Being on the sell side and selling options you can intuitively think of it like this:

An option is like any other product that is being produced out of ingredients and because of the competitive situation of the producer this is done by the cheapest possible production process.

The ingredients are in a simple (Black Scholes) setting a stock and and a risk free bond. So this is where the name "derivative" comes from: It is derived from other, simpler products (the underlying).

Now to make it even simpler think of a call with a zero strike on the underlying. How would you price such a call? Well, you would price it like the stock (up to a correction for the risk free interest rate)! Here the same question could be asked: Shouldn't it be priced higher with the underlying having higher drift? The answer is no, because this is already included in the price of the underlying! You would kind of double count this effect.

With "real" options the reason is the same, the only thing that changes is that you have to adapt the proportion of the stock when the price of the underlying changes. But the original reasoning stays the same: The drift does not enter into the price of the derivative because it is already included in the price of the underlying.

A very readable intuitive paper on this issue is by a giant of the field, Emanuel Derman. It can be found here: The Boy's Guide to Pricing & Hedging

See also my answer to a similar question here: How does the "risk-neutral pricing framework" work?

Being on the sell side and selling options you can intuitively think of it like this:

An option is like any other product that is being produced out of ingredients and because of the competitive situation of the producer this is done by the cheapest possible production process.

The ingredients are in a simple (Black Scholes) setting a stock and and a risk free bond. So this is where the name "derivative" comes from: It is derived from other, simpler products (the underlying).

Now to make it even simpler think of a call with a zero strike on the underlying. How would you price such a call? Well, you would price it like the stock (up to a correction for the risk free interest rate)! Here the same question could be asked: Shouldn't it be priced higher with the underlying having higher drift? The answer is no, because this is already included in the price of the underlying! You would kind of double count this effect.

With "real" options the reason is the same, the only thing that changes is that you have to adapt the proportion of the stock when the price of the underlying changes. But the original reasoning stays the same: The drift does not enter into the price of the derivative because it is already included in the price of the underlying.

A very readable intuitive paper on this issue is by a giant of the field, Emanuel Derman. It can be found here: The Boy's Guide to Pricing & Hedging

See also my answer to a similar question here: How does the "risk-neutral pricing framework" work?

Being on the sell side and selling options you can intuitively think of it like this:

An option is like any other product that is being produced out of ingredients and because of the competitive situation of the producer this is done by the cheapest possible production process.

The ingredients are in a simple (Black Scholes) setting a stock and and a risk free bond. So this is where the name "derivative" comes from: It is derived from other, simpler products (the underlying).

Now to make it even simpler think of a call with a zero strike on the underlying. How would you price such a call? Well, you would price it like the stock (up to a correction for the risk free interest rate)! Here the same question could be asked: Shouldn't it be priced higher with the underlying having higher drift? The answer is no, because this is already included in the price of the underlying! You would kind of double count this effect.

With "real" options the reason is the same, the only thing that changes is that you have to adapt the proportion of the stock when the price of the underlying changes. But the original reasoning stays the same: The drift does not enter into the price of the derivative because it is already included in the price of the underlying.

See also my answer to a similar question here: How does the "risk-neutral pricing framework" work?

Being on the sell side and selling options you can intuitively think of it like this:

An option is like any other product that is being produced out of ingredients and because of the competitive situation of the producer this is done by the cheapest possible production process.

The ingredients are in a simple (Black Scholes) setting a stock and and a risk free bond. So this is where the name "derivative" comes from: It is derived from other, simpler products (the underlying).

Now to make it even simpler think of a call with a zero strike on the underlying. How would you price such a call? Well, you would price it like the stock (up to a correction for the risk free interest rate)! Here the same question could be asked: Shouldn't it be priced higher with the underlying having higher drift? The answer is no, because this is already included in the price of the underlying! You would kind of double count this effect.

With "real" options the reason is the same, the only thing that changes is that you have to adapt the proportion of the stock when the price of the underlying changes. But the original reasoning stays the same: The drift does not enter into the price of the derivative because it is already included in the price of the underlying.

A very readable intuitive paper on this issue is by a giant of the field, Emanuel Derman. It can be found here: The Boy's Guide to Pricing & Hedging

See also my answer to a similar question here: How does the "risk-neutral pricing framework" work?