Investigating the Price of Floating Lookback Option and Fixed Lookback Option Based on Facebook Stock

The lookback option is one of the exotic options but the only option that allows investors to reduce risks by looking back at the option period. Compared with other options, it allows the holder to know history when determining when to exercise their option, which reduces uncertainties and solves the market timing problem. However, not many people currently realize the benefits of the option and why they should invest. In the paper, we analyze the lookback option based on its unique characteristics and options theory. We established this paper with the Black-Scholes Merton method by taking Facebook as an underlying asset to simulate the stock price and the payoffs from the fixed lookback call option and floating lookback call option. At the end of the analysis, we concluded that the change of strike price leads to an obvious change to the fixed lookback option and European Option price, compared to the floating lookback option. The change of both spot price and volatility contributes a clear difference to the lookback option relative to the European Option. Besides, the lookback option solves the market timing problems even though with a higher option price. This paper aims to explain to investors that the lookback option is one of the best options for investment.