Let's develop an intuitive understanding of what drives the option premium and how it behaves.

Specifically, which options tend to have higher premiums and which have lower ones.

A helpful way to approach this is to view the option premium as the sum of two components, the intrinsic value and time value.

Let's start with the intrinsic value.

You can think of it as the current value of the option if it were exercised right now, an option holder will only exercise it when it's in the money.

That is when exercising would be favorable.

So in simple terms, an option only has intrinsic value if it's in the money and the size of this value is the present value of the difference between the options strike price and the relevant market price of the underlying asset today.

Let's break intrinsic value down with examples for both American and European options.

Imagine a three month American call option on a stock that pays no dividend with a strike price of $100.

The current spot price of the stock is $103.

First, we ask, is the option in the money? Well, yes, because the spot price of 103 is higher than the strike price of 100.

Great. Since this is an American option, it can be exercised immediately.

This means we can calculate the intrinsic value simply as the difference between the spot price and the strike price.

So we subtract 100 from 103, which gives us an intrinsic value of $3.

No discounting is needed here because the intrinsic value can be realized immediately.

Now, let's consider the same scenario, but this time it's a European call option, still three months to expiry with a strike price of $100 and a spot price of $103, we'll also assume an annual interest rate of 5%.

Since a European option can only be exercised at expiry, we can't just compare the spot price to the strike price.

Instead, we need to calculate the forward price of the stock, which represents the fair value of the asset at expiry.

This is because the forward price shows what the asset would be worth in the future if we only account for predictable factors like interest rates and if applicable dividends.

Ignoring any market uncertainty.

To calculate the forward price, we multiply the spot price of 103 by one, plus the annual interest rate of 5% adjusted for the three month period Until expiring.

Assuming 90 days and using an actual over 360 day counts, we multiply 103 by one plus 5 cents times 90, divided by 360, which results in a forward price of approximately $104 and 29 cents.

Next, we calculate the future intrinsic value by subtracting the strike price from the forward price.

That's 104.29 minus 100, which equals $4.29.

Finally, we discount this future intrinsic value back to today's value.

We do this by dividing 4.29 by one, plus the interest rate of 5% times 90 over 360, which gives us a present value of approximately $4.23.

Though the European option calculation is more complex, the principle is the same.

We're determining what the option would be worth if exercised under current conditions.

The key difference is that for European options, the current conditions are reflected through the forward price.

Since exercise can only happen at expiry.

But why does intrinsic value even matter? Well, the intrinsic value acts as the minimum price boundary for the option premium.

Imagine if the American option in our example, was trading for a premium of just $2.

Well, you could buy it for $2, immediately exercise it to realize $3 of intrinsic value and make a risk-free profit of $1.

This is known as an arbitrage opportunity, and this arbitrage keeps markets efficient because traders can quickly eliminate such risk-free opportunities, the buying pressure from traders buying the option will push its price up from two towards its intrinsic value of three.

Consequently, in an efficient market, the option premium should never fall meaningfully below its intrinsic value as these opportunities would be exploited immediately.

The same logic applies to European options, even though they can't be exercised early.