## What is Implied Volatility in Options?

Implied Volatilityrefers to the metric that is used in order to know the likelihood of the changes in the prices of the given security as per the point of view of the market and as per the formula Implied Volatility is calculated by putting the market price of the option in the Black-Scholes model.

### Explanation

Implied volatility (IV) measures the likelihood of the change in the price of a security and helps investors where their investment will move in the future by forecasting the supply & demand and the movement of the price of the security which in turn helps to understand the price of options contracts. It is based on certain factors (which include the market expectation of the security’s price) that impact the price of a security and is usually expressed in percentage of the stock price indicating standard deviation that relates to a specific time period. The symbol that is used to denote Implied Volatility is σ (sigma).

If market expectations go up or demand increases, implied volatility increases which in turn increases the options premium price component. Inversely, if the market expectations fall down or the demand for the security drops, implied volatility also goes down and results in a decrease in the options premium price component. It relies on market consensus and depicts the outlook of the market.

### Formula of Implied Volatility in Options

Black – Scholes – Merton Model calculates the appropriate price of a European option on the basis of the stock price, exercise price, risk-free interest rate, time until expiration date and the implied volatility.

If all of the above information except the implied volatility is known, we can use the below formula to reverse calculate implied volatility.

**C = SN (d1) – N (d2) Ke**

^{-rt}Where,

- C = Call Price
- S = Stock Price
- N = Cumulative normal distribution
- K = Strike Price
- e = Exponential term
- r = Risk-free interest rate
- t = Time until expiration date

d1 and d2 are calculated as below:

**d1 = [Ln (S/K) + (r+ σ^2 / 2) ^ t] / [σ -√t]**

**d2 = d1 – σ-√t**

Where,

- σ = Implied Volatility
- Ln = Natural Log

### Implied Volatility Example

Pixer LLP stocks are currently trading at $50 per share in the market. If the market assumes that the price of the share is going to rise which will result in an increased demand for the shares. Since the demand for the shares increases, there will be an increase in the implied volatility which will make the premium for the option much higher.

Let’s assume that the implied volatility for this stock is 20%. The lowest price in one year’s time was $32 and the highest in the same year was $64. The market predicts the price to move within 20%.

- 20% of $50 upwards is $60
- 20% of $50 downwards is $40

The market assumes that the price of the stock by the end of the year will be between $40 and $60. As per the theory, 68% of the market assumes that the price will be within the above-mentioned range whereas the remaining 32% of the market thinks that the price will fall either below $40 or go above $60.

As an investor, looking at the numbers, the most appropriate strategy can be adopted by the investor to reap out maximum profits from his or her investment. Although, these calculations are based on market consensus and are not foolproof and might result in loss of investment for the investor. But looking at the figures one can make a decisive move as to what strategy needs to be adopted for a particular security. The market might not move as expected by the market consensus as seen in many past incidents where the market behaves purely different from what the market participants expect it to do.

### Advantages

- Option prices are decided on the basis of implied volatility.
- It measures the uncertainty of any change in the price of the security on the basis of the market sentiment.
- An investor or a trader can formulate his or her trading strategy on the basis of the analysis of an option’s implied volatility.
- It helps in understanding whether the price movement will be too high or low which gives an idea to the investors on how much to invest in security.

### Disadvantages

- Implied volatility does not indicate the direction in which the price of the security will move. It only shows whether the move will be high or low.
- Any news relating to the security can have an impact on the implied volatility making it sensitive to unforeseen events.
- The fundamentals are not considered while calculating implied volatility and it is based on prices, supply & demand and time value.
- Highly dependent on market consensus and can result in the incorrect decision making of strategies, thereby resulting in loss of investment.

### Important Points

- Implied volatility does not depict whether the price movement will be positive or negative.
- High implied volatility means that there will be a large price swing, it may either move higher in the upward direction or very low in the downward direction or might swing too much in between both the ends.
- Low implied volatility means that the price swing will be minimal.
- It is different from historical volatility which measures the volatility on the basis of historical data.

### Conclusion

- It is a measurement of the change in the price of a security in the near future.
- In a bearish market, it is high since investors assume that the price of the security will fall, whereas in a bullish market it is low since investors assume the price will go up in the future.
- It plays a major role in deciding the pricing of options.
- While calculating Implied Volatility, the determining factors are demand & supply and time value.
- Black – Scholes – Merton model formula can be used to calculate the implied volatility by using reverse calculations if all other values are available.
- It is measured on the basis of the general consensus of the market along with certain parameters and can turn out to be an incorrect prediction of the price movement.

### Recommended Articles

This has been a guide to Implied Volatility and its definition. Here we discuss the formula to calculate implied volatility with an example along with advantages and disadvantages. You can learn more about derivatives from the following articles –