Suppose the exchange rate is $$\frac{1\mathrm{.}08}{}$lon. Let $r_{\text{\$}}=7\%,r_{lon}=8\%,u=1\mathrm{.}4,d=0\mathrm{.}7,p^{**}=0\mathrm{.}41436,$ and $T=2.$ Using the $2-$step currency price tree below, calculate the value of a $$1\mathrm{.}20-$strike American put option on the euro.

$$\frac{2\mathrm{.}1168}{}$lon

$$\frac{1\mathrm{.}512}{}$

$$\frac{1\mathrm{.}08}{}$

$$\frac{1\mathrm{.}0584}{}$lon

$$\frac{0\mathrm{.}756}{}$

$$\frac{0\mathrm{.}5292}{}$

$$0\mathrm{.}2723$

$$0\mathrm{.}3133$

$$0\mathrm{.}2598$

$$0\mathrm{.}2786$

$$0\mathrm{.}2988$