The Black-Scholes options formula is the breakthrough in
valuating options prices. However, the formula is heavily based on several
assumptions that are not realistic in practice. The extensions of the
assumptions are needed to make options pricing model more realistic. This
paper has reviewed the relaxation of the formula to European options on
shares with the focus on its analytical solutions. The assumptions that are
relaxed are non-dividends assumption, constant interest rate, constant
volatility, and continuous time.