Put–Call Parity and Chooser Option Pricing Formula in Uncertain Environment

ABSTRACT

A chooser option is an exotic option that allows investors to select either a call or a put at a predetermined choice time. Previous pricing methods for chooser options under probability theory rely on put–call parity—a relationship that lacks proof in uncertainty theory. This paper presents a rigorous proof of the put–call parity formula in uncertain environments for pricing chooser options. This study uses the US Dollar Futures Index to validate the formula's applicability. Initially, the optimal model is identified via rolling‐window cross‐validation and the least‐squares method. It passes uncertain hypothesis tests successfully. Then, we compare the stochastic differential equation through the in‐sample residual test and out‐of‐sample predictive performance. Finally, the pricing formula is analyzed and compared between the chooser option and the straddle strategy. The analysis illustrates how the option price varies with key parameters and concludes chooser option consistently outperforms the straddle strategy when chosen appropriately.