Lookback Option Pricing Formulas with Floating Interest Rate in Uncertain Environment

Abstract

Uncertainty theory is widely used in the financial field. As a path dependent option, Look back option is favored in the financial market because of its own characteristics and is often used by investors to avoid risks. Based on this, this paper proposes to use the Ornstein Uhlenbeck stock model to study the look back option price, and takes the uncertain mean reversion model as the assumption of interest rate treatment. In the traditional lognormal distribution, the one-way change of stock price with time. When using the Ornstein Uhlenbeck stock model, the stock price follows the index O-U process, this situation is avoided, and the characteristic of interest rate, the average value of interest rate fluctuation, and the interest rate follows the mean reversion model can be well reflected. Therefore, the actual situation of the financial market can be more appropriately reflected by the new stock model. Further, the pricing formula of look back option is further deduced and discussed. At the same time, it is explained through relevant special cases.