Final answer:
The key assumption mentioned in the student's question is the continuously compounded return, which uses the natural logarithm of investment growth and assumes continuous reinvestment of earnings.
Step-by-step explanation:
The continuously compounded return on an asset such as a stock is usually modeled using a normal distribution, which is in line with one of the assumptions of some financial models like the Black-Scholes model. When discussing returns for a stock, a continuously compounded return refers to the natural logarithm of the growth of the investment, which assumes that the investment continuously earns interest on both the principal and the previously earned interest. This is different from a non-compounded return, which would simply be the percentage change in price. Discontinuous returns would suggest a process with jumps, often not suitable for financial modeling of stock prices. Therefore, the key assumption mentioned in the student's question is D. Continuously compounded return.