Submitted Jul $31$ at $2$:$16$pm

Question $1$

$\frac{0}{0}$ pts

Suppose the $1-$year spot rate is $1\%,$ and that a $2-$year $2\mathrm{.}5\%$ annulas coupon, a $3-$year $3\%$ annual coupon bonds are trading at par $($$$100)$

Calibrate a $2-$year binomial interest rate model, assuming that interest volatility sigma $$ is $15\%.$ What is the highest rate at $t=2?$

Assume annual compounding. Round your answer to $4$ decimal places. For example if your answer is $3\mathrm{.}205\%,$ then please write down $0\mathrm{.}0321.$

$0\mathrm{.}0538($with margin: $0\mathrm{.}001)$