Abstract: In this paper we consider a parabolic variational inequality arising from the valuation of European installment put options. We prove the existence and uniqueness of the solution to the problem. Moreover, we obtain C∞ regularity and the bounds of the free boundary. Eventually we show its numerical result by the binomial method.

Abstract The critical price $$S^{*}\left( t\right) $$ S ? t of an American put option is the underlying stock level that triggers its immediate optimal exercise. We provide a new perspecti...