# Daily Volatility

To convert the annual implied volatility (IV) to daily IV, we use the square root of time formula. The square root of time formula states that the daily volatility is equal to the annualized volatility divided by the square root of the number of trading days in a year.

As we can see in the previous example of “CMP of BankNIFTY is 41350.4. 41300PE is trading at 160.15. IV is 14.8. We have 3 days till expiry “, We have the annual IV as 14.8%.

To convert it to daily IV, we divide it by the square root of the number of trading days in a year, which is 255. Therefore, the daily IV can be calculated as follows:

Daily IV
= Annual IV / Square root of trading days per year
= 14.8% / √255
= 0.925%

Hence, the daily implied volatility for the given context is 0.925%. It means that the market is expecting the price of BankNIFTY to move by approximately 0.925% per day over the next three trading days.

Assumptions for Daily Volatility

This is calculated using the Black-Scholes model and the implied volatility of the option, and The assumptions here include:

Normal Distribution: The daily returns of the asset are normally distributed. This implies that the asset returns are symmetrically distributed around their mean, and the tails of the distribution are thin, meaning that extreme returns are unlikely.

Constant Volatility: The volatility of the asset is assumed to be constant over the period of interest. This is a simplification since the volatility of the asset is likely to vary over time.

Independent Returns: The daily returns of the asset are independent of each other. This implies that the return on one day does not affect the return on another day.

No Jumps: The asset price does not experience sudden jumps, and the changes in price occur gradually.

Stationarity: The mean and variance of the daily returns are constant over time. This assumption implies that the statistical properties of the returns do not change over time.

It is important to note that these assumptions are idealized, and in reality, the financial markets are subject to various forms of uncertainty and volatility.

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