Time to expiration-delta for a put option

Why is it negative 1 for a put option when the underlying price is assumed constant and the option is deep ITM?

Is your question about its absolute magnitude or about its negative sign?

It is negative because by default put options have negative deltas (increase in underlying decreases put value).

It is close to one because the option is deep in the money: one dollar change in underlying will change option value by the same amount.

Recall that options have two components of value - time value (that things can go either way) and intrinsic value (things went your way). Near expiration time value becomes closer to zero and all the value is attributed to intrinsic value, i.e. any change in asset price is directly transferred to option price.

Yes, I know this but why is it given that underlying asset is unchanged and then delta would move towards -1 provided that it is in-the-money? Are we saying that time value alone can bring ITM put option value to decrease with time?

What’s the slope of the line:

y = 3_x_ + 5

when x = 2?

Answer: 3.

The fact that you’ve specified an x value doesn’t change the slope; it’s 3. It’s the change in y if x changes by 1.

Similarly with option delta: the fact that you’ve specified a value of the underlying doesn’t change the fact that if the value of the underlying changes, the value of the option changes.

Wow, thanks for this.

You’re welcome.

I don’t get many _wow_s.

haha, this one deserves it though. I have one more question. When they explain theta, they say that time value for a deep ITM put doesnt reduce with time decay. This is counter-intuitive to what was said delta. Could u explain what this means?

For a deep in-the-money put, the price of the underlying is very low, but it cannot go below zero. Therefore, if you wait around, it’s more likely that the price will go up or stay the same than go down, so it’s more likely that you’ll lose value than gain value: the time value is negative.

Note that deep in-the-money call options don’t have this problem because the price of the underlying can continue to increase; there’s no upper limit.

Thanks a lot S2000. Thank you Kroko for breaking down the concept

You’re quite welcome.

Could u explain put option with respect to theta? Provided that intrinsic value is a constant. It says in the Wiley guide, that deep ITM put option would not decrease as time moves forward.

Suppose that you have a put with a $250 strike, the price of the underlying is $5, with one month to go until expiration. Three things can happen in that last month:

  • The price can drop to $4: you gain $1 . . . well, technically, you gain the present value of $1 because you have to wait 1 month to get it.
  • The price can stay at $5; you lose a little bit of time value because you could have had that same value one month earlier.
  • The price can rise to $6, $7, $10, $20; you lose in all of these cases, and possibly more than you could gain if the price drops (because it cannot drop more than $5, but it can rise a lot more than $5).

The net effect is that by waiting for another month, you’re more likely to lose money than gain money (compared to exercising the option today): negative time value.

That’s one fine deep itm put. $250 strike!!! :slight_smile:

When I say “deep”, by golly, I mean _ deep _!

Well explained.


I try.

So, the real value of option, IMO:

  1. its underlying volatility

  2. its time value

  3. all other factors (int.rate, etc).