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What is the difference between the two types of volatility (historical and implied) when it comes to pricing options?

Curtis Davis


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Historical Volatility calculations are based off historical price data; it involves looking backwards. Taking a series of data points, for example the last 20business days closing price for an equity, it is possible to gauge the extent to which price fluctuates. HV involves taking the difference between each daily price and measuring it against the average price for the entire time period. Using principles of Variance and Standard Deviation it is possible to calculate the HV over that time period. The greater the range of prices during this time (in relation to the average price) then the greater the Historical Volatility. Taking the example of two equities, the one that experiences price moves further from the average will be the more ‘volatile’ stock. Historical Volatility can be calculated over varying time periods, but popular ranges are 10, 20 and 30 days. It’s also important to appreciate how HV can change over time because the time period studied is similar to a sliding window. Measuring the 20 day HV of a stock today will involve a different set of 20 days to a calculation processed last week.

Implied Volatility

Implied Volatility focuses on future, or at least current, events more than HV does;however, unlike HV it is not a stand-alone tool that can be used to generate ‘a number’. Instead IV is extracted from the already known market price of an option and is calculated using an option pricing model such as the Black-Scholes Model and the Binomial Model. Take for example an option with an equity underlier where market participants consider there a high risk that the equity price might change dramatically. This could be stock specific or due to a market wide catalyst coming into play. The risk of that event would be ‘priced into’ the options. Premiums would increase because the buyers and sellers of options would factor in the increased chance of the underlier reaching the respective exercise prices.

Comparisons and uses

It’s hard to argue against the statistical integrity of the HV approach but the method’s strength is also its weakness. Historical Volatility calculations are based on past data, so it is easy to question to what extent previous events might bring about a better understanding of what will happen in the future. Implied Volatility is a product of the option price rather than a determinant of it. This does not restrict you from trading based on your analysis and whether, or not, you think volatility of a particular option is being mispriced by others in the market. Calculating IV, however, is based off already knowing the price of the option, not vice versa. Comparing the effectiveness of IV and HV to price options can throw up trading ideas based on pricing anomalies; particularly if a difference between HV and IV can’t be readily explained. It might be equally useful to consider what the two measures show when working in conjunction: whether a particular underlier is considered more or less volatile than its peers or the market in general. Again, something that is studied and possibly traded should you think some kind of mispricing is occurring.
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