Explanation

The correct answer is C: Borrowing and lending is allowed at the risk-free rate.

Let's analyze each option:

Option A: The underlying must pay a dividend.

• Incorrect. The standard Black-Scholes-Merton model actually assumes no dividends are paid during the option's life. There are modified versions for dividend-paying stocks, but the basic model assumes no dividends.

Option B: Asset prices are normally distributed.

• Incorrect. The model assumes that returns (not prices) are log-normally distributed. Asset prices themselves follow a log-normal distribution, which means they cannot be negative and have a right-skewed distribution.

Option C: Borrowing and lending is allowed at the risk-free rate.

• Correct. This is one of the key assumptions:
  • Investors can borrow and lend unlimited amounts at the same risk-free interest rate
  • This enables the creation of riskless portfolios through dynamic hedging
  • It's essential for the no-arbitrage pricing framework

Other key assumptions include:

• No transaction costs or taxes
• Continuous trading
• Known and constant volatility
• European-style options (no early exercise)
• Short selling permitted with full use of proceeds