Instruments with lognormal price distributions such as equities have skewed and asymmetric standard deviations. A one standard deviation move higher will have a higher payout than a one standard deviation move lower when the price distribution is positively skewed in assets such as stocks. The payout will NOT be equal on a 1 SD move with a lognormal price distribution assumption. The mean of a stock's potential price range is to the right (upside) of the ATM strike. That mean moves higher in price terms as volatility increases. Therefore a 1 standard deviation higher move from the mean will naturally be further away from the current ATM/spot price than a 1 standard deviation move lower. You are trying disprove some basic statistical theory. Lognormal vs Normal distribution: Look where the mean is for a lognormal dist vs a normal dist. The 1 standard deviation (variance from the mean) is going to be much further to the right (higher stock price) than it is to the left (lower stock price).
@VolSkewTrader, this all is of no help. Just imagine this simple basic coin toss game applied to options or stocks: I bet it will go up 1SD, you bet it will go down -1SD. Now, shouldn't the payouts for these two events not be the same if the price of the game is same for both? Who is that silly to pay the same for both choices if the payouts are not the same? Do you understand the basic problem?
Your "fair" 100 put is only 20 ITM. It's impossible for it to be worth 25 (5 extra) at expiration with spot at 80.
Because this is nor a PUT but a FairPUT. For FairPUT spot 80 corresponds to +0.743812 SD at the other side from the strike, meaning a spot of 125. Yes, it takes some time to grasp this simple stuff... Have you still not understood the fact that FairPUT is simply the mirror image of CALL? Take yourself a look into your recently posted lognormal distribution graph, the right side of the mean can go to infinity, so has the left side to be mapped accordingly, but only down to 0. Code: Here's the result for the upper side corresponding to spot 80, ie. for spot 125: CALL : Payout=25.000000 Profit=13.076462(109.67%) PUT : Payout=0.000000 Profit=-11.923538(-100.00%) FairPUT: Payout=0.000000 Profit=-11.923538(-100.00%)
I just trademarked “SuperOption”. It’s a new option type that pays both ways, whether the stock is up OR down.This way you don’t need to pay for 2 separate options, call and a put. It’s revolutionary and much better than a CALL, PUT or FairPUT because no one understands then anyway, while learning about 3 different option types is silly. Now, finally, the world will have only a single option to trade and learn about. I’m currently offering it for licensing at $0.01 per trade. Who’s in?
You are confusing stock price return with stock price distribution. The coin toss or daily price returns on a stock are normally distributed, equally weighted, and have same standard deviation moves. But a stock's actual price, or its potential range of prices (as determined by volatility) are lognormally distributed, positively skewed, NOT equally weighted to the downside vs upside, and defintely NOT the same standard deviation price move from the mean. Read what I wrote over and over again, and you'll finally understand.
@VolSkewTrader, it is just you who doesn't want to understand the set goal to give both CALL and FairPUT the same payout. As said: FairPUT has always the same params of the CALL and always costs the same, then the payout has to be the same. This was the set goal of this all.
Btw, nobody is forcing you to use this new FairPUT over the normal PUT. ...not yet, but who knows in a year...
Think of it this way. At higher volatility levels and/or lots of time left to expiration, a stock with a price of $100 is equally as likely to rally to $200 (double) as it is to drop down to $50 (cut in half). Or a $1 stock is just as likely (same probability) to drop to zero ($0) as it is to rally to $10 at very high volatility levels. Notice the standard deviations (probability) are the same but the price moves and payouts are asymmetric, radically different in notional terms.