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 the FTSE® 100 for different expiry months with the underlying FTSE® 100 price of 6220:

Strike	February	March	June
6150	135	158	258
6200	105	131	258
6350	44	72	163
6375	35	62	151
6400	28	53	139

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

Underlying price
The February 6200 call is priced at 105, while the February 6350 call is only worth 44.

Remember, calls are the right to buy. The right to buy at the lower price of 6200 is more desirable than the right to buy at the higher price of 6350, and so the value is greater.

But why is the 6200 call priced at 105?

The right to buy at 6200 when the market is at 6220 must be worth at least 20, 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 85 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 6150 and 6200 calls have intrinsic value. At expiry, with the underlying asset at the same price (6220) 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 February FTSE® call options with an underlying price of 6220 you can see that the time value is greatest for the 6200 call.

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

Strike	Premium	Intrinsic value	Time value
6150	135	70	65
6200	105	20	85
6350	44	0	44
6375	35	0	35
6400	28	0	28

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.

Question

Question 1

Which of these options will tend to have a higher premium?

a An option very close to expiry
b An option on an inherently volatile asset
c An option with a strike price distant from the underlying market

Reveal answer

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.

Homework

Take a look at the prices of call options for gold in your demo account. Notice how they change as you switch from daily to weekly then monthly timeframes.

Lesson summary

Options prices are affected by three key factors: the underlying price, the amount of time left to expiry and volatility
Underlying price determines how much of the option is immediately valuable, and is responsible for a proportion of the premium called the intrinsic value
The other key element of the premium is the time value, sometimes known as the extrinsic value
This time value decays – premiums fall as the time left until expiry decreases
Premiums increase as volatility rises and decrease as it falls
Interest rates and dividends can affect options prices, but their influence is minor
In practice, options are priced by looking at probabilities, by complicated mathematical processes such as the Black-Scholes model, and tend to be set by the writer offering the option