Delta (Δ) – Behavior
- 04:32
How delta behaves for a long call option.
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Glossary
DeltaTranscript
Let's take a closer look at how Delta actually behaves.
For vanilla call options.
Delta generally lies between zero and one or between 0% and 100%.
For vanilla puts options, delta lies between minus one and zero, but what actually drives the delta of an option.
If delta is a likeness factor or participation ratio, then the higher the delta, the more the option behaves, like the underlying asset itself, and that depends on the likelihood of the option being exercised.
Take a deep in the money call option.
Suppose the strike is 100, the stock trades at 200 and there's just one day left to expiry.
Technically, it's still an option, but realistically, there's no doubt it will be exercised.
And as a result, the option price moves almost exactly in line with the underlying assets.
In practice, it behaves like a forward contract and forwards are sometimes called Delta one products because their value moves almost perfectly in line with the underlying.
On the other hand, consider a deep out of the money call with a strike at 100, the underlying stock at 10, and with one day to expiry, there's almost no chance it will ever be exercised.
The option premium is essentially lost, and even a large move in the stock price won't meaningfully change the options value.
In this case, delta is close to zero, but things get most interesting when an option is at the money.
A useful rule of thumb is that an at the money call has a delta of about 0.5.
Strictly speaking, that's not always exact, but as a guidepost it works really well.
So as a call option moves from out the money to at the money and then further into the money its delta increases.
In other words, the option premium behaves more and more like the underlying assets.
Now, if you look at the charts on the screen, you'll notice another pattern.
The time left until maturity of the option also matters.
Short dated options have deltas that change more rapidly as they move through the at the money points.
Longer dated options, they adjust more gradually.
This is more intuitive.
If you think about extremes, imagine two call options, both with a strike of 100 and also a stock price of 100.
For simplicity, let's assume interest rates are zero and the asset pays no dividends.
In that case, the forward price is also 100, but one of these options expires tomorrow.
The other in 10 years time at the start, both are at the money.
So both have a delta of roughly 0.5.
Now, if the stock price rises to 110, the one day option suddenly has a much higher probability of being exercised and its delta increases sharply.
The 10 year option also sees an increase in delta, but to a far lesser degree.
After all, in the remaining 10 years, there's still plenty of time for the stock to move in either direction.
So the overall probability of exercise at expiry hasn't shifted dramatically.
That's why we say short dated options have much sharper deltas near the strike, and that's the key takeaway.
Delta not only depends on money, whether an option is in at or out of the money, but also on time to expiry.