Implementing the Binomial Method Design and implement an algorithm for calculating the value V (M) of a European or American option. Use the binomial method 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.