New invention for the derivatives market - How to profit of it?

thecoder said:
Ok, here's it:
A NEW PAYOUT METHOD FOR CLASSIC PUT (a long due fix since 1973 :)):
Code: 
BSM:
S=100.00 K=90.00 s=30% t=1.0 r=0.0 q=0.0 :
CALL: Value=17.012880 Delta=0.691885  FairDelta=0.637281  Gamma=0.011728 Vega=0.351854 Theta=-0.014460 Rho=0.521757  ...
PUT : Value=7.012880  Delta=-0.308115 FairDelta=-0.362719 Gamma=0.011728 Vega=0.351854 Theta=-0.014460 Rho=-0.378243 ...

If PUT option expires at spot 80 (z=-0.392610 from K; the corrosponding spot at the other side (ie. +z) is 101.25) :
Old/current/flawed/unfair payout: 10.000000 Profit=2.987120(42.59%)
The fair payout has to be:        11.250000 Profit=4.237120(60.42%)
More...

With this improvement we can summarize the recent changes:
- The payout of classic PUT has to be fixed (like shown above).
- Initially FairPut was bound to the CALL (ie. using same premium), but with this new improvement, the FairPut algorithm works also with classic PUT (ie. using the premium of classic PUT instead of the CALL), but the payout of classic PUT has to be changed (ie. fixed) as shown above.
- As can be seen: the new payout of PUT has become the same as of the CALL for the same z-Value off the K, ie:
CALL at expiration @ spot 101.25 (z=+0.392610 from K): Payout=11.250000 Profit=-5.762880(-33.87%)
Ie. now the payout of CALL and PUT is the same for the same z-Distance from K.
This finally brings the fairness into the option payouts for same probabilities for up and down from K as the basis.
- So, the problem with BSM is the unfair payout for the PUT, not the cost of the options.
 
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thecoder said:
Code: 
BSM:
S=100.00 K=90.00 s=30% t=1.0 r=0.0 q=0.0 :
CALL: Value=17.012880 Delta=0.691885  FairDelta=0.637281  Gamma=0.011728 Vega=0.351854 Theta=-0.014460 Rho=0.521757  ...
PUT : Value=7.012880  Delta=-0.308115 FairDelta=-0.362719 Gamma=0.011728 Vega=0.351854 Theta=-0.014460 Rho=-0.378243 ...
More...

INFO ON THE NEW GREEK FairDelta (cf. above):

FairDelta (ie. its absolute value) is the true probability that the option will expire ITM.
This is an improvement (better said a fix) over the normal Delta of BSM.

I had introduced this on 2020-08-12 under the old name "MyDelta" in this posting here:
https://www.elitetrader.com/et/threads/questioning-the-meaning-of-delta.348612/page-2#post-5177632
 
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Btw, my last 2 postings here are IMO the most important research results since the famous Black & Scholes paper in 1973.
My research results fix the problems inherent in the Black-Scholes options pricing model since 1973 (and nobody has noticed these problems for 47 years, up until now :)):

Ie. these postings with my research results:
https://www.elitetrader.com/et/thre...w-to-profit-of-it.348911/page-14#post-5183292
https://www.elitetrader.com/et/thre...w-to-profit-of-it.348911/page-14#post-5183582
 
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Just a clarification regarding Delta and FairDelta:

Delta is the change in the option price when the price of the underlying changes by $1.
But some textbooks additionally interpret abs(Delta) as a proxy for probability that the option will expire in-the-money. This is mathematically wrong. That wrong interpretation is unfortunately used even by wikipedia: https://en.wikipedia.org/wiki/Greeks_(finance)#As_a_proxy_for_probability

The new FairDelta is about "probability for ITM" only.

This means: both Delta and FairDelta are useful metrics.
But to be used in Delta Hedging I would prefer FairDelta over Delta.
 
The reason your FairPut wouldn't work in practice is that z-distance from K of a stock price that's gone to zero is infinite. So it would need to have the same payout as a call on a stock whose price has become infinite. Since stocks do sadly go to zero occasionally, I think you wouldn't be able to find anybody willing to write a FairPut for a finite amount of money. Mathematics works out only if stock prices follow log normal distribution which in practice they don't (otherwise no company would ever go bankrupt!)
 
mr_sandman said:
The reason your FairPut wouldn't work in practice is that z-distance from K of a stock price that's gone to zero is infinite. So it would need to have the same payout as a call on a stock whose price has become infinite. Since stocks do sadly go to zero occasionally, I think you wouldn't be able to find anybody willing to write a FairPut for a finite amount of money. Mathematics works out only if stock prices follow log normal distribution which in practice they don't (otherwise no company would ever go bankrupt!)
More...

@mr_sandman, thanks for this qualified analysis, appreciate it.
It is maybe a little bit hard to understand, and I admit I myself had at times some difficulties to believe the result, as well doubts, but now I'm sure it works, ie. it does not create any arbitrage situation under the condition that FairPUT replaces PUT (ie. if only CALL and FairPUT are possible in the market).

My announced program code (a reference implementation) is almost finished, but I need to set up a new contact email address and also upload the code to the announced GitHub repository (both not done yet, I hope later on Sunday it will be available).

Here's are some preliminary outputs of the program. They have the same input parameters except a different spot for the expiration date.
If you find any discrepancies/bugs in the data, please let me know. Thx.

Code: 
FairPut v1.0a - A BSM options calculator with integrated 'FairPut' payout algorithm and the main Greeks
All rights reserved. Copyright (c) by the copyright owner/author (info@fairput.com). Free for non-commercial use only.
The latest version can be found at https://github.com/FairPut

Args  : ./FairPut.exe 100 100 30 365 365 0.0 0.0 100 1
Params: Spot_S=100.000000 Strike_K=100.000000 AnnVola_s=30.000000% ExpDays_t=365.000000 AnnDays_ty=365.000000 AnnEarningsYield_r=0.000000% AnnDividendsYield_q=0.000000% SpotAtExp_Sx=100.000000 fShowText=1

CALL=11.923538 PUT=11.923538

Internal info:
  S=100.000000 K=100.000000 s=0.300000 t=1.000000 r=0.000000 q=0.000000 Sx=100.000000
  st=0.300000 rt=0.000000 qt=0.000000 u=0.000000 ut=0.000000 exp_mqt=1.000000 exp_mrt=1.000000
  z2=-0.150000 z0=0.000000 z1=0.150000 p2=0.440382 p0=0.500000 p1=0.559618

Other info:
  S2K: z_S2K=0.000000 p_S2K=0.500000
  K2S: z_K2S=0.000000 p_K2S=0.500000
  Sx@: +1SD(p=0.158655)=134.985881 0SD(p=0.5)=100.000000 -1SD(p=0.158655)=74.081822  [based on S]
  Kx@: +1SD(p=0.158655)=134.985881 0SD(p=0.5)=100.000000 -1SD(p=0.158655)=74.081822  [based on K]

Greeks:
  CALL   : Delta=0.559618 FairDelta=0.500000 Gamma=0.013149 Vega=0.394479 Theta365=-0.016211 Rho=0.440382
  PUT    : Delta=-0.440382 FairDelta=-0.500000 Gamma=0.013149 Vega=0.394479 Theta365=-0.016211 Rho=-0.559618
  FairPUT: Delta=-0.440382 FairDelta=-0.500000 Gamma=0.013149 Vega=0.394479 Theta365=-0.016211 Rho=-0.559618


Payouts at expiration for Sx=100.000000(0.000000%):

Long CALL:
  LZ(const): Sx <= K(100.000000;z=0.000000)  POZ(var): Sx > K(100.000000;z=0.000000)  PZ(var): Sx > K+C(111.923538;z=0.375486)
  LZ_MaxLoss=C(11.923538) PZ_MaxProfit=Sx-C(ie. unlimited)
  Credit=-11.923538 Payout=0.000000 Profit=-11.923538(-100.00%)

Short CALL:
  LZ(var): Sx >= K+C(111.923538;z=0.375486)  POZ(var): Sx < K+C(111.923538;z=0.375486)  PZ(const): Sx <= K(100.000000;z=0.000000)
  LZ_MaxLoss=Sx-C(ie. unlimited) PZ_MaxProfit=C(11.923538)
  Credit=11.923538 Payout=0.000000 Profit=11.923538(100.00%)

Long PUT:
  LZ(const): Sx >= K(100.000000;z=0.000000)  POZ(var): Sx < K(100.000000;z=0.000000)  PZ(var): Sx < K-P(88.076462;z=-0.423216)
  LZ_MaxLoss=P(11.923538) PZ_MaxProfit=K-P(88.076462;738.677212%)
  Credit=-11.923538 Payout=0.000000 Profit=-11.923538(-100.00%)

Short PUT:
  LZ(var): Sx <= K-P(88.076462;z=-0.423216)  POZ(var): Sx > K-P(88.076462;z=-0.423216)  PZ(const): Sx >= K(100.000000;z=0.000000)
  LZ_MaxLoss=K-P(88.076462;-738.677212%) PZ_MaxProfit=P(11.923538)
  Credit=11.923538 Payout=0.000000 Profit=11.923538(100.00%)

Long FairPUT:
  LZ(const): Sx >= K(100.000000;z=0.000000)  POZ(var): Sx < K(100.000000;z=0.000000)  PZ(var): Sx < K-P(88.076462;z=-0.423216)
  LZ_MaxLoss=P(11.923538) PZ_MaxProfit=Sup-K-P(ie. unlimited)
  Credit=-11.923538 Payout=0.000000 Profit=-11.923538(-100.00%) (z=0.000000 zUp=0.000000 Sup=100.000000(0.00%)) Smid=100.000000(0.00) Sdown=100.000000(0.00%)

  Long FairPut is a Long PUT with FairPut algorithm. The difference is only in the Payout and Profit.
  Long FairPUT is the mirror image of CALL at same z distance from K.
  This means: Long PUT payout in BSM is wrong since the 1973 Black-Scholes paper, and has to be replaced by Long FairPUT payout.
  ATTN: In a market, Long PUT and Long FairPUT cannot co-exist as this would make arbitrage possible.
  A trademark for 'FairPut' has officially been filed on 2020-08-18; a commercial use of FairPut requires permission, ie. a usage license.
  FairPut officially was first announced to the public on the same day at the EliteTrader (ET) board:
  https://www.elitetrader.com/et/threads/new-invention-for-the-derivatives-market-how-to-profit-of-it.348911/page-5#post-5181715
  In later postings it was refined and extended for more use cases (initially it was bound to the CALL premium, now it works also with the PUT premium).

Short FairPUT (same as Short PUT):
  LZ(var): Sx <= K-P(88.076462;z=-0.423216)  POZ(var): Sx > K-P(88.076462;z=-0.423216)  PZ(const): Sx >= K(100.000000;z=0.000000)
  LZ_MaxLoss=K-P(88.076462;-738.677212%) PZ_MaxProfit=P(11.923538)
  Credit=11.923538 Payout=0.000000 Profit=11.923538(100.00%)

Legend:
  LZ: loss zone, POZ: payout zone, PZ: profit zone
  var: variable/continuous/changing/rising/falling, const: constant/fixed/limited/same/equal

Code: 
FairPut v1.0a - A BSM options calculator with integrated 'FairPut' payout algorithm and the main Greeks
All rights reserved. Copyright (c) by the copyright owner/author (info@fairput.com). Free for non-commercial use only.
The latest version can be found at https://github.com/FairPut

Args  : ./FairPut.exe 100 100 30 365 365 0.0 0.0 120 0
Params: Spot_S=100.000000 Strike_K=100.000000 AnnVola_s=30.000000% ExpDays_t=365.000000 AnnDays_ty=365.000000 AnnEarningsYield_r=0.000000% AnnDividendsYield_q=0.000000% SpotAtExp_Sx=120.000000 fShowText=0

CALL=11.923538 PUT=11.923538

Internal info:
  S=100.000000 K=100.000000 s=0.300000 t=1.000000 r=0.000000 q=0.000000 Sx=120.000000
  st=0.300000 rt=0.000000 qt=0.000000 u=0.000000 ut=0.000000 exp_mqt=1.000000 exp_mrt=1.000000
  z2=-0.150000 z0=0.000000 z1=0.150000 p2=0.440382 p0=0.500000 p1=0.559618

Other info:
  S2K: z_S2K=0.000000 p_S2K=0.500000
  K2S: z_K2S=0.000000 p_K2S=0.500000
  Sx@: +1SD(p=0.158655)=134.985881 0SD(p=0.5)=100.000000 -1SD(p=0.158655)=74.081822  [based on S]
  Kx@: +1SD(p=0.158655)=134.985881 0SD(p=0.5)=100.000000 -1SD(p=0.158655)=74.081822  [based on K]

Greeks:
  CALL   : Delta=0.559618 FairDelta=0.500000 Gamma=0.013149 Vega=0.394479 Theta365=-0.016211 Rho=0.440382
  PUT    : Delta=-0.440382 FairDelta=-0.500000 Gamma=0.013149 Vega=0.394479 Theta365=-0.016211 Rho=-0.559618
  FairPUT: Delta=-0.440382 FairDelta=-0.500000 Gamma=0.013149 Vega=0.394479 Theta365=-0.016211 Rho=-0.559618


Payouts at expiration for Sx=120.000000(20.000000%):

Long CALL:
  LZ(const): Sx <= K(100.000000;z=0.000000)  POZ(var): Sx > K(100.000000;z=0.000000)  PZ(var): Sx > K+C(111.923538;z=0.375486)
  LZ_MaxLoss=C(11.923538) PZ_MaxProfit=Sx-C(ie. unlimited)
  Credit=-11.923538 Payout=20.000000 Profit=8.076462(67.74%)

Short CALL:
  LZ(var): Sx >= K+C(111.923538;z=0.375486)  POZ(var): Sx < K+C(111.923538;z=0.375486)  PZ(const): Sx <= K(100.000000;z=0.000000)
  LZ_MaxLoss=Sx-C(ie. unlimited) PZ_MaxProfit=C(11.923538)
  Credit=11.923538 Payout=-20.000000 Profit=-8.076462(-67.74%)

Long PUT:
  LZ(const): Sx >= K(100.000000;z=0.000000)  POZ(var): Sx < K(100.000000;z=0.000000)  PZ(var): Sx < K-P(88.076462;z=-0.423216)
  LZ_MaxLoss=P(11.923538) PZ_MaxProfit=K-P(88.076462;738.677212%)
  Credit=-11.923538 Payout=0.000000 Profit=-11.923538(-100.00%)

Short PUT:
  LZ(var): Sx <= K-P(88.076462;z=-0.423216)  POZ(var): Sx > K-P(88.076462;z=-0.423216)  PZ(const): Sx >= K(100.000000;z=0.000000)
  LZ_MaxLoss=K-P(88.076462;-738.677212%) PZ_MaxProfit=P(11.923538)
  Credit=11.923538 Payout=0.000000 Profit=11.923538(100.00%)

Long FairPUT:
  LZ(const): Sx >= K(100.000000;z=0.000000)  POZ(var): Sx < K(100.000000;z=0.000000)  PZ(var): Sx < K-P(88.076462;z=-0.423216)
  LZ_MaxLoss=P(11.923538) PZ_MaxProfit=Sup-K-P(ie. unlimited)
  Credit=-11.923538 Payout=0.000000 Profit=-11.923538(-100.00%) (z=0.607739 zUp=0.607739 Sup=120.000000(20.00%)) Smid=100.000000(0.00) Sdown=83.333333(-16.67%)

Short FairPUT (same as Short PUT):
  LZ(var): Sx <= K-P(88.076462;z=-0.423216)  POZ(var): Sx > K-P(88.076462;z=-0.423216)  PZ(const): Sx >= K(100.000000;z=0.000000)
  LZ_MaxLoss=K-P(88.076462;-738.677212%) PZ_MaxProfit=P(11.923538)
  Credit=11.923538 Payout=0.000000 Profit=11.923538(100.00%)

Legend:
  LZ: loss zone, POZ: payout zone, PZ: profit zone
  var: variable/continuous/changing/rising/falling, const: constant/fixed/limited/same/equal

Code: 
FairPut v1.0a - A BSM options calculator with integrated 'FairPut' payout algorithm and the main Greeks
All rights reserved. Copyright (c) by the copyright owner/author (info@fairput.com). Free for non-commercial use only.
The latest version can be found at https://github.com/FairPut

Args  : ./FairPut.exe 100 100 30 365 365 0.0 0.0 80 0
Params: Spot_S=100.000000 Strike_K=100.000000 AnnVola_s=30.000000% ExpDays_t=365.000000 AnnDays_ty=365.000000 AnnEarningsYield_r=0.000000% AnnDividendsYield_q=0.000000% SpotAtExp_Sx=80.000000 fShowText=0

CALL=11.923538 PUT=11.923538

Internal info:
  S=100.000000 K=100.000000 s=0.300000 t=1.000000 r=0.000000 q=0.000000 Sx=80.000000
  st=0.300000 rt=0.000000 qt=0.000000 u=0.000000 ut=0.000000 exp_mqt=1.000000 exp_mrt=1.000000
  z2=-0.150000 z0=0.000000 z1=0.150000 p2=0.440382 p0=0.500000 p1=0.559618

Other info:
  S2K: z_S2K=0.000000 p_S2K=0.500000
  K2S: z_K2S=0.000000 p_K2S=0.500000
  Sx@: +1SD(p=0.158655)=134.985881 0SD(p=0.5)=100.000000 -1SD(p=0.158655)=74.081822  [based on S]
  Kx@: +1SD(p=0.158655)=134.985881 0SD(p=0.5)=100.000000 -1SD(p=0.158655)=74.081822  [based on K]

Greeks:
  CALL   : Delta=0.559618 FairDelta=0.500000 Gamma=0.013149 Vega=0.394479 Theta365=-0.016211 Rho=0.440382
  PUT    : Delta=-0.440382 FairDelta=-0.500000 Gamma=0.013149 Vega=0.394479 Theta365=-0.016211 Rho=-0.559618
  FairPUT: Delta=-0.440382 FairDelta=-0.500000 Gamma=0.013149 Vega=0.394479 Theta365=-0.016211 Rho=-0.559618


Payouts at expiration for Sx=80.000000(-20.000000%):

Long CALL:
  LZ(const): Sx <= K(100.000000;z=0.000000)  POZ(var): Sx > K(100.000000;z=0.000000)  PZ(var): Sx > K+C(111.923538;z=0.375486)
  LZ_MaxLoss=C(11.923538) PZ_MaxProfit=Sx-C(ie. unlimited)
  Credit=-11.923538 Payout=0.000000 Profit=-11.923538(-100.00%)

Short CALL:
  LZ(var): Sx >= K+C(111.923538;z=0.375486)  POZ(var): Sx < K+C(111.923538;z=0.375486)  PZ(const): Sx <= K(100.000000;z=0.000000)
  LZ_MaxLoss=Sx-C(ie. unlimited) PZ_MaxProfit=C(11.923538)
  Credit=11.923538 Payout=0.000000 Profit=11.923538(100.00%)

Long PUT:
  LZ(const): Sx >= K(100.000000;z=0.000000)  POZ(var): Sx < K(100.000000;z=0.000000)  PZ(var): Sx < K-P(88.076462;z=-0.423216)
  LZ_MaxLoss=P(11.923538) PZ_MaxProfit=K-P(88.076462;738.677212%)
  Credit=-11.923538 Payout=20.000000 Profit=8.076462(67.74%)

Short PUT:
  LZ(var): Sx <= K-P(88.076462;z=-0.423216)  POZ(var): Sx > K-P(88.076462;z=-0.423216)  PZ(const): Sx >= K(100.000000;z=0.000000)
  LZ_MaxLoss=K-P(88.076462;-738.677212%) PZ_MaxProfit=P(11.923538)
  Credit=11.923538 Payout=-20.000000 Profit=-8.076462(-67.74%)

Long FairPUT:
  LZ(const): Sx >= K(100.000000;z=0.000000)  POZ(var): Sx < K(100.000000;z=0.000000)  PZ(var): Sx < K-P(88.076462;z=-0.423216)
  LZ_MaxLoss=P(11.923538) PZ_MaxProfit=Sup-K-P(ie. unlimited)
  Credit=-11.923538 Payout=25.000000 Profit=13.076462(109.67%) (z=-0.743812 zUp=0.743812 Sup=125.000000(25.00%)) Smid=100.000000(0.00) Sdown=80.000000(-20.00%)

Short FairPUT (same as Short PUT):
  LZ(var): Sx <= K-P(88.076462;z=-0.423216)  POZ(var): Sx > K-P(88.076462;z=-0.423216)  PZ(const): Sx >= K(100.000000;z=0.000000)
  LZ_MaxLoss=K-P(88.076462;-738.677212%) PZ_MaxProfit=P(11.923538)
  Credit=11.923538 Payout=-20.000000 Profit=-8.076462(-67.74%)

Legend:
  LZ: loss zone, POZ: payout zone, PZ: profit zone
  var: variable/continuous/changing/rising/falling, const: constant/fixed/limited/same/equal

Code: 
FairPut v1.0a - A BSM options calculator with integrated 'FairPut' payout algorithm and the main Greeks
All rights reserved. Copyright (c) by the copyright owner/author (info@fairput.com). Free for non-commercial use only.
The latest version can be found at https://github.com/FairPut

Args  : ./FairPut.exe 100 100 30 365 365 0.0 0.0 83.333333 0
Params: Spot_S=100.000000 Strike_K=100.000000 AnnVola_s=30.000000% ExpDays_t=365.000000 AnnDays_ty=365.000000 AnnEarningsYield_r=0.000000% AnnDividendsYield_q=0.000000% SpotAtExp_Sx=83.333333 fShowText=0

CALL=11.923538 PUT=11.923538

Internal info:
  S=100.000000 K=100.000000 s=0.300000 t=1.000000 r=0.000000 q=0.000000 Sx=83.333333
  st=0.300000 rt=0.000000 qt=0.000000 u=0.000000 ut=0.000000 exp_mqt=1.000000 exp_mrt=1.000000
  z2=-0.150000 z0=0.000000 z1=0.150000 p2=0.440382 p0=0.500000 p1=0.559618

Other info:
  S2K: z_S2K=0.000000 p_S2K=0.500000
  K2S: z_K2S=0.000000 p_K2S=0.500000
  Sx@: +1SD(p=0.158655)=134.985881 0SD(p=0.5)=100.000000 -1SD(p=0.158655)=74.081822  [based on S]
  Kx@: +1SD(p=0.158655)=134.985881 0SD(p=0.5)=100.000000 -1SD(p=0.158655)=74.081822  [based on K]

Greeks:
  CALL   : Delta=0.559618 FairDelta=0.500000 Gamma=0.013149 Vega=0.394479 Theta365=-0.016211 Rho=0.440382
  PUT    : Delta=-0.440382 FairDelta=-0.500000 Gamma=0.013149 Vega=0.394479 Theta365=-0.016211 Rho=-0.559618
  FairPUT: Delta=-0.440382 FairDelta=-0.500000 Gamma=0.013149 Vega=0.394479 Theta365=-0.016211 Rho=-0.559618


Payouts at expiration for Sx=83.333333(-16.666667%):

Long CALL:
  LZ(const): Sx <= K(100.000000;z=0.000000)  POZ(var): Sx > K(100.000000;z=0.000000)  PZ(var): Sx > K+C(111.923538;z=0.375486)
  LZ_MaxLoss=C(11.923538) PZ_MaxProfit=Sx-C(ie. unlimited)
  Credit=-11.923538 Payout=0.000000 Profit=-11.923538(-100.00%)

Short CALL:
  LZ(var): Sx >= K+C(111.923538;z=0.375486)  POZ(var): Sx < K+C(111.923538;z=0.375486)  PZ(const): Sx <= K(100.000000;z=0.000000)
  LZ_MaxLoss=Sx-C(ie. unlimited) PZ_MaxProfit=C(11.923538)
  Credit=11.923538 Payout=0.000000 Profit=11.923538(100.00%)

Long PUT:
  LZ(const): Sx >= K(100.000000;z=0.000000)  POZ(var): Sx < K(100.000000;z=0.000000)  PZ(var): Sx < K-P(88.076462;z=-0.423216)
  LZ_MaxLoss=P(11.923538) PZ_MaxProfit=K-P(88.076462;738.677212%)
  Credit=-11.923538 Payout=16.666667 Profit=4.743129(39.78%)

Short PUT:
  LZ(var): Sx <= K-P(88.076462;z=-0.423216)  POZ(var): Sx > K-P(88.076462;z=-0.423216)  PZ(const): Sx >= K(100.000000;z=0.000000)
  LZ_MaxLoss=K-P(88.076462;-738.677212%) PZ_MaxProfit=P(11.923538)
  Credit=11.923538 Payout=-16.666667 Profit=-4.743129(-39.78%)

Long FairPUT:
  LZ(const): Sx >= K(100.000000;z=0.000000)  POZ(var): Sx < K(100.000000;z=0.000000)  PZ(var): Sx < K-P(88.076462;z=-0.423216)
  LZ_MaxLoss=P(11.923538) PZ_MaxProfit=Sup-K-P(ie. unlimited)
  Credit=-11.923538 Payout=20.000000 Profit=8.076462(67.74%) (z=-0.607739 zUp=0.607739 Sup=120.000000(20.00%)) Smid=100.000000(0.00) Sdown=83.333333(-16.67%)

Short FairPUT (same as Short PUT):
  LZ(var): Sx <= K-P(88.076462;z=-0.423216)  POZ(var): Sx > K-P(88.076462;z=-0.423216)  PZ(const): Sx >= K(100.000000;z=0.000000)
  LZ_MaxLoss=K-P(88.076462;-738.677212%) PZ_MaxProfit=P(11.923538)
  Credit=11.923538 Payout=-16.666667 Profit=-4.743129(-39.78%)

Legend:
  LZ: loss zone, POZ: payout zone, PZ: profit zone
  var: variable/continuous/changing/rising/falling, const: constant/fixed/limited/same/equal

Code: 
FairPut v1.0a - A BSM options calculator with integrated 'FairPut' payout algorithm and the main Greeks
All rights reserved. Copyright (c) by the copyright owner/author (info@fairput.com). Free for non-commercial use only.
The latest version can be found at https://github.com/FairPut

Args  : ./FairPut.exe 100 100 30 365 365 0.0 0.0 125 0
Params: Spot_S=100.000000 Strike_K=100.000000 AnnVola_s=30.000000% ExpDays_t=365.000000 AnnDays_ty=365.000000 AnnEarningsYield_r=0.000000% AnnDividendsYield_q=0.000000% SpotAtExp_Sx=125.000000 fShowText=0

CALL=11.923538 PUT=11.923538

Internal info:
  S=100.000000 K=100.000000 s=0.300000 t=1.000000 r=0.000000 q=0.000000 Sx=125.000000
  st=0.300000 rt=0.000000 qt=0.000000 u=0.000000 ut=0.000000 exp_mqt=1.000000 exp_mrt=1.000000
  z2=-0.150000 z0=0.000000 z1=0.150000 p2=0.440382 p0=0.500000 p1=0.559618

Other info:
  S2K: z_S2K=0.000000 p_S2K=0.500000
  K2S: z_K2S=0.000000 p_K2S=0.500000
  Sx@: +1SD(p=0.158655)=134.985881 0SD(p=0.5)=100.000000 -1SD(p=0.158655)=74.081822  [based on S]
  Kx@: +1SD(p=0.158655)=134.985881 0SD(p=0.5)=100.000000 -1SD(p=0.158655)=74.081822  [based on K]

Greeks:
  CALL   : Delta=0.559618 FairDelta=0.500000 Gamma=0.013149 Vega=0.394479 Theta365=-0.016211 Rho=0.440382
  PUT    : Delta=-0.440382 FairDelta=-0.500000 Gamma=0.013149 Vega=0.394479 Theta365=-0.016211 Rho=-0.559618
  FairPUT: Delta=-0.440382 FairDelta=-0.500000 Gamma=0.013149 Vega=0.394479 Theta365=-0.016211 Rho=-0.559618


Payouts at expiration for Sx=125.000000(25.000000%):

Long CALL:
  LZ(const): Sx <= K(100.000000;z=0.000000)  POZ(var): Sx > K(100.000000;z=0.000000)  PZ(var): Sx > K+C(111.923538;z=0.375486)
  LZ_MaxLoss=C(11.923538) PZ_MaxProfit=Sx-C(ie. unlimited)
  Credit=-11.923538 Payout=25.000000 Profit=13.076462(109.67%)

Short CALL:
  LZ(var): Sx >= K+C(111.923538;z=0.375486)  POZ(var): Sx < K+C(111.923538;z=0.375486)  PZ(const): Sx <= K(100.000000;z=0.000000)
  LZ_MaxLoss=Sx-C(ie. unlimited) PZ_MaxProfit=C(11.923538)
  Credit=11.923538 Payout=-25.000000 Profit=-13.076462(-109.67%)

Long PUT:
  LZ(const): Sx >= K(100.000000;z=0.000000)  POZ(var): Sx < K(100.000000;z=0.000000)  PZ(var): Sx < K-P(88.076462;z=-0.423216)
  LZ_MaxLoss=P(11.923538) PZ_MaxProfit=K-P(88.076462;738.677212%)
  Credit=-11.923538 Payout=0.000000 Profit=-11.923538(-100.00%)

Short PUT:
  LZ(var): Sx <= K-P(88.076462;z=-0.423216)  POZ(var): Sx > K-P(88.076462;z=-0.423216)  PZ(const): Sx >= K(100.000000;z=0.000000)
  LZ_MaxLoss=K-P(88.076462;-738.677212%) PZ_MaxProfit=P(11.923538)
  Credit=11.923538 Payout=0.000000 Profit=11.923538(100.00%)

Long FairPUT:
  LZ(const): Sx >= K(100.000000;z=0.000000)  POZ(var): Sx < K(100.000000;z=0.000000)  PZ(var): Sx < K-P(88.076462;z=-0.423216)
  LZ_MaxLoss=P(11.923538) PZ_MaxProfit=Sup-K-P(ie. unlimited)
  Credit=-11.923538 Payout=0.000000 Profit=-11.923538(-100.00%) (z=0.743812 zUp=0.743812 Sup=125.000000(25.00%)) Smid=100.000000(0.00) Sdown=80.000000(-20.00%)

Short FairPUT (same as Short PUT):
  LZ(var): Sx <= K-P(88.076462;z=-0.423216)  POZ(var): Sx > K-P(88.076462;z=-0.423216)  PZ(const): Sx >= K(100.000000;z=0.000000)
  LZ_MaxLoss=K-P(88.076462;-738.677212%) PZ_MaxProfit=P(11.923538)
  Credit=11.923538 Payout=0.000000 Profit=11.923538(100.00%)

Legend:
  LZ: loss zone, POZ: payout zone, PZ: profit zone
  var: variable/continuous/changing/rising/falling, const: constant/fixed/limited/same/equal
 
Last edited:
thecoder said:
Ok, here's it:
A NEW PAYOUT METHOD FOR CLASSIC PUT (a long due fix since 1973 :)):
Code: 
BSM:
S=100.00 K=90.00 s=30% t=1.0 r=0.0 q=0.0 :
CALL: Value=17.012880 Delta=0.691885  FairDelta=0.637281  Gamma=0.011728 Vega=0.351854 Theta=-0.014460 Rho=0.521757  ...
PUT : Value=7.012880  Delta=-0.308115 FairDelta=-0.362719 Gamma=0.011728 Vega=0.351854 Theta=-0.014460 Rho=-0.378243 ...

If PUT option expires at spot 80 (z=-0.392610 from K; the corrosponding spot at the other side (ie. +z) is 101.25) :
Old/current/flawed/unfair payout: 10.000000 Profit=2.987120(42.59%)
The fair payout has to be:        11.250000 Profit=4.237120(60.42%)
More...

Hey Einstein, the most any ITM 90 strike "FairPut", "DumbPut", or regular vanilla put (what most of us prefer to trade), could be worth at expiration with spot at 80, is 10.00. At an expiring price of 11.25 you are synthetically valuing worthless OTM 90 calls at 1.25 (put call parity). Your ITM "FairPut" can't have any extrinsic or time value (1.25) at expiration. Your expiring "FairPut" price of 11.25 cannot exceed [K (strike price) - Spot price] = 10.00 at expiration....theoretically and mathematically impossible. I would sell you as many "FairPuts" as you want and buy the same amount of regular vanilla puts to lock in the 1.25 difference. Your "FairPuts" are going to be grossly overvalued with exaggerated deltas. Nobody but you will be buying them...and you'll lose all your poor parent's money paying too much for them and then overhedging them with incorrect deltas. These "FairPuts" defy any logic and fail all rigours of mathematics. Your puts are bunk.
 
@VolSkewTrader, you still have not understood what the topic is. You are stuck in what you know.
I OTOH am saying that there is an error in the payout of the Black-Scholes PUT option.

Please do me/us a favor and don't spam this thread any longer by repeating over and over the same argumentations about the status-quo. But it's not about the status-quo here, it's something new that aims to replace and overcome the status-quo. So, it's a different thing than what you know. It's not helpful when you over and over repeat how current things are as they are and should be and has to be... but this here is a different, new thing...
 
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