Calculating Historical Volatility

by admin on 19/07/09 at 11:38 am

Zymogenetics, Inc. (ZGEN), September 2006 Calls – Trade Strategy

The following steps were taken to evaluate and eecute the trade:

  • Calculate the actual historical volatility of Zymogenetics common stock
  • Calculate the implied volatility of currently traded options
  • Compare actual versus implied volatility
  • Execute the option trade
  • Set a protective conditional “buy” order for the underlying stock

When the options expired ten days later, the author was able to calculate his return expressed as an annualised “internal rate of return” (IRR). He has kindly made available the spreadsheet template he used.

Calculating historical volatility

The goal is to calculate historical volatility in a robust way. Sometimes volatility over the past month differs from volatility over a longer period – six months or a year – so the best approach is to calculate the volatility over several time periods. Also, sometimes stocks swing widely on a day-to-day basis, but on a week-to-week basis they are not quite as wild. This is called “mean reversion” – the prices gravitate towards a midpoint. Mean reversion skews the “volatility” input of the Black-Scholes formula. In order to adjust for this, a good idea is to measure volatility using both daily and weekly price data for comparison.
The spreadsheet template allows you to copy and paste historical price data downloaded directly from Yahoo!’s finance pages. The cells that do the actual calculation are programmed into the template, so every time you copy and paste new data from Yahoo, the calculations are automatically updated.

The next step is to go to Yahoo and download daily historical price data for ZGEN in .csv format. Copy and paste the data directly into the correct range in the spreadsheet template. Repeat the process with weekly price data.

In the example, the author found actual historical volatility to be in a normal range. Depending on the time period measured and the price data interval, the volatility ranged from 42% to 49%. This was a tolerable amount of latitude within the range. Since he was looking at a short-term (ten day) trade, he determined the most relevant measure for the analysis would be daily price data over a recent period – one to three months. Volatility ranged from 44% – 48% during this period. He used the average of 46% for his calculation.