## What is implied volatility?

Volatility is defined as the dispersion or fluctuations in the price of an asset. Generally, two types of volatility are calculated for the pricing of the options contract -  historical and implied.

Historical volatility is calculated based on the prices of the past while implied volatility is a forward-looking measure of volatility. Implied volatility tells us about the price changes (fluctuations) a stock will experience over a future period.

It forecasts the likely movement in the price of a security. Mathematically, it returns the theoretical value of an option equal to the current market price of the option by taking into account the demand, supply, and time value by using the Black-Scholes model (BSM).

In the case of options, it informs us how large the value of a security will move up and down between now and the expiration date. Implied volatility is influenced by the expectations of the market price of the security and is the key factor in valuing the options contract.

## How implied volatility works and how it is used in options

Implied volatility is the perception of how security, asset, or market will act in the future. This perception is ultimately reflected in its price and options contract.

To put it in another way, based on the demand, supply, and time value of the options traded in the market the implied volatility informs us about how volatile the security’s price will be.

In simple words, it’s the market belief about volatility. If a stock has a price of \$100 and implied volatility of 20%, then the price will remain between \$120 and \$80 over the year for one standard deviation.

During major economic events in the economy or for a company the implied volatility increases sharply and there is an increase in the value of the options contracts.

On the other hand, when we expect stable periods, the implied volatility is lower, and the option’s premium is decreased. Implied volatility can be seen as a measure of future risk a company will face and therefore is priced in the options contract.

Higher implied volatility indicates higher expected risk and therefore the premium for the option increases and vice versa.

## Implied volatility formula

In order to calculate implied volatility Black-Scholes Model (BSM) is used which considers:

i) Contract’s time until expiration (Time to maturity)

ii) Strike price

iii) Underlying asset price (spot price) and

iv) Risk-free rate

Mathematically Black-Scholes model is written as:

Where:

C = Call option price

St = Current stock price (Spot price)

N= A normal probability distribution with miu=mean=0 and sigma=standard deviation=1

K= Strike price

𝛾= Risk-free interest rate

t= Time to maturity

𝜎= Volatility of asset

The main discrepancy in this model is the assumption that the price follows a normal distribution. The Black-Scholes model assumes that a stock follows normal distribution which is a discrepancy in the model.

The price of an asset can go up to infinity while at a minimum it can be zero. For example, a \$40 stock can go up by \$60 but it cannot go down \$60 as the minimum it will go to zero.

However, normal distribution assumes that the price moves equally in both directions (positive and negative).

Therefore, some analysts use log-normal distributions as it accounts for positive movements more than negative ones.

## Implied Volatility Example

We take an example of an option contract for Procter and Gamble (PG) trading on 07/18/22 with a spot price of 145.07, strike price of 155, and time to maturity was 35 days (35/365=0.959) at a price of 0.63.

By trial and error, we put the values for volatility so that we get a higher and lower call price closest to the call price (0.63). These values are calculated by applying the Black-Scholes Method which is the industry standard.

After calculating the call price for higher and lower volatility by hit and trial we use the method of interpolation for the calculation of the implied volatility. The formula to calculate the values of the call price and the implied volatility in Excel is also given below:

## What is low implied volatility?

If it is predicted that a stock will not experience larger ups and downs in its value and the price of the stock will remain stable in the future then it is said to have lower implied volatility.

Lower implied volatility leads to lower options prices and there will not be many unpredictable changes in the price of the security and it will remain within the current trading range.

## What is high implied volatility?

On the other hand, if we expect that the stock will experience higher ups and downs in its price and these fluctuations will be more frequent then there will be higher implied volatility. Higher implied volatility will result in higher option premiums because of the underlying risk and reward.

If the market participants feel that a major event will happen to a company that will influence the price of the security, it is probable that the implied volatility will be higher. The market price of the security and the option’s price will drastically change in response to the event. Higher implied volatility also triggers higher demand or supply of the options in the market ultimately affecting the price of the options.

## What implied volatility tells option traders

Implied volatility tells investors about the future price fluctuations of security. It also gives traders a hint on how large the fluctuations in the price of security in the future will be.

For example, if an oil company transports oil from the Panama Canal and it is expected that a war will erupt in the Panama region and it will disrupt the supply of the oil the investors will be expecting higher changes in the value of stocks.

As a result of this event, the implied volatility (future price fluctuations) will be higher and the demand or supply for the oil company’s options will also be higher and the investors will be expecting a higher premium for the higher risk.

As the risk and return go hand in hand, higher implied volatility will result in investors demanding higher premiums for the options. Implied volatility does not tell us about the direction of the price movement but it guides us about whether a stock will undergo large or small price swings and how frequent they would be and thus it warns investors about future price fluctuations.