A Parabolic Variational Inequality Arising From The Valuation Of The Russian Option

In this paper we use a PDE argument to deal with the theoreticalanalysis of the valuation of the Russian option. As the valuation of the Americanoption, the valuation of the Russian options can be formulated as a one-dimensionalparabolic variational inequality. First we introduce a penalty function and provethe existence and uniqueness of the solution of the variational inequality. Then westudy the properties of the free boundary, such as monotonicity, smoothness andthe location of the free boundary.