call option theta when deep in money

[here_it_is]

Hi all,
do you have any idea why wouldn’t a European call option have a positive delta, while a put option deep in money has positive delta?
Sorry if the questions is too long. We know that both call and put options have negative theta. However, put has an exception that if it is deep in money its price should increase towards maturity. I’m wondering why wouldn’t call option has this exception.
Thanks a lot if someone could answer!

 

[EddieChen]

here_it_is wrote:
Hi all,
do you have any idea why wouldn’t a European call option have a positive delta, while a put option deep in money has positive delta?
Sorry if the questions is too long. We know that both call and put options have negative theta. However, put has an exception that if it is deep in money its price should increase towards maturity. I’m wondering why wouldn’t call option has this exception.
Thanks a lot if someone could answer!

First, long call and short put will give you positive delta while short call and long put will give you negative detla.
When the price of a stock increases, let’s say, a dollar, the call option will increase in the value of delta. But it makes no sense that the call option will decrease its price. Therefore, the delta is always positive for a call option.
By the same token, long put has a negative delta.
I suggest you go read the definitions from the book first.

 

[cleverCFA]

I believe the situations where theta is positive occur for a put is when the price of the option is smaller than it’s intrinsic value (i.e. the value of the option is increasing as time goes by towards it’s intrinsic value)
One of the proofs we looked at for L1 was showing min/max for American/Euro Call/Put options.
Min bound values are as follows:
European Call: c >= max( 0, S - X / (1 +RFR)^t) << note that this number can only be greater than (S - X). Euro calls can only ever be worth more than their intrinsic value.
European Put: p >= max( 0 , X / (1 + RFR)^t - S) << note that this number can only be less than (X - S). This lower bound does NOT prevent a put being worth less than it’s instrinsic value.
The strike is always discounted (i.e. as time goes by, that discounted strike value increases towards X).
So, if all stays constant, as time goes by the min bound for Euro calls only decreases towards (S - X), whereas the euro put min bound increases towards (X - S).
There’s a good chance you’re confused by what I’ve just written. I think the key to understand this is to 1) understand that positive theta situations only arrise when option values are less than instrinsic (option price is increasing towards intrinsic i.e. a positive theta), 2) understand that euro call options are min bounded by spot minus the discounted strike, therefore are always greater than instrinsic value, and therefore cannot have situation 1 occur in the first place.
This is at least my understanding. Someone else may have better explanation.

 

[cleverCFA]

here_it_is wrote:
do you have any idea why wouldn’t a European call option have a positive delta, while a put option deep in money has positive delta?

Did you amend your post? I just caught your first line. Where have you heard that deep in the money put options ever have positive deltas and euro call options don’t have a positive delta?

 

[here_it_is]

sorry cleverCFA. I didn’t amend my post, “delta” should have been “theta” in the first place. my confusion was only about theta. I’ll try to understand your explanation abour price limits of options.
Thanks a lot for your and Eddie Chen’s time!