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HISTORICAL & IMPLIED VOLATILITY

By ProbabilityofProfit.com

Assessing the valuation of an option in large part is due to the expected volatility—the measurement of how much the stock price is expected to fluctuate over the expected life of the option.
These measurements include implied volatility and historical volatility for when looking at publicly traded companies and  peer company volatility and industry indices volatility when analyzing private companies. In this guide we will be analyzing the differences between implied and historical volatility, how they are calculated, and how the valuation factor of volatility can impact the value of an option.

KEY VOLATILITY MEASUREMENTS

HISTORICAL VOLATILITY VS IMPLIED VOLATILITY

Historical Volatility (HV) is the change in standard deviation of an assets underlying price over a specific period of time. 
  • Measurement of past variability of a stock or stock(s).
    • A general time period range or look-back period used in analyzing historical volatility is the 52 week range. 
    • Emphasis on ‘historical’ as this measurement pertains to past volatility. 
  • Can be used in comparison with the underlying assets current price to gauge future prices. 
  • Can be used in option pricing models such as the Black-Scholes model to calculate the fair value of an option.

 

Implied Volatility (IV) is the anticipated level of volatility for a stock, derived from the pricing of the stock's options. 
  • Measurement of future variability of a stock or stocks(s).
    • Based on the price of an option.
    • Looks at the price of stock’s options to gauge the expected volatility of the stock. 
  • Can be compared from what the implied volatility was in the past to measure if a stock is more volatile or not.
  • Can also be used in option pricing models to calculate the fair value of an option but is difficult to calculate since it is calculated using the price of other options.

ALTERNATIVE VOLATILITY MEASUREMENTS

Peer Company Volatility is a collection of companies that are usually of a similar industry that are used as a benchmark to estimate volatility. 
  • Measurement of past variability to measure current, present, or past variability.
    • Generally used to estimate volatility for private companies. 
    • Companies within the peer group are usually selected following these requirements: 
    1. Publicly traded
    2. Similar industry and/or business model
    3. Minimum to 2 to 3 companies chosen 
  • Works similar in the context of historical volatility as the variability of the stock price of the peer group companies are used to compare with that of the private company being analyzed. 
  • Cannot be used in option pricing models to calculate the fair value of an option since private companies don’t have publicly traded options on stock exchanges.
    • Private companies may still issue stock options to employees or investors. 

 

Industry Indices Volatility is specific industry-specific index or indices used to gauge volatility within particular sectors. 
  • Measurement of past variability of an index of a collection of industry stock or stocks(s). 
    • Typically used to estimate volatility for private or public companies.
    • Companies within indices used are usually chosen considering these requirements:
    1. Sector or industry specific
    2. Specific liquidity requirements
    3. Availability of options data (if options data is being used to measure volatility)
  • Functions similarly to other methods to measure volatility except for the fact that it uses an index to compare volatility to the stock being observed. 
  • Volatility of those indices can be used in option pricing models to calculate the fair value of an option for only publicly traded companies. 
    • Common indices used to measure volatility in different contexts: 
    1. CBOE Volatility Index (VIX) - measures options volatility of the overall stock market.
    2. CBOE NASDAQ Volatility 100 Index (VXN) - measures options volatility of short-term options.
    3. CBOE DJIA Volatility Index (VXD) - measures options volatility of the Dow Jones Industrial Average index.

HISTORICAL VOLATILITY CALCULATION

HOW TO CALCULATE HISTORICAL VOLATILITY

Historical Volatility Calculation is calculated using historical stock price data to find the standard deviation of the logarithmic returns over a specified period of time.
  • While there are other methods to calculate historical volatility, the method described above is considered as one of the most common universal ways to calculate it. For the purposes of this guide, we will be discussing the standard method to calculate historical volatility. 
    • Standard Deviation Method uses the standard deviation of logarithmic returns to quantify historical volatility. By analyzing the variance in historical stock price data, this method provides a measure of how much the price of an asset has fluctuated over a specific period.

 

Calculation Steps: 
  • Step 1: Collect historical price data data to be used in your analysis. 
  • Step 2: Calculate the logarithmic returns for each data point in your dataset. 
    • Pt is the price at time t 
    • Pt-1 is the price at the previous time period
  • Step 3: Calculate the mean of the logarithmic returns. 
  • Step 4: Calculate the squared deviations of each logarithmic return from the mean. 
  • Step 5: Sum the squared deviations and divide by the number of observations to get the variance. 
  • Step 6:  Take the square root of the variance to get the standard deviation, which represents historical volatility.
  • Step 7: If necessary, annualize the historical volatility by multiplying it by the square root of the number of trading periods in a year (usually 252).

IMPLIED VOLATILITY CALCULATION

HOW TO CALCULATE IMPLIED VOLATILITY

Implied Volatility Calculation can be calculated using prices of other options that have recently been traded and back-solving a Black-Scholes equation, through methods of reiteration, or through complex inverse functions.
  • In this guide, we will discuss the applications of the reiteration method since it is the most practical and least convoluted option to follow. 
    • Reiteration Method follows a principle of trial and error that uses the Black-Scholes formula to calculate the price of the option while incrementally adjusting the implied volatility in the formula until  the calculated option price resembles the observed market price.

 

Calculation Steps: 
  • Step 1: Using the black-scholes formula, calculate the price for either a put or call and use any number for your implied volatility. This will represent the starting point for your iterative process.
  • Step 2: Depending on what price you get from using this implied volatility percentage, iterate through the implied volatility percentages and repeat this process, incrementally increasing or decreasing your implied volatility until the price that equates to the observable market price. 

 

  • Alternative methods to finding the designated volatility may require computation using computational programs and calculators.

IMPLICATIONS

VALUATION

Increase in Historical and Implied Volatility: 
  • An increase in historical volatility can lead to higher option premiums because options become more valuable when there is a greater chance of price swings. 
  • An increase in implied volatility can lead to higher option premiums because of the rise in the uncertainty of anticipated volatility. 
Decrease in Historical and Implied Volatility: 
  • A decrease in historical volatility can lead to lower option premiums since the likelihood of significant price movements decrease.
  • A decrease in implied volatility can lead to lower option premiums as the perceived risk decreases.

CONCLUSION

To wrap up this guide, understanding the dynamics of historical and implied volatility is crucial for accurately assessing the valuation of options. The change in historical and implied volatility both have different importance for options valuation as they both can provide opportunity for predicting future price movements as well as determining the fair value of the option. The different calculations are just as fundamental as they too provide insight into how these measurements are both forward looking into the market and past. 

 

Today, many online brokerages and third-party websites provide free and premium tools to analyze this data. We trust that this guide has been as helpful in your understanding as it is in ours for calculating implied and historical volatility.Thank you for joining us on this insightful journey through historical and implied volatility. We wish you success as you continue to navigate the exciting world of financial markets and options ahead.

REFERENCES

At ProbabilityofProfit.com, we are dedicated to delivering accurate and trustworthy content to our readers. Our team meticulously researches each topic, ensuring that the information we provide is both comprehensive and reliable. We reference high-quality sources, including academic journals, industry reports, and market analysis, to support our content. Additionally, we draw upon original studies and data from respected publishers to provide a well-rounded perspective. 
 
Our commitment to accuracy means we constantly review and update our articles to reflect the latest developments and trends in options trading. We strive to present unbiased information, allowing our readers to make informed decisions based on solid evidence. Discover more about our rigorous standards and our dedication to excellence on our website.
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