In the project, we first analyze the effect of asset diversification across various stocks on the portfolio return and variance. We demonstrate by separate investment across various stocks that the portfolio volatility can be reduced, and an optimized portfolio can be found. Then, we investigate the fundamental hypothesis that the log return of a stock follows a normal distribution using statistical testing methods with real market data. Our result shows that the log returns do not follow a normal distribution. At last, we further investigate the option pricing model, including the rate of change of option price with respect to expiration date and spot price, and the effect of non-constant variance on modeling the stock price movement.