Archive · 16 Aug 2026
Mastering Derivatives: Model Versus Actual Volatility in Options Trading
Some smart formulas help people guess how much an option should cost.
An option is a promise that lets you decide later whether to buy or sell something.
One famous formula is called the Black-Scholes-Merton model.
The formula pretends that prices wiggle up and down by the same amount every day.
That means it thinks volatility — the bounciness of prices — never changes.
But real-world bounciness comes in waves: if prices jump around a lot today, they usually keep jumping around tomorrow.
To use the model, people work out the one-day bounce and multiply it by the square root of the days left until the option expires.
Most traders do not rely on that calculated guess; they look at what option prices in the market say instead.
That market-based measure is called implied volatility, and it helps traders see whether an option is expensive or cheap.
The Black-Scholes-Merton (BSM) model assumes volatility is constant, unlike real-world volatility, which clusters.
The volatility input into the BSM model must be that of the underlying returns, such as the Nifty Spot Index for Nifty options.
Valuing an option requires five factors: underlying price, strike price, time to expiry, risk-free rate and volatility.
Under the constant volatility assumption, one-day volatility is scaled by the square root of days to expiry for the model input.
Traders prefer implied volatility, derived from traded option prices, as a relative factor to judge whether an option is rich or cheap.
- Who
- Options traders and individual investors using the Black-Scholes-Merton model; the author offers training programmes for personal investment management.
- What
- A comparison of the BSM model's constant volatility assumption with real-world volatility clustering, and how to use volatility in options trading.
- When
- Published on August 16, 2026, as that week's derivatives column.
- Where
- Not explicitly stated in the article; examples reference the Nifty Index.
- Why
- To help readers understand how to correctly use volatility, both model-based and implied, when trading options.
Model (Theoretical) View
Real-World (Trading) View
Volatility behaviour
Model (Theoretical) View
The BSM model assumes volatility is constant, which enables a closed-form solution for calculating option value.
Real-World (Trading) View
Real-world volatility is not constant; it clusters and tends to persist at elevated levels until it suddenly decreases.
Choosing a volatility measure
Model (Theoretical) View
Volatility for the model is calculated from a data set of underlying price returns, ideally from a larger data set.
Real-World (Trading) View
Traders prefer implied volatility derived from traded option prices, applied as a relative factor to judge whether an option is rich or cheap.
- Model
- Black-Scholes-Merton (BSM)
- Volatility assumption in model
- Constant
- Real-world volatility behaviour
- Clusters; tends to stay higher after a jump until it suddenly decreases
- Inputs to value an option
- Underlying price, strike price, time to expiry, risk-free rate, volatility
- Volatility scaling rule
- One-day volatility multiplied by square root of days to expiry
- Implied volatility source
- Derived from traded option prices
- Implied vs realised volatility
- Need not be equal; implied volatility changes whenever option prices change
- Publication date
- August 16, 2026