Option strategy Collar

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).

• It's actually what I did and i still got a wired shape of p&l, do you think we need to discount the theoretical payoff ? Nov 19 '20 at 18:27
• I'm just a retail guy who has traded options for 30+ years. Anything theoretical is above my pay grade. It might be useful if you posted some numbers (the actual position and what the weird shape is). What are you using to model this? Nov 19 '20 at 18:34
• I'm just student trying to make sense of this nonsense ... You can show me an example with any numbers you want and just to be in the full details right can you provide the formula of theoretical p&l of the collar ? Nov 19 '20 at 18:37
• I provided the formula for the P&L of a collar in my answer. Post the price of the underlying as well as the details of the two options (strike price, expiration, and premium). Be aware that a long stock collar is the synthetic equivalent of a bullish vertical spread. Nov 19 '20 at 19:23
• Okay here's my params: underlying price 50\$, call strike 60, put strike 30, rf is 0.05 and volatility is 35% and maturity is 1 year Nov 19 '20 at 19:31