Abstract
In this paper, we consider the nonlinear complementary problem (NCP) arising from the pricing American options in a liquidity switching market. The NCP arises from discretising a coupled system of Hamilton-Bellman-Jacobi (HJB) equations whose solutions are the American option buyer indifference prices. In order to price American options, we derive a complementary problem. Due to the form of liquidity assumptions, the system of (HJB) equations are nonlinear which when discretised give rise to a NCP. We apply two Newton-like methods and perform various numerical experiments to illustrate the method.
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