Implementing the Binomial Method Design and implement an algorithm for calculating the value V (M) of a European or American option. Use the basic version of Algorithm 1.4. INPUT: r (interest rate), σ (volatility), T (time to expiration in years), K (strike price), S (price of asset), and the choices put or call, and European or American. Control the mesh size Δt = T /M adaptively. For example, calculate V for M = 8 and M = 16 and in case of a significant change in V use M = 32 and possibly M = 64. Test examples:

a) put, European, r = 0.06, σ = 0.3, T = 1, K = 10, S = 5

b) put, American, S = 9, otherwise as in

a) c) call, otherwise as in

a) d) The mesh size control must be done carefully and has little relevance to error control. To make this evident, calculate for the test numbers

a) a sequence of V (M) values, say for M = 100, 101, 102,..., 150, and plot the error |V (M) − 4.430465|.