Help please, with two " Standard Deviation " questions ......

Good Evening,
I was reading up on Probabilities and Standard Deviation, Volatility, Implied Volatility, IV Rank , etc. for Options trading, and 2 statements that I came across, still have me a bit confused..... mainly on what is meant by them and how to calculate them out .

The first one is .....

1. 1 SD = a strike with a 15 Delta

So I am guessing that this is referring to , that on average ..... Options of whose Strike Prices have Deltas of .15 , that it's safe to assume that at these Strike Prices , they are at the " 1 Standard Deviation " Level ?

2. Selling a Call or a Put with an OTM probability of 85% means that .... 85% is " 1 Standard Deviation " OTM

This is similar to the first question , in that at 85% , and using the ,15 Delta in the first question ..... that 85 + 15 = 100%

So I guess that it all boils down to me being confused at to how we come to the number of 85% ( and thus the .15 Delta ) ?

I know and understand the premise of 1 SD , in that a stocks price will stay within that 1 SD range " 68% ) of the time , and then will only go with the outer bounds via the 2 SD range only 5% of the time, and so on for the 3 SD range at the only 1% of the time


Any help and breakdown as to how we come to 85% ad .15 Delta would be much appreciated

Thanks so much - Michael

 

1 SD deviation is 68% of observed values around the mean. So that is +/- 34% around the mean.

If ATM (also the mean) is a .50 delta and you accept delta as an approximation of probability, then:

(50+34)=84 is your lower bound call delta
(50-34)=16 is your upper bound call delta

2 SD deviation is 95%....

 

Open a spreadsheet and type in this formula:

=normsdist(1)
which returns .8413, meaning 84% percent of the area under the "bell curve" lies to the left of 1 std. Sell a call option 1 std OTM, and you have an 84% chance of winning at expiration.

=normsdist(-1) returns 0.15685, meaning 16% of the area under the curve lies to the left of -1 std. Sell a put 1 std OTM and you have an 84% chance of winning at expiration.

What happens in the time before expiration? Probability of touch is roughly twice the probability of finishing ITM, or 30% in the example.

 

Also, before you run out and short 100 1SD put contracts per tastytrade doctine, know that you're compensated accordingly the closer you are to the money and net premium requires way less short contracts.

 

This is true in dollar premium terms, but that can be misleading. If the vol surface is convex (as it should be with stoch vol/discrete hedging/jumps under threat of arbitrage), the near-the-money options will likely trade around a local minimum in IV terms. So while you're bringing in more raw dollars due to the bigger premiums, your expected profit could actually be smaller. If the near-the-money, liquid options represent a decent vol forecast, it could be reasonably argued that they are likely fairly priced. If I juxtapose 2 different trades, (1) being I sell an ATM straddle (10%) and (2) I sell OTM puts (20%), I'll bring in far more dollars of premium off the straddle, and maybe only nickels and dimes on my puts, but my expected P&L for the "cheap" puts is actually higher than that of the straddle (for which I expect to earn $0). The premium in dollar terms may be appealing, but it's priced like that for a reason. The near-the-money is local. It's in play. The market is making a vol forecast and expects that on average all of that fat time value will ultimately turn to intrinsic and you'll make nothing.

Within the +/- 3 sigma world of the normal distribution, price in IV terms not $ premium. Outside of that, valuation is virtually meaningless. They're binary event tail options. 5,6,7+ sigmas hits....you either owned them or didn't (should probably own them).

 

LTW: IMO, the difference however is risk. In the OTM case you're exposed to hideous risks as opposed to the NTM/ATM case which is always going to have decreasing gamma.

At the end of the day one has to have a directional or volatility take on what it is they're trading. Probability alone is a great way to get killed.

 

Fair enough. I definitely agree on taking a view on vol / probability theory alone.

 

Thanks to everyone for all of the input and replies

I think the Light Bulb has finally gone off and clicked on my forementioned question

I have attached a screenshot of the Options page on BIDU ( with boxes drawn around the 16% and 84% OTM strikes, as well as the corresponding Deltas with each ..... .16 and .84 )

Thanks again