Why calls more expensive than puts of equal width when cost of carry = 0 ?

Assuming 0% cost of carry in Black Scholes, why a 120 1y call, ln(120/100) = 18.2%, valued at $2.15, while a 83.3 put, ln(83.3/100) = -18.2%, at $1.78? Aren't the strikes the same width from spot? Is it because the tail areas beyond the strikes, so even the probability of reaching those areas are equal, the right tail is unbounded?

 

Dude, quote the forward (ATM long call, short put) on the duration in question as the options are marked to the forward. Ask yourself why the RFR is a model input. And your last comment (lognormal distro, constant drift).

 

it should be the same, atm put call parity dictates so. the difference is mostly risk free interest rate and “carry cost”.

 

thx. so lognormal/skewed to right even flat vol etc.

 

Below shows where the forward is on NDX 1Y out. You should get into the habit of first quoting the synthetic(fwd). NDX forward out to Dec25:

 

fed overnight funds rate is at or around 4.58, compounding 365 days, more or less closer to 5.20, put call parity must be held.

 

Option Premiums calculated wrt Discounted / Present Value of Strike

 

When markets are very bullish and lose all sense of fear, calls can get distorted, and vice-versa.