Abstract
In this paper, fitted finite volume method is developed to solve a nonlinear degenerate Black-Scholes equation applied in the valuation of unit-linked policy with surrender option, based on the fitting idea in S. Wang [IMA J. Numer. Anal., 24 (2004), 699--720]. Unlike the conventional pricing method mentioned in [1] which is using the free boundary method to calibrate the valuation PDE, here we develop a power penalty method to solve numerically the linear complimentary problem in the variational inequality arising from the valuation of unit-linked policy with surrender option. With the degenerate boundary and non-smooth final condition, we will show that it is essential to refine the mesh to remain the convergence and super-convergence order.
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