Options are contracts to buy or sell an underlying asset for a given price, called the strike price, on or before an expiration date. Calls are options to buy, and puts are options to sell. The price, or premium, of an option is influenced by a number of factors. The effects of these price factors are complex and are usually calculated using sophisticated mathematical models. The major risk factors are the price and volatility of the underlying asset, time until expiration, and interest rates.

## Price of Underlying Asset

Call and asset prices move in the same direction, but puts move opposite to assets. The rate of change of an option price is not linear, in that a $1 change in the asset price does not necessarily yield a $1 change in the option. Premiums change dynamically based on the distance between the asset price and the option strike price. A deep in-the-money, or ITM, option is a call with a strike well below the current asset price or a put with a high strike compared to the underlying asset’s current price. These options are highly sensitive to asset price changes. Deep out-of-the-money, or OTM, options are the reverse and have low sensitivities.

## Time to Expiration

Options have time value. The more time until expiration, the greater the time value and the higher the option premium. Time value reflects the fact that the underlying asset’s price has more time to change when expiration periods are far away. Stock options are usually available with three-, six-, nine- and 12-month expiration dates. Longer-dated options sell for more than ones with shorter expirations because of time value. Time value does not decay in a straight line. Instead, the graph of time remaining versus time value has a rounded shape, showing that the relationship is not linear.

## Volatility of the Underlying Asset

Volatility is a measure of how quickly an asset changes prices. A high volatility implies the asset is “twitchy," meaning that its price can rise or fall easily. Volatility is measured in terms of historical price changes in the underlying asset. Option premiums expand when volatility rises. The reason is that option sellers perceive greater risk during highly volatile times, and need to collect higher premiums to offset that risk.

## Interest Rates

Higher interest rates yield higher option premiums. The reasoning behind this is that high interest rates compete for an investor’s money more than low interest rates do. When interest rates are high, investors would rather control an asset for the price of an option premium than through its outright purchase. The difference between the option premium and asset purchase price can be invested in interest-bearing instruments like bonds and receive a high rate of return. Thus, high interest rates cause investors to choose options over assets. This drives up option premiums.

#### References

#### Resources

- The Complete Guide to Option Pricing Formulas; Espen Gaarder Haug
- Trading Options Greeks: How Time, Volatility, and Other Pricing Factors Drive Profits; Dan Passarelli, William J. Brodsky
- Option Pricing: Black-Scholes Made Easy; Jerry Marlow

#### Photo Credits

- Ryan McVay/Photodisc/Getty Images

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