Volatility is one the most important inputs used in options pricing and so it is often a consideration as to where to obtain the estimate of volatility from. It is very important to be careful in the inputs used with any of the methods, and this especially applies to volatility.

While the historical volatility function is available in our options software, it is very important to understand the assumptions behind the model and the limitations of the models. In one sense, they are trying to provide a good and reliable estimate of what a particular option is doing and its value, but presumably market makers and the market itself, are able to decide themselves just what to value an option at, and so they may use different inputs, assumptions and models to do this.

Hence there can be differences in the prices you see from a model you choose, with particular inputs and what you see in the market. So the results of a given model may or may not be close to what you find in the market place. It is not at all guaranteed that using a historical volatility value over a given time period will accurately give the prices/greeks for a given option over time. This is the warning notice we have in the help file regarding this issue and the use of the Historical Volatility function:

"The user is strongly cautioned to take considerable care before deciding whether to use this function. The values obtained from this function, will be subject to the usual problems encountered in statistics, such as outliers, choice of data sample, number of data points and so on. This means, that the values obtained could vary significantly from what may be considered either useful, or a reasonable estimate of what the implied volatility of a given security is. Hence, the user should only use this function if they have a thorough understanding of the limitations and practical value of the results obtained."

Using an historical volatility over any period of time and then inputting it to a function will result in the theoretical price/greeks for the particular model used. So you are obtaining only a model output, which may or may not match up with the markets current values. If it doesn't match up with the market, then it is an issue with deciding whether the model or the input data are appropriate for what you are working with.

It seems to be reasonably well recognized that using measured historical volatility, particularly over just one time period, as input to a pricing modelis not always used, as it can be very risky. As far as I am aware, the volatility that is normally used in price/greek models is over a longer time scale than just one day. I think there is not necessarily a standardized time to use for historical volatility. I think you would need to study this in depth yourself. There are a few chapters on this topic in "Options as a Strategic Investment", Lawrence G. McMillan, for example, see pp. 728-731. Also see "Options, Futures and Other Derivatives", John C. Hull, 5th Ed, pp. 239. where he gives some thoughts on estimating volatility from historical data. Hull suggests 90-180 days, or otherwise to use the period of time over which the option is to expire.

We highly recommend that you need to understand fully the assumptions and limitations of the models, and recognize that the differences between model outputs and what is observed in the market is to be expected, and it can be due to multiple factors - inadequacies of the models, invalid or inaccurate input data, and so on.

In summary, and in regard to using Historical Volatility:

1. You should be extremely cautious in using Historical Volatility in your calculations, since:
   
   a) Past behaviour does not indicate future behavior
   
   b) The algorithms may or may not correspond to what the actual market behavior is, both in terms of HV and in terms of pricing using the input HV.
   
   c) Practitioners in my opinion, seem to not use HV and if they do, it can be with multiple HV values over different time periods. See the remarks in the books "Options as a Strategic Investment" by Lawrence McMillan and also Hull, for more details.
   
2. There are some examples showing how to input data and obtain HV values in Visual Basic in the demos supplied. The method syntax is also defined in the Help file.

The information given here is subject to our usual terms and conditions, and is presented as a matter of opinion only and should not be relied upon to make trading decisions. We encourage you to read more on this subject.