FRONT FIXING METHOD FOR SOLVING INSTALLMENT OPTION

‎In this paper we consider the European continuous installment call‎ ‎option on foreign currency exchange rate as underlying asset‎. ‎By arbitrage pricing theory‎, ‎one can model the installment option under Black-Scholes model‎. ‎Therefore‎, ‎non homogeneous parabolic partial differential equation governing installment option is derived‎. ‎The non homogeneous term in this parabolic partial differential equation is the installment rate that must be paid by option holder‎. ‎The pricing problem for installment option on foreign currency exchange rate is parabolic partial differential equation with initial an boundary conditions called free boundary problem‎. ‎Then‎, ‎to determine the value of the European installment option and the location of the stopping boundary‎, ‎the front fixing method will be applied‎. ‎In this method‎, ‎we transform the free boundary problem to a nonlinear parabolic partial differential equation with fixed known boundary‎. ‎In the next step‎, ‎finite difference method will be applied to discretize the problem‎. ‎Hence one can get formula for finding the price of European continuous installment call‎ ‎option and the location of the stopping or free boundary‎.