Volatility

What Is Volatility in the Context of Options?

Stock prices rarely remain constant—they rise and fall, sometimes gradually and sometimes with sharp swings. This fluctuation is what we refer to as volatility. It measures the rate at which a stock’s price changes over time.

It’s important to note that volatility doesn’t indicate direction—it doesn’t tell you whether the price is going up or down. It simply reflects how erratic or stable the price movement has been. If a stock frequently hits new highs and lows within a short timeframe, it is considered highly volatile. On the other hand, if it shows minimal fluctuation, it is said to exhibit low volatility.

For an options trader using a platform like m.Stock, understanding volatility is crucial for better decision-making and to avoid unexpected market shocks.

Types of Volatility

There are two primary types of volatility every options trader must be familiar with:

• Historical Volatility (HV):
  This measures the actual daily price fluctuations of a stock over a given period—typically a year. It provides a backward-looking view.
  For example, a stock that starts the year at ₹200 and ends at ₹205 after hitting ₹210, ₹230, ₹190, ₹170, and ₹240 during the year, has experienced significant volatility—even if the final price is close to where it started.
• Implied Volatility (IV):
  This is forward-looking and is derived from the current market price of options. It reflects what the market expects the stock’s volatility to be in the future.

How to Measure Volatility

Volatility is quantified using standard deviation, which captures how much price data deviates from its average (mean) value over time. Standard deviation is expressed as a percentage.

Example:

If the monthly standard deviation of Nifty returns is 10%, it suggests that over the next 12 months, Nifty could move up or down by 10%.

• Current Nifty level: 17,000
• 1 standard deviation range: 17,000 ± 10% = 15,300 to 18,700

To calculate this, you can use:

• Daily closing prices or
• Daily returns as data points

Tools like spreadsheets provide built-in formulas to calculate standard deviation easily. Once you determine the daily returns, calculate the average daily return, and then apply the standard deviation function.

To extrapolate this to monthly or yearly figures:

• Multiply the average daily return by the number of trading days (e.g., 30 for a month or 252 for a year)
• Multiply the result by the square root of the same period (√30 or √252)

This method gives you a forecast range of potential movement for the index or stock.

The Bell Curve and Standard Deviations

Plotting the frequency of daily returns creates a normal distribution curve, also known as the bell curve. This curve helps visualize the likelihood of price movements.

• 68% of price movements fall within ±1 standard deviation
• 95% fall within ±2 standard deviations
• 99.7% fall within ±3 standard deviations

This tells us that most outcomes cluster around the average, while extreme outcomes (both positive and negative) are rare but possible—such as during significant market events or “black swan” incidents.

Key takeaway:

Historical volatility gives a clear picture of past price swings, but it does not influence option prices directly. For that, we need to understand implied volatility.

Implied Volatility (IV)

Implied volatility reflects the market’s expectation of how volatile a stock might be in the future. It is extracted using options pricing models, such as the Black-Scholes model, by inputting known variables like:

• Underlying price
• Strike price
• Time to expiry
• Interest rate
• Dividend
• Option price

All of these inputs are readily available—except for volatility. Hence, using the actual market price of the option, the model backs out the implied volatility.

However, one limitation of models like Black-Scholes is that they assume constant volatility, which doesn’t align with real-world dynamics. IV, being market-driven, is dynamic and changes based on sentiment, news, and events.

For instance, option prices may rise even if the stock remains flat during times of anticipation—such as earnings announcements, budget declarations, or RBI rate decisions. That’s due to rising implied volatility. Conversely, falling IV can drive option prices lower even if the stock price remains unchanged.

Using Implied Volatility Strategically

Implied volatility helps traders estimate the potential range of a stock’s price movement within a specific timeframe.

Example:

If a stock is trading at ₹100 and has an IV of 10%, it implies:

• The stock may trade between ₹90 and ₹110 over the next 12 months
• This range reflects a 68% probability based on the 1 standard deviation rule

Understanding this helps traders on m.Stock craft strategies around expected movements. For instance, they can decide whether to buy or sell options based on whether IV is relatively high or low compared to historical norms.

Points to Remember

• Volatility measures the intensity of price movement, not the direction.
• It is calculated using standard deviation, a statistical tool showing how much prices deviate from their average.
• Two key types:
  • Historical volatility shows past fluctuations
  • Implied volatility influences option prices and reflects future expectations

Implied volatility helps determine the probable price range of a stock, aiding traders in strategy planning.