Hi there,
For option traders we know option probabilities for in the money (ITM) or out the money (OTM) options can be calculated for expiry dates) as they are derived from the Black Scholes model which assumes market prices follow a normal price distribution.
The idea being when you trade options and are looking at probabilities of options being either ITM or OTM at expiry. If you’re shorting options as a seller and receiving premiums for taking on the risk that prices exceed your strike price(s) you need to have a good idea of the probability of those prices being wider than the strike prices you’re trading. Unfortunately as brilliant as the the Black Scholes option pricing model is it assumes a normal price distribution to derive those expiry probabilities, which makes the kind of probability derivations — example below — unreliable because market prices don’t follow a normal distribution — mainly because although prices can fall to zero there is no bounded upper limit to how high prices can climb:
Eg//
US Crude Current Price = $66
Put Strike Price = $63
Black Scholes derived Implied Vol = 24.95% (annual)
Therefore there is a 68% chance of the price being +/- $16.46 within a year ($66 x 0.2495) because the B.S model equates implied volatility with a 1 standard deviation move over a year.
Therefore expect:
1 Std Dev – 68% probability of the oil closing between $49.54 and $82.46 a year from now
2 Std Dev – 95% probability of the oil closing between $33.08 and $98.92 a year from now
2.57 Std Dev – 99% probability of the oil closing between $23.69 and $108.30 a year from now
3 Std Dev – 99.7% probability of the oil closing between $16.62 and $115.38 a year from now
Therefore:
Strikes with a probability of 16% ITM / 84% OTM capture a 1 standard deviation range for an OTM option
Strikes with a probability of 2.5% ITM / 97.5% OTM capture a 2 standard deviation range for an OTM option
That then got me thinking about the Fisher Transform which attempts to normalise the price distribution to be able to spot those extreme prices and turning points. My question is how can we use the Fisher Transform (oscillator) which attempts to convert prices into a Normal Gaussian probability density function so that the probabilities in the example above can be more reliable? I have also found this Historical Probability Rank (link below) very useful and wanted to combine this with the Fisher Transform to get a better edge when selling (to open) options.
https://www.prorealcode.com/topic/historical-iv-calculation/
Cheers for any thoughts or insights,
Best
Bard
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