Shouldn't (according to the Black-Scholes model) the price of a call option with a strike of an arbitrary amount away from the current asset's price, be equal to the price of a put option with the same "distance to exercise", just in the opposite direction? In other words: Shouldn't a call and put with symmetric strikes around the asset's value be priced equally? According to my calculation, they don't equate for neither ITM, nor OTM options. What's the reason for this inequality of option prices?
I'm aware that this does not apply to observed market prices. But shouldn't this hold for option prices computed with the traditional Black-Scholes OP model, as this formula assumes normally distributed returns?