This video illustrates how to calculate the historical volatility (moving average volatility), using the example of historical returns. Historical daily volatility is the square root of the daily variance estimate. 

<iframe width="600" height="450" src="http://www.youtube.com/embed/v17M0glWCHA" frameborder="0" allowfullscreen></iframe>

This video is developed by David from Bionic Turtle.

How to Calculate Historical Volatility

There are lots of ways to estimate volatility. This video provides you an overview of the different approaches. It talks about implied volatility (forward looking) and deterministic (constant) and focus on stochastic volatility: volatility that changes over time, either via (conditional) recent volatility and/or random shocks.

<iframe width="600" height="450" src="http://www.youtube.com/embed/mTmfsOwy5_I" frameborder="0" allowfullscreen></iframe>

This video is developed by David from Bionic Turtle.

Approaches to Estimating Volatility

In this video, you will learn how to estimate implied volatility. Using the market price for an option on Google's stock, the video demonstrates how to use Excel's GOAL SEEK function to estimate implied volatility. Implied volatility is a reverse-engineering exercise: we find the volatility that produces a Model Value = Market Price.

<iframe width="600" height="450" src="http://www.youtube.com/embed/TevtNOSqFsM" frameborder="0" allowfullscreen></iframe>

<em>This video is developed by David from Bionic Turtle.</em>

Using Excel's Goal Seek Function to Estimate Implied Volatility

Within stochastic volatility, moving average is the simplest approach. It simply calculates volatility as the unweighted standard deviation of a window of X trading days. This video demonstrates three "flavors:" population variance (volatility = SQRT[variance]), sample, and simple.

<iframe width="600" height="450" src="http://www.youtube.com/embed/8D9jEFSI1w8" frameborder="0" allowfullscreen></iframe>

<em>This video is developed by David from Bionic Turtle.</em>


Volatility: Moving Average Approaches

The EWMA approach to volatility is an improvement over simple volatility because it assigns greater weight to more recent observations (in fact, the weights are proportional).

This video explains the EWMA approach.

<iframe width="600" height="450" src="http://www.youtube.com/embed/P_tr9_Ue220" frameborder="0" allowfullscreen></iframe>

This video is developed by David from Bionic Turtle.

Volatility: Exponentially Weighted Moving Average (EWMA)

This video provides an introduction to the GARCH approach to <a href="https://financetrain.com/approached-to-estimating-volatility/" title="Approached to Estimating Volatility">estimating volatility</a>, i.e., Generalized AutoRegressive Conditional Heteroskedasticity.

GARCH is a preferred method for finance professionals as it provides a more real-life estimate while predicting parameters such as volatility, prices and returns.

GARCH(1,1) estimates volatility in a similar way to <a href="https://financetrain.com/volatility-exponentially-weighted-moving-average-ewma/" title="Volatility: Exponentially Weighted Moving Average (EWMA)">EWMA</a> (i.e., by conditioning on new information) except that it adds a term for mean reversion. It says the series is "sticky" or somewhat persistent to a long-run average.

<iframe width="600" height="450" src="http://www.youtube.com/embed/o-Kf6Y419hU" frameborder="0" allowfullscreen></iframe>

<em>This video is developed by David from Bionic Turtle.</em>

Using GARCH (1,1) Approach to Estimate Volatility

This video discusses how to use <a href="https://financetrain.com/using-garch-approach-to-estimate-volatility/" title="Using GARCH (1,1) Approach to Estimate Volatility">GARCH(1,1)</a> to forecast future volatility. The key parameter is persistence (alpha + beta): high persistence implies slow decay toward the long run average.

GARCH models were developed by Robert Engle to deal with the problem of auto-correlated residuals (which occurs when you have volatility clustering for example) in time-series regression. One reason why the ARCH family of models is popular is that you only need price data to generate the model. ARCH is great for looking at volatility over very long periods. 

<iframe width="600" height="450" src="http://www.youtube.com/embed/KJbR0nRinD4" frameborder="0" allowfullscreen></iframe>

<em>This video is developed by David from Bionic Turtle.</em>

How to Forecast Volatility Using GARCH (1,1)

Volatility is the most commonly used measure of risk. Volatility in this sense can either be historical volatility (one observed from past data), or it could implied volatility (observed from market prices of financial instruments.)

The historical volatility can be calculated in three ways, namely:
<ol>
	<li>Simple volatility,</li>
	<li>Exponentially Weighted Moving Average (EWMA)</li>
	<li><a href="https://financetrain.com/using-garch-approach-to-estimate-volatility/">GARCH</a></li>
</ol>
One of the major advantages of EWMA is that it gives more weight to the recent returns while calculating the returns.  In this article, we will look at how volatility is calculated using EWMA. So, let’s get started:

<strong>Step 1: Calculate log returns of the price series</strong>

If we are looking at the stock prices, we can calculate the daily lognormal returns, using the formula ln(P<sub>i</sub>/P<sub>i</sub>-1), where P represents each day’s closing stock price. We need to use the natural log because we want the returns to be continuously compounded.  We will now have daily returns for the entire price series.

<strong>Step 2: Square the returns</strong>

The next step is the take the square of long returns. This is actually the calculation of simple variance or volatility represented by the following formula:

<img class="aligncenter size-full wp-image-9654" alt="ewma-eq1" src="https://financetrain.com/wp-content/uploads/ewma-eq1.gif" width="238" height="117" />

Here, <i>u</i> represents the returns, and <i>m</i> represents the number of days.

<strong>Step 3: Assign weights</strong>

Assign weights such that recent returns have higher weight and older returns have lesser weight. For this we need a factor called Lambda (λ), which is a smoothing constant or the persistent parameter. The weights are assigned as (1- λ)λ<sup>0</sup>. Lambda must be less than 1. Risk metric uses lambda = 94%. The first weight will be (1-0.94) = 6%, the second weight will be 6%*0.94 = 5.64% and so on. In EWMA all the weights sum to 1, however they are declining with a constant ratio of λ.

<strong>Step 4: Multiply Returns-squared with the weights</strong>

<strong>Step 5: Take the summation of R<sup>2</sup>*w</strong>

This is the final EWMA variance. The volatility will be the square root of variance.

The following screenshot shows the calculations.

<img class="aligncenter size-full wp-image-9655" alt="ewma-excel" src="https://financetrain.com/wp-content/uploads/ewma-excel.gif" width="572" height="504" />

The above example that we saw is the approach described by RiskMetrics. The generalized form of EWMA can be represented as the following recursive formula:

<img class="aligncenter size-full wp-image-9656" alt="ewma-eq2" src="https://financetrain.com/wp-content/uploads/ewma-eq2.gif" width="486" height="54" />

Calculate Historical Volatility Using EWMA

Volatility

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Volatility

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