How are options priced?

Option premiums are derived from the Black-Scholes formula. This is a well-established model that calculates prices based on a number of variables, including:

• The current price of the underlying market
• The expiry of the option. Options with more distant expiries have higher premiums than options with closer expiries
• The strike price of the option
• Volatility

It can be useful to understand the different factors that affect prices.

So here are some sample mid-prices for call options on Nymex Crude Oil for different expiry months with the underlying Nymex Crude Oil price of 11200:

Some options are more expensive than others. Why is this?

Underlying price
The May 11200 call is priced at 700, while the May 12400 call is only worth 350.

Remember, calls are the right to buy. The right to buy at the lower price of 11200 is more desirable than the right to buy at the higher price of 12400, and so the value is greater.

But why is the 11200 call priced at 700?

The right to buy at 11200 when the market is at 11300 must be worth at least 100, which explains a portion of the premium called the intrinsic value. It measures how much of the option is immediately valuable.

But what about the other 600 points? Where do they come from?

Time left to expiry
The extra premium on top of the intrinsic value is called the time value, or sometimes extrinsic value.

The longer the time remaining to expiry, the greater the chance of further movements in the underlying asset and therefore the greater probability that the option may acquire intrinsic value.

Option premium = intrinsic value + time value

Not all options have intrinsic value. In the table, only the 11200 calls have intrinsic value. At expiry, with the underlying asset at the same price (11300) all the other strikes would be worthless (time value = 0 at expiry). Their current value reflects that the price of the underlying asset may change between now and the expiry.

Options which have intrinsic value are described as being in the money.

Options which have no intrinsic value, and therefore only have time value, are described as being out of the money.

What about at the money? This is simply the option which has the closest strike price to the price of the underlying asset.

Time decay
If you look at the value of these May Nymex call options with an underlying price of 11300 you can see that the time value is greatest for the 11200 call.

This is the closest strike to the underlying price out of the options listed.

So the more time left to expiry, the more an option will cost. In other words, the time value of an option decays as the expiry draws closer, while the rate of decay increases as an option approaches expiry.

How the time value of an at-the-money option decays as time passes

The passage of time is bad if you have bought an option. Every passing day means a decrease in the value of your option.

Conversely, the passage of time is good if you are short – have sold or written – an option.

Strike price
At-the-money options will always have the greatest time value.

Options that are deeply in the money are almost inevitably going to be exercised. Deeply out-of-the-money options will expire unexercised.

There is more uncertainty with at-the-money options. Uncertainty means risk for anyone writing the option, and therefore means a higher time value.

Volatility
The last important factor is volatility.

Volatility measures the rate at which the price of an asset varies. If the price alters rapidly over short periods of time, it has high volatility. If the price seldom changes, it has low volatility.

If the volatility of a security is high, there is a greater risk for an options writer, and they will demand higher premiums. If volatility is low, the premiums required will be reduced.

At times of emergency or radical change, such as wars, political unrest or pandemics, volatility can increase dramatically. If this happens, options premiums will increase accordingly.

Determining how volatile a market is going to be in the future is tricky. Typically, options traders make assumptions about the future volatility of a market by looking at its past volatility.

Interest rates and dividends

Two other factors that could affect the price of an option are interest rates and – for share options – dividends.

The effect of changes in interest rates tends to be insignificant. Dividends paid out to shareholders by a company will cause the share price to drop by the amount of the dividend. Consequently this will affect the price of options on that share. However, as the drop in share price is predictable, the impact of the fall will be priced into the premium well in advance.