# Maximal increase payoff

I am interested in the following problem.

We have a Multi-Step Binomial Model with discrete time $$T=1,\dots,n$$. We also assume that the stock $$S_t$$ is a martingale and there is a risk-free bond with $$r=1$$.

How to evaluate the price of the European option $$X_n=\max_{1\le i \le n}S_i-\min_{1\le j \le n}S_j$$ $$=\max_{1\le i < j \le n}|S_i-S_j|?$$

Here $$X_n$$ represents the biggest change of the stock price during the given time period. Is this option well known or maybe can it be rewritten as a combination of well known payoffs? How should one proceed in order to find it's price?