I've question regarding Collar strategy (long Put with strike $k_1$ and short Call strike $k_2$ and long stock), when calculating the theoretical P&L of the collar for large up movements of the underlying my theoretical P&L surpass maximum payoff or for large down movements of the underlying the opposite happens, I'm wondering if this actually makes sense ? Also do we need to discount the values theoretical P&L for collar ?
The maximum profit for a collar is the call strike less the collar's cost (at expiration).
The maximum loss is the collar's cost less the put strike (at expiration).
Prior to expiration, the speed at which the profit or loss approaches the maximum depends on the time remaining and is accelerated (or decelerated) by the implied volatility.
If there's a dividend, it must be accounted for but that merely changes the potential P&L.
It makes no sense that theoretical payoff exceeds the maximum payoff because the option on the side of the move can only attain intrinsic value (while the other side goes to zero).