Pricing Asian Lookback Option based on Monte Carlo simulation

Abstract

With the emergence and development of exotic options, the diversity of securities has largely increased. However, existing types of popular exotic options seem to be either limited or inflexible to satisfy buyers' personal needs. As for the Lookback option and Asian option, the Lookback option’s application is limited in the OTC area with a high price. The Asian option is cheap but used mostly for hedging, leaving relatively little space for speculating. Thus, we created a new exotic option called the Asian Lookback option (ALB) as a combination and derivative of these two options with a flexible implementing way enabling both the requirements for hedging and speculating. In the process of building the model of ALB, these two options’ models are referenced, together with the widely used option pricing method Monte Carlo Simulations based on the assumptions of the Black-Scholes model. To simulate the practical function and price of ALB, we set a control experiment of the prices of four options: two types of ALB, Asian option, and Lookback option in three different markets (S&P 500, Corn, COMEX Gold). It is shown that the price of ALB can be switched from Asian-like to Lookback-like, realizing the function of customized usage from hedging to speculating. These results shed light on a more flexible and personalized development tendency of derivatives.