Please refer to the material on defaultable bonds and credit$-$default swaps $($CDS$)$ to answer this question.

Construct a $n=10-$period binomial model for the short$-$rate, $r_{i,j}(i=0,1,2$dots$9).$ The lattice parameters are:

$r_{0,0}=5\%,u=1\mathrm{.}1,d=0\mathrm{.}9$ and $q=1-q=\frac{1}{2}.$ This is the same lattice that you constructed in

Assignment $5.$

Assume that the $1-$step hazard rate in node $(i,j)$ is given by $h_{ij}=a{b}^{j-\frac{i}{2}}$ where $a=0\mathrm{.}01$ and $b=1\mathrm{.}01.$

Compute the price of a zero$-$coupon bond with face value $F=100$ and recovery $R=20\%.$

Submission Guideline: Give your answer rounded to two decimal places. For example, if you compute the

answer to be $73\mathrm{.}2367,$ submit $73\mathrm{.}24.$