Sorry, my Q&D formula had some minor errors, fixed in the following posting, but the overall result stays the same: https://www.elitetrader.com/et/threads/the-fairput-initiative.349291/page-5#post-5189690
Updated / fixed version: Here's the proof that BSM is wrong: BSM(S=100, K=100, t=1, s=0.001%, r=25%, q=0%): CALL=22.1199, PUT=0 This means: say we have a company where the volatility is nearly 0% (ie. 0.001%) and it earns 25% p.a. So, after the year the expected stock price will be (at least): 100 * exp(0 * 0.00001 * 1 + (0.25 - 0) * 1) = 128.4025 Ie. applying the formula: S * exp(z * s * sqrt(t) + (r - q) * t) by using z=0 for getting the expected spot, ie. the mean spot at expiration. So, the CALL will have made 128.4025 - 100 - 22.1199 = 6.2826 This is IMO an arbitrage in the BSM pricing model, because the CALL premium should rather be 28.4025 instead of the 22.1199. Setting r higher gives even more arbitrage! Q.E.D. PS: this works the same also with normal, higher volatilities. I chose volatility s=0.001% intentionally to simplify the calculations. PS2: for those having difficulties understanding the "r as earnings": just think of it as the more commonly used term "risk-free rate"... PS3: this result shows that whenever r is different from 0, then there is inherently arbitrage in the BSM model! And: IMO, even for r=0 the BSM is wrong! .
I think OP should write a thriller: The Fairput Initiative "Johnny Fairput always thought that the BSM model of option pricing was wrong. On a fateful day of researching the subject, he discovers a conspiracy, hidden deep inside the original code of price discovery. Who wrote the code? What is it good for? Can the international markets collapse if the truth come out?" Order it now, get it by Thanksgiving (if the markets still exist). Only $19.99!!!
I’m Laughing because you found the criminal conspiracy. it’s a lot of work to disprove you. It’s not really worth it as you aren’t really looking to learn. You are looking to prove you are smarter than everyone else.
I'm doing just my research, nothing more, nothing less. Maths is king! If you now got an inferiority complex or so then it's surely not my fault, man... And I hereby publicly and officially invite you and everybody from all around the world, including the highest and brightest academics of our time, to disprove my above proof. Come on folks, prove me wrong! If you can
I hereby publicly admit: I don't have the Hull book!... But I'm sure I don't need it since maths is maths and logic is logic. Update: I think I found the said 3 chapters very officially here at wiley, the publisher: https://onlinelibrary.wiley.com/doi/full/10.1111/j.1540-6261.1987.tb02568.x So, @newwurldmn, just show where therein the answer is supposed to be I would say, everybody in the academics and the industry is so to say "self delusioned" or "self deceiving" or so.. (I'm not a native English speaker, so maybe I made the wrong choice of words here, but it should be clear what I mean).