Option pricing formulas for uncertain exponential Ornstein–Uhlenbeck model with dividends

Abstract

Uncertain finance is an application to the finance of the uncertainty theory which provides an alternative analysis method from the probability theory under the circumstance that few samples are available. Under the research paradigm of uncertain finance, some financial assets are investigated and modeled with various tools in order to describe the price fluctuation accurately. This paper models the prices of stocks under uncertain finance based on the exponential Ornstein–Uhlenbeck model with periodic dividends. Through the $$\alpha $$ -path method, the pricing formulas are derived for European call and put options whose underlying assets follow the proposed stock model. In addition, some numerical algorithms to calculate the option prices are designed.