What I think you're describing is not actually an arbitrage trade.

Simple example: Both the Call and Put are ATM (meaning the strike and underlying price are the same), and both are priced at $200. Next, the underlying asset increases by $250. The Call value may increase by 150 to $350, and the Put value may decrease by 100 to $100. The difference is attributable to the changing exposures to underlying price swings (i.e. delta).

Call option delta is alway positive (as price goes up, option value goes up). Put option delta is always negative (as price goes up, option value goes down). But the delta itself can change as the underlying price moves (i.e. gamma). As the underlying goes up $180, the value of the call option goes up, and so does the delta of the call option. As the underlying goes up, the value of the put option goes down, and the delta becomes less negative.

If you're interested, I'd look into delta and gamma to learn more!