Delta is roughly described as a risk metric that measures the change in the premium of an option with a one point change in the underlying stock. A current delta value will only influence the premium with a subsequent one point move. In other words, a change needs to occur. The current delta value does not affect the current premium.

An option can be split into two components, intrinsic value (IV) and extrinsic value (EV), assuming an option is in-the-money (ITM). Does anyone have a crispy clear understanding of how Delta contributes the two premium components of an in-the-money option? All of the resources I have consulted do not clearly spell out how delta affects different components, or whether it only affects one of them. Resources only state that delta affects the "premium," which is vague.

If an option is out-the-money (OTM) or at-the-money (ATM), there is only EV. Any delta score would only contribute to the EV of an option with every point move in the underlying. How does this change when the option becomes ITM?

IV is a simple function of the difference between the current stock price and the strike. Does delta contribute to IV and EV, or only IV?

As an example, I used a rudimentary BSM calculator to spit out some call option figures and greeks to illustrate the question I am asking. I only change the stock price. I keep all other parameters constant when moving from initial to new assumptions. These figures are read verbatim off the options calculator coming from the interactive brokers website. I also used other BSM excel calculators to check the figures and they are pretty close.

Initial assumptions at time zero (T0):

current stock price: 100

strike price: 95

interest rate: 2

implied volatility: 25

days to expiration: 90

dividend: 0

The total call option premium =

**8.026**

The IV =

**5**(100 - 95)

The EV =

**3.026**(8.026 - 5)

Delta:

**0.697**

The delta is a "close" approximation to how the premium will change with a one point move in the underlying. For the next step, I am going to assume the stock price rises by one (1) point. This would mean that in accordance with the previous delta calculation, the premium should increase by 0.697, however it is not clear where this 0.697 will go (extrinsic or intrinsic value).

New assumptions at time one (T1, fractions of moment later):

current stock price: 101

strike price: 95

interest rate: 2

implied volatility: 25

days to expiration: 90

dividend: 0

The total call option premium =

**8.768**

The IV =

**6**(101 - 95)

The EV =

**2.768**(8.768 - 6)

I would like to unpack what just happened. I kept all parameters constant apart from increasing the underlying stock price by one point.

1. The total option premium

**increased**by

**0.742**(8.768 - 8.026)

2. The IV has

**increased**by

**1**(6-5)

3. The EV has

**decreased**by

**0.258**(3.026 - 2.768)

With these results it becomes confusing as to how the delta value (0.697) for the initial assumptions at T0 impacted the various components (IV and EV) of the premium AFTER the one point move took place at T1.

The total option premium increased which makes intuitive sense. That is not the question though.... The IV increased by a full point. The EV decreased. Is the delta fully contributing to IV? If so, there is 0.303 missing (1 - 0.697). Or is delta only contributing to EV? If so, why did EV decrease?

How did the 0.697 delta contribute to IV and EV? In which ratios? Did delta increase IV and decrease EV? Or did delta only decrease EV?

In a nutshell, where is the 0.697 delta going, and how is it influencing the two separate components?

**Any help in understanding would be most appreciated!**