Asian Rainbow Option Pricing Problem Based on Uncertain Fractional Differential Equations

Abstract

Option pricing is a core issue in option trading, which directly affects investors’ trading decisions and risk management. With the growing maturity of uncertainty theory, the research on option pricing problems based upon uncertainty theory has been gradually deepened. However, the volatility of stock price is not only related to the price at the current moment, but also related to all the previous stock price changes. Uncertain fractional differential equations can well portray the memory and history dependence of financial markets. Its nonlocal nature can more accurately describe the long-term memory effect and the phenomenon of spiky fat tails of stock market fluctuations. Thus, this paper mainly explores the pricing of Asian rainbow option in uncertain financial environments, where the underlying asset price is viewed as uncertain fractional processes. First, two models are presented for discussing the price of Asian rainbow option in two-asset cases, respectively. Then the pricing problems of different types of Asian rainbow options under [Formula: see text]-assets case are further discussed. Finally, empirical analysis is conducted on the proposed models with real stock data to verify the validity of the pricing formulas.