European Option Pricing Problems with Fractional Uncertain Processes

Abstract Compared to canonical Liu processes, fractional Liu processes possess the property of long memory which makes them more flexible in modeling stock prices. This paper calculates the moments of a fractional Liu process and the expected value of a geometric fractional Liu process. It derives some pricing formulas of the European options with the stock as underlying asset whose price is assumed to follow a geometric fractional Liu process. Algorithms are designed to compute the option prices based on the pricing formulas, and numerical experiments are performed to verify the effectiveness of the algorithms.

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