HTZ Option Probability

What is the probability distribution chart?

An options probability distribution describes the likelihood of the stock price reaching a certain level at expiration. It can be used to help predict the probability of future events and to make decisions about investment strategies.

This chart displays the probability of options expiring at each strike price. The option strikes are displayed on the x-axis, and the probability of an option expiring at the price is shown on the y-axis. Options with the highest probability of expiring tend to be located in the middle of the curve, while those with the lowest probability of expiring are located at the tail ends of the curve. The percentage shown in the tooltip is the probability of the option expiring at or above that price at expiration.

How is the probability distribution chart calculated?

OptionCharts produces probability distributions for both the lognormal probability distribution and the market-implied probability distribution.

The lognormal probability distribution of an option chain is calculated by taking the natural logarithm of the prices of the options and then graphing the resulting data. In the Black-Scholes model, the prices of the underlying contract are assumed to be lognormally distributed and use a constant volatility. OptionCharts will use the average IV of the options chain for the volatility.

The implied distribution is the distribution that the marketplace believes the underlying contract will follow at expiration, using current options prices in the market. The probability associated with each underlying price is determined by computing the value of synthetic butterfly spreads at each strike, then normalizing across the chain to get the probability at each strike. OptionCharts constructs a continuous implied volatility smile from out-of-the-money calls and puts, then re-prices butterfly spreads at fine strike intervals to produce a smooth probability density. The implied probability distribution is an approximation and depends on market liquidity and accurate option prices.

Further information on how the implied distribution is calculated can be found in Ch. 24 of "Option Volatility and Pricing: Advanced Trading Strategies and Techniques, 2nd Edition."

How to use the probability distribution chart?

If a trader has a very different view of the market-implied probability, then this could be a good opportunity to make a trade. However, if the trader has the same view of the probability as the market, then generally speaking, there is no point in making a trade.

The probability shown on the tooltip when hovering is the probability of the option expiring at or above the strike price at expiration.

Hover over a strike to show the probability of the underlying price expiring above the strike. You can toggle data series on or off by selecting the data series located just below the x-axis.

Zoom in or out to get the probability between two strikes. The probabilities appear in the table below the chart.

Sources

• "Lognormal Distribution".  Investopedia.  https://www.investopedia.com/terms/l/log-normal-distribution.asp.
• "The Basics of Probability Density Function (PDF)".  Investopedia.  https://www.investopedia.com/terms/p/pdf.asp.
• Natenberg, S. (2014). Option volatility and pricing: Advanced trading strategies and techniques (2nd ed.). McGraw-Hill.