Market and historical volatility

Traders who deal with options in the markets have only one word on their lips – volatility. While volatility is indeed a fundamental principle in finance, it is a concept that can be difficult to grasp. 

The volatility of a stock, or of an asset in general, calculated as a percentage, reflects the magnitude of changes in that stock, both up and down, over a given period.
Indeed, the valuation of options requires the anticipation of future market movements, which, if they were to become erratic, would entail an increased risk for the option writer. Volatility is a statistical measure of the dispersion of returns on an asset. The purely mathematical definition would be the standard deviation of the returns of the underlying asset. Clearly, the higher the volatility, the greater the potential gain for the option buyer, the greater the risk taken by option writers. 

Volatility often refers to the degree of uncertainty or risk associated with the magnitude of changes in the value of the underlying asset. Volatility can be used to assign value to an asset and to assess the risk associated with holding it. High volatility means that the value of a security can potentially be spread over a wider range of values, the standard deviation has increased, and extreme events are more likely. This means that the price of the security can change significantly over a short period of time in either direction. Lower volatility means that the value of a security does not fluctuate greatly and tends to be more stable. It is common to distinguish between: 

• Historical volatility is a risk indicator calculated from historical prices. It describes the past and is therefore a picture of past movements.
• On the other hand, implied volatility – also known as market volatility – reflects the expectations of market participants regarding the magnitude of future variations. 

The greater the uncertainty about a stock, the higher its implied volatility. It can therefore be higher than the historical volatility. Similarly, after a strong crisis period, implied volatility may be lower than historical volatility if the market anticipates a period of calm after the storm.