The Black-Scholes formula assumes thatI) the risk-free interest rate is constant over the life of the option.II) the stock price volatility is constant over the life of the option.III) the expected rate of return on the stock is constant over the life of the option.IV) there will be no sudden extreme jumps in stock prices.
A) I and II
B) I and III
C) II and III
D) I, II, and IV
E) I, II, III, and IV

Question

Quizplus · Accepted Answer

The Black-Scholes formula indeed assumes that the risk-free interest rate and the stock price volatility are constant over the life of the option (I and II). It also assumes that stock prices follow a continuous geometric Brownian motion with constant drift and volatility, which implies no sudden extreme jumps in stock prices (IV). It does not, however, assume that the expected rate of return on the stock is constant (III), as the formula focuses on replicating the option's payoff through a risk-free hedge portfolio, making the stock's expected return irrelevant to the pricing model.

The Black-Scholes Formula Assumes ThatI) the Risk-Free Interest Rate Is