Valuation of Parisian Option Under Uncertain Exponential Ornstein–Uhlenbeck Model

Parisian option is a special type of barrier option. A general barrier option only requires a hitting time reaching the barrier level to activate (or terminate) the contract, which may be easily influenced by some short-term fluctuations in the market, when the price is close to the barrier. Thus, Parisian option is created to avoid exposure to such kind of risk. It requires the price should maintain below or above a certain level for a sustained period to trigger the contract. Considering the phenomenon of mean reversion in the market, this paper mainly investigates four different Parisian options’ pricing formulas based on the uncertain exponential Ornstein–Uhlenbeck model and designs the algorithms to calculate the price of the option. Besides, several numerical examples are given in this paper.