The Black-Scholes-Merton (BSM) model makes a volatility assumption that is a far cry from how the real-world volatility behaves. This week, we compare the characteristics of the model’s volatility with that of actual volatility to understand how to use volatility in options trading.
Constant volatility
The BSM model assumes volatility is a constant. Suffice it to know that this assumption helps in arriving at closed form solution- calculating option value from an equation. Note that the volatility is that of the underlying returns, not that of the option. That is, if you are valuing options on the Nifty Index, the volatility that you must input into the BSM model should be that of the Nifty Spot Index returns.
Suppose you want to go long on a call that has 10 days to expiry. You must input five factors into the BSM model to value an option-underlying price, the strike price, time to expiry, risk-free rate and volatility. The volatility you input must be determined from the underlying price returns. So, you need to build a data set to first determine the one-day volatility. Should you take the last one-year data, six months or three months data to calculate the one-day volatility?
Simple calculation
The constant volatility assumption tells you that it should not matter. You should theoretically arrive at the similar number, though statisticians would tell you that larger the data set the better. Then, calculating the volatility for the remaining days to expiry is simple. You simply scale the one-day volatility. That is, you multiply the one-day volatility by the square root of numbers of the days to expiry to arrive at the volatility to input into the model. The scaling property of volatility arises from the constant volatility assumption. Note that variance is proportional to time. That is, the two-year variance is double that of the one-year variance. Standard deviation, captured by volatility, is the square root of variance.
Therefore, volatility is proportional to the square root of time. Real-world volatility is, however, not a constant. It clusters. That is, if today’s volatility suddenly jumps, compared to yesterday’s , tomorrow’s volatility is likely to stay higher, in line with today’s . This behaviour continues until volatility suddenly decreases. This characteristic of volatility is captured by more sophisticated models. Suffice it to know that these models are not helpful for short-term trading.
Optional Reading
Traders prefer implied volatility instead of calculating volatility from a data set of underlying returns. Implied volatility is derived from the traded option price. As discussed previously in this column, implied volatility indicates the annualised returns volatility of the underlying expected by option traders, which must be converted into relevant period volatility. Note that implied volatility need not be equal to the actual (realised) volatility. This is because implied volatility will change whenever option prices change. It is best to apply implied volatility as a relative (not absolute) factor to determine whether an option is rich or cheap.
(The author offers training programmes for individuals to manage their personal investments)
Published on August 16, 2026
