An Example of Markov Chain and multinominal option pricing

One sample of the pricing of double barriers knock-in binary put option by using multinominal, Marko

As a coursework, we are required to price a double barriers knock-in binary put option. We used finite difference method in 24 ways and multinomial lattice in 12 ways. We also implemented analytic and Markov chain method. At the end, we compared these four methods and Monte Carlo method.
In this coursework, we discussed the speed, convergence rate and monotonicity of convergence for these methods. We also discussed whether extrapolation improves convergence.