Explanation

The Black-Scholes-Merton model makes several key assumptions:

• Continuous trading is available (Option A) - This is correct. The model assumes that trading can occur continuously, which allows for perfect hedging through dynamic portfolio rebalancing.

• Early exercise of the option is not allowed - Option B is incorrect. The model assumes European-style options that can only be exercised at expiration, not American-style options that allow early exercise.

• The volatility of the underlying is known and constant - Option C is incorrect. The model assumes volatility is known and remains constant over the option's life.

Other key assumptions include:

• No dividends are paid during the option's life
• No transaction costs or taxes
• Risk-free rate is known and constant
• Returns are log-normally distributed
• Markets are efficient

Therefore, the correct answer is A.