Suppose that $S=$$$100,K=$$$100,r=0\mathrm{.}06,=0\mathrm{.}25,=0\mathrm{.}03,$ and $T=1.$ Use the following equations to answer the questions:

$u=e^{(r-)h+\sqrt[\phantom{2}]{h}}$

$d=e^{(r-)h-\sqrt[\phantom{2}]{h}}$

$p^{**}=\frac{e^{(r-)h}-d}{u-d}$

$C=e^{-rh}[p^{**}{C}_u+(1-p^{**})C_d]$

$($i$)$ Consider stock price averages computed by averaging the $6-$month and $1-$year prices. Determine a two$-$period binomial tree for the arithmetic and geometric averages after $1$ year.

$($ii$)$ Determine the prices of Asian arithmetic average and Asian geometric average price call. Comment on your answers.

$($iii$)$ Determine the prices of Asian arithmetic average and Asian geometric average strike call. Comment on your answers.

$8$