Estimating Historical Volatility from a Few Closing Prices
Summary
The document asks how to calculate volatility from three closing prices: 101, 100, and 102. The response treats the changes between consecutive closes as returns and says their standard deviation can serve as a proxy for historical volatility. With three prices, however, there are only two returns, leaving an extremely small sample.
The response emphasizes that this estimate cannot support a confident statistical conclusion about the underlying volatility. In particular, two observations are insufficient to reject the possibility of zero volatility. No calculation convention is specified, such as whether to use simple or logarithmic returns, and no annualization method is given. The example therefore introduces the basic idea of measuring return dispersion while highlighting that a numerical estimate from so few prices is highly limited.
Key ideas
- Three closing prices produce only two consecutive returns.
- The standard deviation of those returns can be used as a rough historical volatility proxy.
- Two observations provide too little evidence for a reliable conclusion about volatility.
- The response does not specify return conventions or how to annualize the estimate.
Tags
Full text
# Calculating Volatility Parameter using Closing Prices # Calculating Volatility Parameter using Closing Prices Say you have 3 closing prices... 101 100 102 How would one calculate the standard volatility parameter using these values? I am quite confused, it seems simple enough though. ## Answer by phdstudent (score 1) https://quant.stackexchange.com/a/22203 With 3 closing prices you have 2 returns. You can compute standard deviation of those two returns as a proxy of historical volatility. However, with that number of observations there is nothing you can conclude as for sure the you will not be able to reject the null of 0 volatility.
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