First of all, I never said nor would ever expect a linear relation between the option price and the underlying stock price. And: a simple linear relation wouldn't be worth a Nobel Prize Black and Scholes won... I know the distribution curve very well: lognormal, or alternatively said: the natural logarithms (ln) of the changes are normally distributed, ie. a bell-like shape (Gauss, the famous German mathematican discovered and formulated it some centuries ago)... But these are basic things, I'm over them since at least 5 years... My deficit is in options selling and the use of the greeks for an optimal hedging when needed, ie. to prevent a loss. But I'll have mastered it soon; it's not rocket science... Well, I guess you mean that according to you a zero-loss strategy is impossible, right? That's IMHO not an open question anymore. With correct hedging one can prevent a loss. But that I already stated in my previous postings. For me the still open question is at what point should the hedge be initiated, IMHO the later the better, but it should be not too late... Ie. one needs to find the right point in time...
"The Cauchy distribution is often used in statistics as the canonical example of a "pathological" distribution since both its mean and its variance are undefined" --> https://en.wikipedia.org/wiki/Cauchy_distribution I mean the "usual" normal distribution with mu=0, sigma=1, ie. that one: https://en.wikipedia.org/wiki/Normal_distribution
By this, it sounds like you believe the put value initially will fall. This is not always the case. You may experience that the put is sold at the lowest possible value and remains the same (or higher) than initially sold. The lowest loss will be if you buy them back at the same value (and looses the bid/ask spread), but in this case a loss is impossible to avoid. To put it simple... The Greeks is used to try to predict how the options will react on stock price movement (or lack of) and time "movement". If you don't want to understand and use this, option Trading is more like gambling. Fun, if that is how you want to spend your money. Option trading is all about statistics, probability and knowledge (and thus reduce the effect of randomness). You sound like a smart and creative guy. I guess we all have been I'm the same situation. Please use Google or read books if you won't believe what people here are trying to tell you. And to answer your question: The best exit strategy is to exit before any loss. This, however, not possible at all trades...
You don't "hedge" or micro-manage in anyway .......... All options positions including Short Puts should be left alone while the trade is open. If the trade is too risky for your comfort level then make changes before you open it.
The following tables can explain much and would be useful in hedging (for example in the PEP case): Code: Spot=100.000 Strike=90.00 ExpDays=94 HoldDays=94 Interest=0.000% Dividend=0.000% VolaPctS=21.00000% --> Call=11.406355 Put=1.406355 Cdelta=0.812085 Pdelta=-0.187915 Day 0 : Annual : Vola=21.00% +1SD=23.37% -1SD=-18.94% Daily : Vola=1.32% +1SD=1.33% -1SD=-1.31% Period(0 days) : Vola=1.32% +1SD=1.33%(101.33) -1SD=-1.31%( 98.69) C@+1SD=12.5058(9.6%) C@-1SD=10.3579(-9.2%) P@+1SD=1.1741(-16.5%) P@-1SD=1.6721(18.9%) deltaSpot% spot call put cprm0PL% pprm0PL% -cprm0PL% -pprm0PL% Cdelta Pdelta --------------------------------------------------------------------------------------------------------------------------------- 10.00% 110.00000 20.32179 0.32179 78.16197% -77.11913% -78.16197 77.11913 0.94831 -0.05169 9.50% 109.50000 19.84859 0.34859 74.01341% -75.21344% -74.01341 75.21344 0.94444 -0.05556 9.00% 109.00000 19.37738 0.37738 69.88236% -73.16580% -69.88236 73.16580 0.94033 -0.05967 8.50% 108.50000 18.90830 0.40830 65.76990% -70.96730% -65.76990 70.96730 0.93595 -0.06405 8.00% 108.00000 18.44147 0.44147 61.67719% -68.60866% -61.67719 68.60866 0.93131 -0.06869 7.50% 107.50000 17.97703 0.47703 57.60542% -66.08018% -57.60542 66.08018 0.92640 -0.07360 7.00% 107.00000 17.51512 0.51512 53.55583% -63.37176% -53.55583 63.37176 0.92119 -0.07881 6.50% 106.50000 17.05589 0.55589 49.52973% -60.47292% -49.52973 60.47292 0.91568 -0.08432 6.00% 106.00000 16.59949 0.59949 45.52844% -57.37276% -45.52844 57.37276 0.90986 -0.09014 5.50% 105.50000 16.14608 0.64608 41.55337% -54.05999% -41.55337 54.05999 0.90372 -0.09628 5.00% 105.00000 15.69582 0.69582 37.60595% -50.52295% -37.60595 50.52295 0.89725 -0.10275 4.50% 104.50000 15.24889 0.74889 33.68767% -46.74959% -33.68767 46.74959 0.89043 -0.10957 4.00% 104.00000 14.80545 0.80545 29.80006% -42.72749% -29.80006 42.72749 0.88325 -0.11675 3.50% 103.50000 14.36570 0.86570 25.94468% -38.44389% -25.94468 38.44389 0.87571 -0.12429 3.00% 103.00000 13.92980 0.92980 22.12317% -33.88569% -22.12317 33.88569 0.86780 -0.13220 2.50% 102.50000 13.49796 0.99796 18.33716% -29.03949% -18.33716 29.03949 0.85951 -0.14049 2.00% 102.00000 13.07035 1.07035 14.58836% -23.89157% -14.58836 23.89157 0.85083 -0.14917 1.50% 101.50000 12.64719 1.14719 10.87848% -18.42796% -10.87848 18.42796 0.84175 -0.15825 1.00% 101.00000 12.22867 1.22867 7.20927% -12.63447% -7.20927 12.63447 0.83227 -0.16773 0.50% 100.50000 11.81499 1.31499 3.58251% -6.49667% -3.58251 6.49667 0.82238 -0.17762 0.00% 100.00000 11.40635 1.40635 0.00000% 0.00000% -0.00000 -0.00000 0.81208 -0.18792 -0.50% 99.50000 11.00297 1.50297 -3.53645% 6.87026% 3.53645 -6.87026 0.80137 -0.19863 -1.00% 99.00000 10.60506 1.60506 -7.02501% 14.12890% 7.02501 -14.12890 0.79024 -0.20976 -1.50% 98.50000 10.21281 1.71281 -10.46386% 21.79075% 10.46386 -21.79075 0.77869 -0.22131 -2.00% 98.00000 9.82644 1.82644 -13.85116% 29.87067% 13.85116 -29.87067 0.76672 -0.23328 -2.50% 97.50000 9.44616 1.94616 -17.18510% 38.38341% 17.18510 -38.38341 0.75434 -0.24566 -3.00% 97.00000 9.07217 2.07217 -20.46386% 47.34366% 20.46386 -47.34366 0.74155 -0.25845 -3.50% 96.50000 8.70468 2.20468 -23.68566% 56.76592% 23.68566 -56.76592 0.72835 -0.27165 -4.00% 96.00000 8.34389 2.34389 -26.84873% 66.66446% 26.84873 -66.66446 0.71475 -0.28525 -4.50% 95.50000 7.99000 2.49000 -29.95135% 77.05329% 29.95135 -77.05329 0.70077 -0.29923 -5.00% 95.00000 7.64319 2.64319 -32.99184% 87.94606% 32.99184 -87.94606 0.68640 -0.31360 -5.50% 94.50000 7.30365 2.80365 -35.96857% 99.35602% 35.96857 -99.35602 0.67167 -0.32833 -6.00% 94.00000 6.97157 2.97157 -38.87995% 111.29594% 38.87995 -111.29594 0.65659 -0.34341 -6.50% 93.50000 6.64711 3.14711 -41.72447% 123.77809% 41.72447 -123.77809 0.64117 -0.35883 -7.00% 93.00000 6.33045 3.33045 -44.50071% 136.81411% 44.50071 -136.81411 0.62543 -0.37457 -7.50% 92.50000 6.02172 3.52172 -47.20730% 150.41501% 47.20730 -150.41501 0.60940 -0.39060 -8.00% 92.00000 5.72109 3.72109 -49.84297% 164.59108% 49.84297 -164.59108 0.59309 -0.40691 -8.50% 91.50000 5.42868 3.92868 -52.40655% 179.35184% 52.40655 -179.35184 0.57652 -0.42348 -9.00% 91.00000 5.14461 4.14461 -54.89697% 194.70600% 54.89697 -194.70600 0.55973 -0.44027 -9.50% 90.50000 4.86900 4.36900 -57.31328% 210.66124% 57.31328 -210.66124 0.54273 -0.45727 -10.00% 90.00000 4.60192 4.60192 -59.65476% 227.22337% 59.65476 -227.22337 0.52557 -0.47443 ... Day 30 : Annual : Vola=21.00% +1SD=23.37% -1SD=-18.94% Daily : Vola=1.32% +1SD=1.33% -1SD=-1.31% Period(30 days) : Vola=7.25% +1SD=7.51%(107.51) -1SD=-6.99%( 93.01) C@+1SD=17.7142(55.3%) C@-1SD=5.5518(-51.3%) P@+1SD=0.1995(-85.8%) P@-1SD=2.5412(80.7%) deltaSpot% spot call put cprm0PL% pprm0PL% -cprm0PL% -pprm0PL% Cdelta Pdelta --------------------------------------------------------------------------------------------------------------------------------- 10.00% 110.00000 20.11744 0.11744 76.37049% -91.64913% -76.37049 91.64913 0.97436 -0.02564 9.50% 109.50000 19.63093 0.13093 72.10516% -90.69046% -72.10516 90.69046 0.97168 -0.02832 9.00% 109.00000 19.14581 0.14581 67.85212% -89.63224% -67.85212 89.63224 0.96875 -0.03125 8.50% 108.50000 18.66222 0.16222 63.61245% -88.46553% -63.61245 88.46553 0.96557 -0.03443 8.00% 108.00000 18.18028 0.18028 59.38733% -87.18074% -59.38733 87.18074 0.96211 -0.03789 7.50% 107.50000 17.70016 0.20016 55.17804% -85.76766% -55.17804 85.76766 0.95835 -0.04165 7.00% 107.00000 17.22199 0.22199 50.98590% -84.21539% -50.98590 84.21539 0.95427 -0.04573 6.50% 106.50000 16.74594 0.24594 46.81236% -82.51234% -46.81236 82.51234 0.94986 -0.05014 6.00% 106.00000 16.27218 0.27218 42.65892% -80.64622% -42.65892 80.64622 0.94510 -0.05490 5.50% 105.50000 15.80090 0.30090 38.52720% -78.60402% -38.52720 78.60402 0.93995 -0.06005 5.00% 105.00000 15.33229 0.33229 34.41888% -76.37199% -34.41888 76.37199 0.93441 -0.06559 4.50% 104.50000 14.86656 0.36656 30.33574% -73.93565% -30.33574 73.93565 0.92846 -0.07154 4.00% 104.00000 14.40391 0.40391 26.27968% -71.27980% -26.27968 71.27980 0.92206 -0.07794 3.50% 103.50000 13.94457 0.44457 22.25265% -68.38847% -22.25265 68.38847 0.91521 -0.08479 3.00% 103.00000 13.48878 0.48878 18.25670% -65.24502% -18.25670 65.24502 0.90787 -0.09212 2.50% 102.50000 13.03678 0.53678 14.29398% -61.83206% -14.29398 61.83206 0.90004 -0.09996 2.00% 102.00000 12.58882 0.58882 10.36672% -58.13153% -10.36672 58.13153 0.89170 -0.10830 1.50% 101.50000 12.14517 0.64517 6.47722% -54.12474% -6.47722 54.12474 0.88281 -0.11719 1.00% 101.00000 11.70610 0.70610 2.62786% -49.79234% -2.62786 49.79234 0.87338 -0.12662 0.50% 100.50000 11.27189 0.77189 -1.17889% -45.11444% 1.17889 45.11444 0.86337 -0.13663 0.00% 100.00000 10.84282 0.84282 -4.94053% -40.07061% 4.94053 40.07061 0.85279 -0.14721 -0.50% 99.50000 10.41919 0.91919 -8.65448% -34.63998% 8.65448 34.63998 0.84161 -0.15839 -1.00% 99.00000 10.00131 1.00131 -12.31812% -28.80128% 12.31812 28.80128 0.82983 -0.17017 -1.50% 98.50000 9.58946 1.08946 -15.92878% -22.53291% 15.92878 22.53291 0.81744 -0.18256 -2.00% 98.00000 9.18397 1.18397 -19.48377% -15.81308% 19.48377 15.81308 0.80444 -0.19556 -2.50% 97.50000 8.78513 1.28513 -22.98040% -8.61983% 22.98040 8.61983 0.79081 -0.20919 -3.00% 97.00000 8.39326 1.39326 -26.41594% -0.93120% 26.41594 0.93120 0.77657 -0.22343 -3.50% 96.50000 8.00866 1.50866 -29.78771% 7.27470% 29.78771 -7.27470 0.76172 -0.23828 -4.00% 96.00000 7.63165 1.63165 -33.09303% 16.01957% 33.09303 -16.01957 0.74625 -0.25375 -4.50% 95.50000 7.26251 1.76251 -36.32926% 25.32477% 36.32926 -25.32477 0.73020 -0.26980 -5.00% 95.00000 6.90155 1.90155 -39.49382% 35.21125% 39.49382 -35.21125 0.71356 -0.28644 -5.50% 94.50000 6.54905 2.04905 -42.58420% 45.69935% 42.58420 -45.69935 0.69635 -0.30365 -6.00% 94.00000 6.20529 2.20529 -45.59799% 56.80869% 45.59799 -56.80869 0.67861 -0.32139 -6.50% 93.50000 5.87052 2.37052 -48.53286% 68.55807% 48.53286 -68.55807 0.66035 -0.33965 -7.00% 93.00000 5.54501 2.54501 -51.38663% 80.96530% 51.38663 -80.96530 0.64160 -0.35840 -7.50% 92.50000 5.22899 2.72899 -54.15722% 94.04705% 54.15722 -94.04705 0.62241 -0.37759 -8.00% 92.00000 4.92267 2.92267 -56.84275% 107.81877% 56.84275 -107.81877 0.60280 -0.39720 -8.50% 91.50000 4.62625 3.12625 -59.44147% 122.29455% 59.44147 -122.29455 0.58282 -0.41718 -9.00% 91.00000 4.33991 3.33991 -61.95183% 137.48699% 61.95183 -137.48699 0.56251 -0.43749 -9.50% 90.50000 4.06380 3.56380 -64.37247% 153.40714% 64.37247 -153.40714 0.54192 -0.45808 -10.00% 90.00000 3.79805 3.79805 -66.70236% 170.06329% 66.70236 -170.06329 0.52110 -0.47890 ...
That's indeed the question: should one apply hedging or not. I just wanted to study/analyse all these alternatives. I was thinking about applying hedging for example if after 30 days the spot is say 5% lower, vola staying the same. But hedging it only if such a critical situation arises; not hedging from the beginning on. According to the above table, in this situation (spot=95) we are already 35% in the reds... The good point is that there is still much time till expiration. And that time can be used for the hedging strategy to develop its effect...
Yes, for those cases where one can't exit that easily b/c it would mean a big loss I just try to find alternatives to limit losses or even prevent losses by using some intelligent hedging... Still experimenting...
I think this online options calculator is calculating the delta wrong when Interest and/or Dividend is >0: http://www.fintools.com/resources/online-calculators/options-calcs/options-calculator/ The following has Delta correct: