I have a question and I literally don't know where to begin. I am provided with a table of stock prices of Microsoft from August 13 to November 1, 2001.  It includes the following headings:  Date, Open, High, Low, Close, and Volume.  I am supposed to estimate the volatility parameter, sigma, using the "standard estimator of volatility".  I have that the formula is sigma=S times the square root of 252.  I also have the formula for S.  As I said, I don't know where to start or what I need to do to solve the problem.  Thanks!

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Asked Jun 24, 2019
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I have a question and I literally don't know where to begin. 

I am provided with a table of stock prices of Microsoft from August 13 to November 1, 2001.  It includes the following headings:  Date, Open, High, Low, Close, and Volume.  

I am supposed to estimate the volatility parameter, sigma, using the "standard estimator of volatility".  I have that the formula is sigma=S times the square root of 252.  I also have the formula for S.  As I said, I don't know where to start or what I need to do to solve the problem.  Thanks!

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Expert Answer

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Step 1

Let me explain to you, what you have been asked to do. But before that let me explain what information you have in your hand:

  • You have the historical data on the daily stock price of Microsoft from August 13 to November 1, 2001. The stock prices are available for the trading days.
  • Please consider the "Close" Price. This is the price at which the stock closed at, on that rading day.

What you have been aseked to do?

  • You have been asked to calculate the volatility in the returns of the Microsoft stock. 
Step 2

How will we achieve what you have been asked to do?

  • Based on the daily close price, we will first calculate the daily return on the stock.
  • Mathematically, daily return can be calculated as = Pn / Pn-1 - 1 where Pn = Close price on nth day and Pn-1 = Close Price on the day before i.e. on (n - 1)th day
  • Once you have the daily returns, you now need to estimate the volatility in daily returns. This parameter is what you are calling S in your question. You have mentioned that you have the formul...

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