Consider an at-the-money call option and an at-the-money put option. Both options are European. They have difference Black-Scholes implied vols. a. By put-call parity, there is an arbitrage b. By put-call parity, one cannot tell if there is an arbitrage

I would say A. Put call parity means both sides of the equation are equal. however if they have different volatility then one is overpriced and the other is under priced. therefore an arbitrage opportunity exists.

Itâ€™s an arbitrage.

Definitely an arbitrage.