Stock prices don't move in a preconceived path. Of course, financial analysts put forth forecasts about a particular sector or asset to reach certain price targets. These forecasts may be right or may prove to be wrong later, but that’s not the matter of contention for us.

The path for prices of Nifty may be currently quoting at 18000; let’s assume it is forecasted by market experts to move to 19000 over the period of 1 year. Inspite of the forecasted target of the stock, or index like Nifty (underlying), the path, price takes over the period of 1 year is unknown. Nobody knows, Would the index go to 16000 first and then move to about 19000, later, or would the prices move to 19000 directly in a gusto move; or would the prices meander about the current price 18000 to then, transition to 19000?

Even Black-Scholes option pricing model is a mathematical model used in pricing of options, giving a theoretical estimate for European-style options. This model, also, assumes the stock prices (or underlying prices) follow a geometric Brownian motion, a pattern of motion typically consists of random fluctuations in a particle's position inside a fluid sub-domain.

Volatility is nothing but the Path Taken. So, learning volatility and its impact on option pricing is pivotal for option traders.

Volatility in financial markets is a term that describes erratic moves in the financial markets of an underlying like Nifty or BankNifty or F&O stocks. These erratic moves as discussed earlier can occur on either side of the current market price, either higher or lower.

Volatility is a measure of uncertainty of returns of a given security, usually measured statistically by standard deviation of the returns of the given security. It is a metric for fluctuation possibility in the financial security, as it increases with the size of swings in either direction (upward or downward). 

The volatility measure i.e., standard deviation which is estimated using the historical price data series of the financial instrument/security, is named as historical volatility. The measure indicates the behaviour of the prices over a pre-determined time period. A rise in historical volatility is suggestive of higher price fluctuations, while the drop in historical volatility suggests calmer performance.

Historical Volatility Of Tata Steel from Nov 1, 2021.

Historical Volatility of JSWSTEEL from Nov 1, 2021

Historical Volatility Of Hindustan Unilever from Nov 1, 2021.

Historical Volatility of Infosys from Nov 1, 2021.

Historical Volatility of JSWSTEEL from Nov 1, 2021

Historical Volatility of JSWSTEEL from Jan 1, 2019

An example of Fall in Nifty and Rise in Volatility during COVID crash, around Mar-Apr 2020.

An example of drop in Nifty and rise in Volatility in April 2022.

An example of rise in Nifty and drop in Volatility in Aug 2022 and Oct 2022.

Historical volatility of Nifty or Bank Nifty or any underlying F&O stock, is computed by calculating a statistic, namely, standard deviation of daily log returns of closing prices for say about 252 days. This is daily volatility of the stock or index.

However, to annualise the daily volatility, it is multiplied by square root of time i.e. approx. 252 days.
Annualised volatility = Daily volatility * √252

Similarly, daily volatility can be computed, if annualised volatility of an asset is published, by re-arranging the above formula.
Daily Volatility =  (Annualised Volatility)

                                        √252

But historical volatility isn’t a forward looking metric and traders always desire or yearn for a forecast to be able to trade the markets. This brings, implied volatility into the context, as we continue to build on the trading framework.

As stock price movement cannot be pre-conceived, the price path taken by the stock could be filled with unpredictable and sometimes sharp moves, also known as price turbulence. A measure of this turbulence/unpredictability is what defines volatility.

The 3 types of volatility are:

1. Historical volatility
2. Implied volatility
3. Future realized volatility

The erratic moves as discussed earlier can occur on either side of the current market price, either higher or lower. So, the wider and wilder the fluctuations, the more the higher, the volatility measure.

No, volatility of a stock varies across time. While different stocks could have different measures of volatility at the same point in time.

As option price and the option greeks (which shall be explained in later modules) are dependent on volatility of a stock, it is important parameter which is tracked by market participants.