Valuation of forward start option with mean reverting stock model for uncertain markets

Abstract

A forward start option is an exotic option with delayed activation and reduced premium that allows investors to avail market opportunities in the future. Moreover, mean-reversion explores the investment strategies. This study examines the pricing of forward start options based on the uncertain mean-reverting stock model by applying Liu’s uncertain finance. Call and put options pricing formulas are derived. The study depicts that the pricing patterns in uncertain environments are consistent with the common characteristics of financial markets.

Keywords

• option pricing
• forward start option
• mean-reversion
• uncertain calculus