Historical Volatility Calculation

VolatilityCalc uses the logarithmic method to calculate stock volatility. This method, also referred to as the log-normal or log return method, is a common approach used in finance to measure the variability (i.e. risk) associated with stock price movement over time.

Volatility and Option Pricing

Volatility is a key parameter in pricing options and other derivatives. Higher volatility increases the premium of options due to the greater risk of price movement (and thus more value in protection). Traders and quantitative analysts use volatility charts to identify opportunities and strategies in the options market

Moving Average

Calculates the volatility over a fixed time horizon as of a given date. For the current version of VolatilityCalc, that horizon is equal to the preceding six (6) months.

Moving average charts seek to tone down periodic fluctuations into a smooth trend to provide a clearer picture of historical volatility. They are especially useful in helping to identify periods of time with particularly heightened volatility.

Regulatory guidance in ASC 718 Section 718-10-55-37 allows companies to “disregard an identifiable period of time in which its share price was extraordinarily volatile.”

Regulatory Guidance

ASC 718 Section 718-10-55-37

Factors to consider in estimating expected volatility include:

a.) Volatility of the share price, including changes in that volatility and possible mean reversion of that volatility, over the most recent period that is generally commensurate with (1) the contractual term of the option if a lattice model is being used to estimate fair value or (2) the expected term of the option if a closed-form model is being used.

For example, in computing historical volatility, an entity might disregard an identifiable period of time in which its share price was extraordinarily volatile because of a failed takeover bid or a restructuring if a similar event is not expected to recur during the expected or contractual term. If an entity’s share price was extremely volatile for an identifiable period of time, for instance, due to a general market decline, that entity might place less weight on its volatility during that period of time because of possible mean reversion.

Return Rate Frequency Distribution

This chart plots the frequency distribution of the stock’s periodic logarithmic returns. The horizontal axis is the return rate, and the vertical axis is the frequency at which each return rate occurs over the selected data range.

Normal vs. Actual

The Normal series is the theoretical normal (Gaussian) distribution implied by the mean and standard deviation of the returns. The Actual series is the observed distribution of historical returns. Comparing the two reveals how closely the returns follow a normal distribution, with differences in the peak and tails relating directly to the skewness and kurtosis reported in the Advanced Metrics

A return series that is approximately normal underlies many option pricing and risk models, so the degree to which the Actual curve departs from the Normal curve is a useful diagnostic when estimating expected volatility.

Periodic Returns Over Time

The Market Voice chart plots the periodic logarithmic return of the stock against time. For each date on the horizontal axis, the corresponding point on the chart is the calculate return from the previous date.

Reading the Chart

The chart gives an immediate sense of how the market “spoke” over the selected period—the amplitude of the line reflects the size of price moves, while clusters of large positive and negative returns highlight periods of elevated volatility. Returns are shown as a percentage on the vertical axis.

Volatility by Number of Data Points

The Volatility Horizon chart shows how changing (increasing) the number of price observations in the given date range changes the calculated volatility. The horizontal axis is the number of price observations, and the vertical axis is the resulting volatility, expressed as a percentage.

Choosing a Time Horizon

Volatility estimates are sensitive to the length of the historical time horizon. Plotting volatility against the size of the data set helps reveal where the estimate stabilizes and where it is still being driven by a short, possibly unrepresentative, sample. This is a useful context when selecting an appropriate horizon for an expected-volatility assumption.

Start Date

Volatility is calculated using a specific data range; the start date is the first historical stock price from which the volatility will be computed. Select a start date using the calendar control or typing in a date using the mm/dd/yyyy format.

End Date

The end date is the last historical stock price from which the volatility will be computed. Select a start date using the calendar control or typing in a date using the mm/dd/yyyy format.

Data Frequency

For monthly, weekly, and daily data, the assumption is that for any two consecutive stock prices, the corresponding time interval is constant. The monthly assumption is 12 data points per year, the weekly assumption is 52.14 data points per year, and the daily assumption is 252 data points (trading days) per year.

Autocorrelation

The expected value of the product of a random variable (here, returns) with a time-shifted version of itself. It gives a measure of the randomness of data.

Kurtosis

The degree of “peakedness” of a distribution, defined as a normalized form of the fourth central moment. It indicates the extent to which a distribution has “fat tails”, and it is an important parameter to determine if the data is normally distributed.

Lomb Periodogram

Detects periodicity in unevenly spaced data.

Skewness

The degree of asymmetry of a distribution. If the distribution is skewed to the left, then the skewness is negative; if it is skewed to the right - the skewness is positive. If the distribution is symmetrical, then the skewness is zero. It is an another important parameter to determine if the data is normally distributed.

Volatility

The measure of the amount by which a price has fluctuated (historical volatility) or is expected to fluctuate (expected volatility) during a period. The volatility of a stock is the standard deviation of the continuously compounded rates of return on the stock over a specified period. The higher the volatility, the more the returns on the stock can be expected to vary—up or down. Volatility is typically expressed in annualized terms that are comparable regardless of the time period used in the calculation, for example daily, weekly, or monthly price observations.