Problem 4. Implicit method. Assume the Black-Scholes framework. Write a program to price an American put option using the fully implicit method after transforming the complementary differential equation into a problem with constant coefficients. Use LU decomposition (Thomas' algorithm in Section 4.3.1 of the finite-difference notes) to solve the resulting system of linear equations and appropriate Dirichlet boundary condition for an American put option. For extra credit, visualize the exercise boundary. 1 Problem 4. Implicit method. Assume the Black-Scholes framework. Write a program to price an American put option using the fully implicit method after transforming the complementary differential equation into a problem with constant coefficients. Use LU decomposition (Thomas' algorithm in Section 4.3.1 of the finite-difference notes) to solve the resulting system of linear equations and appropriate Dirichlet boundary condition for an American put option. For extra credit, visualize the exercise boundary. 1