Volatility Cone

Volatility cones are a tool that may be useful in your attempt to do something about predicting the future volatility of an asset. "Historical" volatility is a backward-looking statistical parameter. You simply define a previous period of time and study the fluctuations in price of the asset under consideration. When we enter the options arena, we want to be able to compare current levels of implied volatility with recent historical volatility in an effort to assess the relative value of the option under consideration. Volatility cones are an effective tool to help us with this assessment.

A volatility cone is an analytical tool designed to help determine if the current levels of historical or implied volatilities for a given underlying or its options are likely to persist in the future. As such, volatility cones are intended to help the user assess the likely volatility that an underlying will go on to display over a certain period of future time. Those who employ volatility cones are applying the principle of "reversion to the mean." Unusually high levels of volatility are expected to return (revert) to their average (mean) levels, and low volatility readings are expected to rise to more "normal values.

The following table and chart show a real example using some close prices. The cone can then be compared with the implied volatility of real options. The example on this page is calculated in real time.

C# Code Sample // The number of days for which we wish to create the cone for int[] wNumValues = new int[9] { 10, 20, 30, 45, 60, 75, 90, 105, 120 }; // create a datatable to simplify display System.Data.DataTable oDT = new System.Data.DataTable("tblVolCone"); oDT.Columns.Add("NumDays", typeof(double)); oDT.Columns.Add("VolMax", typeof(double)); oDT.Columns.Add("VolMin", typeof(double)); oDT.Columns.Add("VolAve", typeof(double)); oDT.Columns.Add("VolLast", typeof(double)); // calculates the cone values for each period for (int i = 0; i < wNumValues.Length; i++) { List<double> wVolValues; // The volatility cone is returned as a statistical object from which we can easily get the Min, Max, Average, Median values QuantExpress.Maths.Statistics.DescriptiveStatistics oStat = QuantExpress.Finance.DerivPricing.Historical.HistoricalVolatility.VolatilityCone(m_PriceForCone, wNumValues[i], null, out wVolValues); // insert the volatility cone data into the datatable for display System.Data.DataRow oDRow = oDT.NewRow(); oDRow["NumDays"] = wNumValues[i]; oDRow["VolMax"] = oStat.Max * 100.0; oDRow["VolMin"] = oStat.Min * 100.0; oDRow["VolAve"] = oStat.Average() * 100.0; oDRow["VolLast"] = wVolValues[wVolValues.Count - 1] * 100.0; oDT.Rows.Add(oDRow); }