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Friday, May 27th 2022

# Options 101: Implied Volatility Calculation And Uses

Options pricing models produce theoretical values for options and implied volatilities. Here we show common methods for calculating IV and how to interpret them.

Summary

Implied volatility (IV) is a crucial data point in options trading, allowing for normalization of options prices. IV is calculated using an options pricing model, with volatility being the least known and most important input. Monthly IV, constant maturity IV, IV skew, and IVs at various deltas are all commonly used measurements of IV. The low strikes of equities typically have a higher IV than high strikes due to the options implied volatility skew. Showing IVs for deltas can be helpful in comparing over time and across constant maturities.

Implied volatility (IV) is the most important options data point next to options prices. Implied volatility allows users to make sense of options prices by normalizing to a more uniform metric. In a perfect world, all of the options at all strikes and expirations for an underlying would have the same implied volatility even through the options prices are different. In the real world, implied volatility has a slope or skew and each month is different. For most equities, the low strikes have a higher IV than the high strikes as seen below.

Implied volatility is calculated by using an options pricing model. The typical use of a pricing model is to use the following inputs to create a theoretical options value:

- Options strike price

- Time to expiration

- Underlying stock price

- Interest and dividend rates

- Volatility

Of these inputs, volatility is the least known, has a large impact and because of this, the most important. The options pricing model assumes that you have a volatility to input. However, if you do not have a volatility but you have a theoretical or market price, you can solve for the implied volatility by gradually changing the volatility until the theoretical price matches the options price. The final volatility that produces the equal price is the implied volatility of the option.

There are other measurements of implied volatility that are typically used, like monthly IV, constant maturity IV, skew of the IV, and IVs at various deltas.

Communicating the implied volatility of a particular expiration is important to options traders. In the graphic above, the monthly IVs are shown as is the change on the day. The monthly IV is found by taking all the options and calculating a weighted average, weighting the ones towards the middle 50 delta higher.

Typical constant maturities of 30, 60 and 90 days to expiration are useful to compare to each other and over time. Constant maturities are calculated by taking a weighted average of the IVs for the two closest expirations to the days of the constant maturity.

The difference in implied volatility of lower strikes to the higher strikes in a particular expiration produces a sloped line referred to as the options implied volatility skew. Typically, the low strikes have a higher IV because underlying equity prices tend to fall faster than they rise and options investors are willing to pay more for lower striked options.

Another way to present IVs are to show them at various deltas. The delta of an option ranges between 0 and 1 for calls and 0 and -1 for puts and is defined as the amount of the change in options theoretical price for every one dollar change in the underlying price. Showing IVs for deltas are helpful to compare over time and across constant maturities. For example, the 5 delta out of the money IVs have risen relative to other deltas since the RobinHood retail effect of buying these calls hit the market.

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