Consider a two$-$period securities market model, with two risky securities $S^1,S^2.$ The dynamics of the price processes $(S_t^1,S_t^2)$ are shown in the tree below.

In addition, there is a riskless bank account $S^0.$ The $($discretely compounded$)$ interest rate $r$

which governs the dynamics of $S^0$ is constant.

$($a$)$ Show that the model is indeed arbitrage$$free$,$ by finding an EMM for this model.

$($b$)$ Is this model complete? Why or why not?

$($c$)$ Consider a chooser option X on S$^1,$ which allows the holder to decide, at time t $=1,$ whether the option is a call on S$1^$ with strike K $=21\mathrm{.}60$ and maturity T $=2,$ or a put with strike K $=21\mathrm{.}60$ and maturity T $=2.$ What are the t $=1$ and t $=0$prices of this option?