Comparative analysis of Asian and European options based on Monte Carlo simulation

Option is one of the most special representative products in the financial market. This paper shows that the basic concept of Asian options and European options. Then we make a summary for Asian and European options about formers' studies, respectively. Further, we present a Monte Carlo simulation to sample asset price paths for both Asian options and European options. Apple Inc. Common Stock (AAPL) is chosen as a market example which we can obtain market prices. This paper introduces the classic's formula for geometric Brownian motion, then simulating financial asset prices. Monte Carlo simulation can solve the pricing problem well because of its obvious advantages such as flexibility, easy realization, and estimation error. This paper focuses on the characteristics of Asian options and European options. Scatterplots obtained from the simulation data are used to compare and analyze the difference between Asian options and European options. It is concluded that the investment risk of Asian options is smaller than European options