Problem 2

Im In Problem 2. Crank-Nicolson. In Section 4.2 of finite-difference notes we saw that the Crank-Nicolson method was based on the following finite- difference approximations: Ru st 1024 day 17 en otm1, On) + 377tm.n 1/ultm+1, 2n+1) 2u(tm+1, 2'n) + u{tm+1, 17-1) 82? ultman+1) 2u(tmyan) + ultmy 2n-1) 822 Use Taylor expansions to deduce the error between the left and right sides of each of the two approximation above. +; == Problem 3. Explicit method. Assume the Black-Scholes framework. Write a program to price a European put option using the explicit method after transforming the Black-Scholes equation to a terminal value PDE with constant coefficients (see Eqs. (2.5).(2.6) in the finite-difference notes). Test your algorithm using the exact Black-Scholes formula. For extra credit, extend your code to price an American put option. Im In Problem 2. Crank-Nicolson. In Section 4.2 of finite-difference notes we saw that the Crank-Nicolson method was based on the following finite- difference approximations: Ru st 1024 day 17 en otm1, On) + 377tm.n 1/ultm+1, 2n+1) 2u(tm+1, 2'n) + u{tm+1, 17-1) 82? ultman+1) 2u(tmyan) + ultmy 2n-1) 822 Use Taylor expansions to deduce the error between the left and right sides of each of the two approximation above. +; == Problem 3. Explicit method. Assume the Black-Scholes framework. Write a program to price a European put option using the explicit method after transforming the Black-Scholes equation to a terminal value PDE with constant coefficients (see Eqs. (2.5).(2.6) in the finite-difference notes). Test your algorithm using the exact Black-Scholes formula. For extra credit, extend your code to price an American put option