 155.50 31.10 207.50 41.50 5 1.8% 363.00 72.60 4.2%
ZS 102.41 1 108.0 1.58 153.50 30.60 539.50 107.90 5 1.5% 693.00 138.60 6.8%
PLAN 44.83 3 48.0 0.53 154.50 30.60 931.50 186.30 5 1.1% 1086.00 217.20 8.1%
PINS 20.87 7 22.5 0.23 156.50 30.60 1121.50 224.30 5 1.0% 1278.00 255.60 8.7%
PCTY 128.33 1 140.0 1.58 153.50 30.60 1147.50 229.50 5 1.2% 1301.00 260.20 10.1%
ENPH 48.63 3 55.0 0.53 154.50 30.60 1891.50 378.30 5 1.0% 2046.00 409.20 14.0%
CYBR 98.12 1 101.0 1.58 153.50 30.60 268.50 53.70 5 1.6% 422.00 84.40 4.3%
CRWD 93.13 1 99.0 1.55 150.50 30.10 568.00 113.60 5 1.6% 718.50 143.70 7.7%
SFIX 23.44 6 26.0 0.25 145.50 29.10 1516.50 303.30 5 1.0% 1662.00 332.40 11.8%
ROKU 108.08 1 117.0 1.50 145.50 29.10 872.50 174.50 5 1.3% 1018.00 203.60 9.4%
PCTY 128.33 1 135.0 1.50 145.50 29.10 647.50 129.50 5 1.1% 793.00 158.60 6.2%
DOMO 31.07 4 35.0 0.38 147.50 29.10 1552.50 310.50 5 1.2% 1700.00 340.00 0.7%
GLOB 141.26 1 150.0 1.48 143.50 28.60 854.50 170.90 5 1.0% 998.00 199.60 7.1%
ZEN 80.14 1 82.5 1.43 138.50 27.60 216.50 43.30 5 1.7% 355.00 71.00 4.4%
SQ 86.71 1 90.0 1.42 137.50 27.40 309.50 61.90 5 1.6% 447.00 89.40 5.2%
WORK 30.86 4 34.5 0.35 135.50 27.10 1436.50 287.30 5 1.1% 1572.00 314.40 12.7%
ZS 102.41 1 109.0 1.35 130.50 26.10 639.50 127.90 5 1.3% 770.00 154.00 7.5%
ROST 92.44 1 95.0 1.35 130.50 26.10 236.50 47.30 5 1.4% 367.00 73.40 4.0%
QCOM 85.24 1 87.0 1.35 130.50 26.10 156.50 31.30 5 1.5% 287.00 57.40 3.4%
EVER 55.50 2 60.0 0.68 131.50 26.10 880.50 176.10 5 1.2% 1012.00 202.40 9.1%
MTCH 87.23 1 89.0 1.30 125.50 25.10 157.50 31.50 5 1.4% 283.00 56.60 3.2%
CYBR 98.12 1 102.0 1.28 123.50 24.60 368.50 73.70 5 1.3% 492.00 98.40 5.0%
ROKU 108.08 1 118.0 1.26 121.50 24.30 972.50 194.50 5 1.1% 1094.00 218.80 10.1%
ROST 92.44 1 95.5 1.20 115.50 23.10 286.50 57.30 5 1.2% 402.00 80.40 4.3%
QCOM 85.24 1 87.5 1.20 115.50 23.10 206.50 41.30 5 1.4% 322.00 64.40 3.8%
CRWD 93.13 1 100.0 1.20 115.50 23.10 668.00 133.60 5 1.2% 783.50 156.70 8.4%
ROKU 108.08 1 119.0 1.19 114.50 22.80 1072.50 214.50 5 1.1% 1187.00 237.40 11.0%
CRWD 93.13 1 101.0 1.18 113.50 22.60 768.00 153.60 5 1.2% 881.50 176.30 9.5%
ZS 102.41 1 110.0 1.15 110.50 22.10 739.50 147.90 5 1.1% 850.00 170.00 8.3%
ROST 92.44 1 99.0 1.15 110.50 22.10 636.50 127.30 5 1.2% 747.00 149.40 8.1%
SQ 86.71 1 91.0 1.15 110.50 22.00 409.50 81.90 5 1.3% 520.00 104.00 6.0%
MTCH 87.23 1 90.0 1.13 108.50 21.60 257.50 51.50 5 1.2% 366.00 73.20 4.2%
CYBR 98.12 1 107.0 1.13 108.50 21.60 868.50 173.70 5 1.1% 977.00 195.40 10.0%
SQ 86.71 1 91.5 1.12 107.50 21.50 459.50 91.90 5 1.2% 567.00 113.40 6.5%


A work still in progress!

Denny Schlesinger
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