# Models comparison simulation

We compare on the graph below the convergence of all the models.

We compare the prices to the analytical and semi-analytical solutions, computed with Quantlib library.

We notice that all the models have a common characteristic : depending on the parity of the number of time steps, the price is overestimated or underestimated . Hence, in order to get a better approximation, here we will compute and display the mean of the prices estimated with $$N$$ and with $$N+1$$ time steps.

For each model, we search also for the first time steps size $$N \in [N_{min}, N_{max}]$$ such that the error between the analytical and the computed solution is smaller than a fixed $$\varepsilon$$. $$N$$ can be smaller of $$N_{min}$$ or greater than $$N_{max}$$.