Knock-in options of an uncertain stock model with floating interest rate

Abstract

Abstract Knock-in options are a type of barrier options which are path-dependent and get activated if the prices of underlying assets reach predetermined levels. This paper studies knock-in options in an uncertain market where the stock price follows a geometric process and the interest rate is dynamic. Pricing formulas of the knock-in call options and put options are derived by means of α-paths of uncertain differential equations. Numerical algorithms are designed and illustrated via some numerical experiments.