Question

Stock price today at $100. A binary PUT with strike of 85 is priced at $0.15. What is the implied standard deviation?

Answer 1

your ans is One standerd devation...

explanation:

options trading, it’s important to understand the probabilities associated with certain multiples of standard deviations:
1 standard deviation encompasses approximately 68.2% of outcomes in a distribution of occurrences
2 standard deviations encompasses approximately 95.4% of outcomes in a distribution of occurrences
3 standard deviations encompasses approximately 99.7% of outcomes in a distribution of occurrences

The standard deviation of a particular stock can be quantified by examining the implied volatility of the stock’s options. The implied volatility of a stock is synonymous with a one standard deviation range in that stock.

For example, if a $100 stock is trading with a 20% implied volatility, the standard deviation ranges are:
Between $80 and $120 for 1 standard deviation
Between $60 and $140 for 2 standard deviations
Between $40 and $160 for 3 standard deviations

From this, we can conclude that market participants are pricing in a:
68% probability of the stock closing between $80 and $120 a year from now
95% probability of the stock closing between $60 and $140 a year from now
99.7% probability of the stock closing between $40 and $160 a year from now

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

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