Rannacher smoothing, Financial Management

Explain what is meant by a positive coefficient discretization in the context of valuing options using numerical PDE methods. What is the main benefit of using a positive coefficient discretization? Are there any drawbacks? (You should contain some
discussion related to the computation of option prices, deltas, and gammas, as well as the rate of convergence for both fully implicit and Crank-Nicolson time stepping schemes.)   
 
b)  Describe what "Rannacher smoothing" is and why it is used.

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