The question is the following:

• The theoretical price of a barrier booster was calculated to be ~$1,860 after replicating the portfolio. If the price of the barrier booster is actually $1,810, is there necessarily an arbitrage opportunity? If not explain why. Assume that the S&P/TSX 60 index futures with contract multiplier $1 are actively traded whose price follows the theoretical formula.

Since the theoretical price is estimated from the BSM model based on assumptions that are typically not true in practice and is not directly derived from constructing arbitrage portfolios, the discrepancy between market and BSM prices does not necessarily entail arbitrage opportunities. However, here we are assuming that the price of the underlying follows the theoretical formula so does that suggests that there should not be any discrepancies between market price and theoretical price?