A Variational Inequality Arising from European Installment Call Options Pricing

Abstract

In this paper we consider a parabolic variational inequality arising from European continuous installment call options pricing and prove the existence and uniqueness of the solution to the problem. Moreover, we obtain $C^\infty$ regularity and the bounds of the free boundary, as well as the limit of the free boundary as $\tau=T-t\rightarrow+\infty$. Eventually we show its numerical result by the binomial method.

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